Latest revision as of 12:41, 8 January 2021

Problem definition

The coronavirus pandemic is an ongoing pandemic, the first case confirmed in Switzerland was on February 25th, 2020 and has known an exponential growth since. We know that the virus is spread from an infected person to a healthy one during close contact or via touching a contaminated surface. The aim of the simulation is to display the dynamics of the reaction time of the government to take measures and to see if the hospital capacity play a key role in the spread of the COVID-19

Method

Vensim modelling approach was selected due to dynamic behavior of the simulated system.

the model shows the evolution of the number of people who got infected by the covid-19 virus in countries where the population have a high health care protection and where the government have decided to make a decision about the virus propagation. The model will explain how fast the virus spreads itself and how political decisions can change the number of infected people at a given point in time. The construction of the model is simple: at the beginning one person is infected and will, then, infect other people. When you are infected many possibilities are open:

You can be a healthy virus carrier. In that case you will not know that you have the virus and after 19 days you will be recovered.
After 5 days you get symptoms, but you do not have any important health problems, you will recover in the next 14 days.
After 5 days, you get symptoms and you are very sick and have respiratory problems, after 3 more days, still feeling bad, you decide to go to the doctor to get a diagnosis. The doctor has than two options: to send you back home, where you will recover after 11 more days or hospitalized you the next day.
The doctor had decided to hospitalize you, you then spend two weeks in intensive care, where you will need artificial ventilation and 24-hour nursing care. You can then recover or unfortunately die.

The higher the hospital utilization, the greater the probability to die. Indeed, if hospitals get busier, the medical staff will be less available and health care quality might decrease. When the number of diagnosed and hospitalized people (which are the official number of cases) is greater than a certain percentage of the population, the government will take decisions to slow down the spread of the virus. This is to say that governments will take some measures, such as installing a forced lockdown of the population to decrease the number of contacts per habitant. Moreover, such a decision will have an impact on the population, which will be more aware of the situation and will be more careful to not spread or contract the virus. So, the contagion rate as the number of contacts per people will slow down. They will be less hospitalized people, that means less people in the hospital, meaning a better service and so less people who die.

Model

Following vensim model was developed based on the study.

COVID-19 pandemic in Switzerland Stock Flow Diagram

Variables

Initial population

The Population of Switzerland can be found here: https://en.wikipedia.org/wiki/Demographics_of_Switzerland

=8 500 000

Ratio susceptible people

Decrease the susceptible people by the number of deaths due to the COVID-19.

=Susceptible population / (Initial population-Dead)

Susceptible population

Decrease the susceptible population by the number of new infections.

=-New infections

contact

Lockdown: Function IF THEN ELSE that bring the number of new people you meet (contact) from 5 to 0.05 if the ratio exceed 0.015%

=IF THEN ELSE("Ratio official cases/pop"> 0.00015, 0.05 , 5 )

Contagion Rate

Lockdown: contagion rate: IF THEN ELSE that bring the contagion rate from 0.1 to 0.075 if the ratio exceed 0.015%. Function of the awareness in the population (washing more often their hands if lockdown)

=IF THEN ELSE("Ratio official cases/pop" > 0.00015 , 0.075 , 0.1 )

New infections

It represent the new number of people infected each day.

=contact*Infected*Ratio susceptible people*Contagion Rate

Infected

It represent the stock of the new people infected. We start the model with 1 infected people.

=New infections-New recoveries from infected-New symptoms ///// Initial value: 1

New recoveries from infected

It represent the number of people without symptoms and they go in the recovered stock after 19 days.

=((1-Ratio Symptoms)*Infected)/TTA recoveries

New symptoms

It represent the number of new people that develop symptoms during 5 days before going to the symptomatic stock.

=(Infected*Ratio Symptoms)/TTA Symptoms

Ratio Symptoms

The ratio of people who develop some symptoms.

=0.2

Symptomatic

The stock of people symptomatic.

=New symptoms-New Diagnostic-New recoveries from symptoms

New recoveries from symptoms

It represent the number of people that have symptoms but that were not to the doctor, after 14 they are in the recovered stock.

=(1-Ratio Diagnost)*Symptomatic/TTA sympt

New Diagnostic

It represent the number of new people that are diagnosed each day, they stay 3 days before having the diagnostic.

=Symptomatic*Ratio Diagnost/TTA Diagnostic

Ratio Diagnost

the ratio of people that are diagnosed by a doctor.

=0.4

Diagnosed

The stock of people that are diagnosed by a doctor.

=New Diagnostic-New Hospitalization-New Recovery from Diagnostic

New Recovery from Diagnostic

It represent the number of people that are diagnosed and not sent to the hospital. they stay 11 days before going in the Recovered stock.

=(1-Ratio Hospitalize)*Diagnosed/TTA diag

New Hospitalization

It represent the number of people that are diagnosed and sent to the hospital. they stay 1 day before being sent.

=(Diagnosed*Ratio Hospitalize)/TTA Hospitalization Ratio Hospitalize

Ratio Hospitalize

The ratio of people that are Hospitalized.

=0.3

Hospitalized

The stock of people that are hospitalized before being Recovered or Dead.

=New Hospitalization-New Death-New Recovery

New Recovery

The number of people that recover each day from the hospitalization. It depends on the Taux Mortality which is depend from the hospital utilization (capacity or number of beds...).

=((1-Taux Mortality)*Hospitalized)/TTA Hospitalization

New Death

The number of people that die each day from the hospitalization. It depends on the Taux Mortality which is depend from the hospital utilization (capacity or number of beds...).

=(Hospitalized* Taux Mortality)/TTA Hospitalization

hospital bed

The number of bed in Switzerland is 356 beds for 100k people with 8.5M people it gives that number: https://www.swissinfo.ch/eng/coronavirus-crisis-_has-switzerland-got-enough-hospital-beds--/45671704

=30260

hospital utilization

For the utilization of the hospital I assumed that there is already 8260 beds used for regular patient (outside the covid pandemic). The more utilization we have, the greater the probability to die. Indeed, if hospitals get busier, the medical staff will be less available and health care quality might decrease.

=(Hospitalized/(hospital bed - 8260))

lookup mortality

The lookup function is used to described the taux mortality.

[(0,0)-(1000,0.3)],(0,0.065),(0.6,0.065),(0.8,0.12),(1,0.25),(1.2,0.3),(10,0.3),(1000,0.3)

Taux Mortality

The mortality rate depends on the hospital utilization. For example based on the above function, if the capacity reach 100% the hospital is full and the chance to die is then 25%.

=lk mortality (hospital utilization)

Dead

The stock of Dead people killed by the pandemic.

=New Death

Recovered

The Total amount of people who recovered from the pandemic.

=New recoveries from infected+New recoveries from symptoms+New Recovery+New Recovery from Diagnostic

official active cases

It represent the number of people that were tested and it's this number that will be used by the government to follow the pandemic and take decision of lockdown.

=Diagnosed+Hosptitalized

Ratio official cases/pop

The ratio that will be used for lockdown.

=official active cases/ Initial population

New Diagnosed.1

It's is just the same as New Diagnostic, it is used in the model to have the Total Diagnosed.

=New Diagnostic

Total Diagnosed

Used in the model to have the official number of cases in the model.

=New Diagnosed.1

TTA recoveries

Time to recover after being infected and not having symptoms.

=19

TTA Symptoms

The time you take to develop symptoms.

=5

TTA sympt

The time you take for recovering after being symptomatic.

=14

TTA Diagnostic

Time to go to the doctor and have the result.

=3

TTA diag

The time you take for recovering after being diagnosed.

=11

TTA Hospitalization

Time to go to the Hospital.

=1

TTA Hospital

The time you stay at the hospital before recovering or dying.

=14

Results

As explained in the problem definition we will focused our results on 3 cases.

The first one is the normal scenario, with classic lockdown and regular numbers of beds for Switzerland
The second is the same scenario as for the 1st one but the lockdown is delayed by 1 day,
The third scenario is the normal scenario with a number of hospital beds reduce by 10 000 beds.

Normal Scenario

The first scenario take place in Switzerland with 8 500 000 peoples and a hospital capacity of 356 beds for 100k people. The first case was detected the 25 february 2019 and 20 days after the Government of Switzerland have decided to take some serious measures that is in our case represented by a lockdown.

The following table show us the official number of new cases per day:

From the simulation we get:

We can see that the model is reality closed to the reality with a pic of 1350 after 35 days. The simulation stopped after 100 days so we just focused on these first 100 days. The reality display a pic at 1243 days after 30 days.

The true number of new death per day, and the number from the simulation is also display below:

We can see that the model is one more time really closed to the reality with a pic of 43 deaths after 50 days, while the reality display a pic at 44 days after 36 days.

We have seen that the simulation is really closed from the data obtained for the Switzerland, but now lets go trough some special cases to see the impact of some decisions on the variables.

Scenario 1: Late lockdown

In this scenario we will see what could have happened if the government take 1 more day to react and to set up the lockdown. To simulate such a scenario I simply increased the number of "Ratio official cases/pop" in the function IF THEN ELSE in "contact" and "contagion rate" from 0.00015 to 0.00018 and it delay the reaction of the government by 1 day.

As you can see in the first graph, the total number of official cases (=total diagnosed) jump from 33 000 to 45 000 cases. An increase of 35% in the number of official cases by just delaying for 1 day the government decisions. It illustrates well the exponential effect on the model, indeed we don't have to forget that the delay is just one day but if it has been 4-5 days the number of cases would have been exponentially higher. The second graph shows the deaths jumping from 1600 to 2300, that is due to increasing number of cases and the hospital capacity reaching more than 60% utilization. Indeed due to the lookup function if the hospital capacity exceed 60% the mortality increase in the hospital. This is a very interesting scenarios that shows quite well the importance of the early lockdown and highlight the most important point in our model, the reaction time.

Scenario 2: Small Hospital capacity

In this scenario the number of hospital beds goes from 356/100k people to 238/100k people, a loss of -10 000 in variable hospital bed for Switzerland. This number of beds corresponds to the number of beds for a less developing country, such as Iceland (https://www.swissinfo.ch/eng/coronavirus-crisis-_has-switzerland-got-enough-hospital-beds--/45671704).

As you can see in the first graphs, the hospital utilization reach almost 80%. Patients are not treated as well as they would if the utilization was lower, and it involves more deaths for these patients (right graph). We can see the importance of hospital capacity and for government to have a good amount of hospitals.

Conclusion

To conclude I would say that it has been quite difficult to deal with the real data because I had to find every number or to adjust some variables to fit with the reality. Another difficulty that I had to faced was all times and units to setup.

The model display almost the same numbers as the ones communicated by the Swiss government, what could indicate that the model are not too far from what is happening in real-life.

The most important variable in the simulation is the reaction time of the government in order to take some measures against the fast spread of the virus, such as bringing more awareness or imposing a lockdown.

A further exogenous variable here is the number of hospital beds, which is a good proxy for modeling different countries. Having a smaller number of beds is a sign of vulnerability for the health care system and will impact mortality. A solution to this pandemic could therefore be to increase the number of beds in order to avoid exceeding capacity.

A limit to this simulation would be that it is a real pandemic, for example I first tried to simulate the full pandemic with the second pic (higher) as you can see in the graph of Switzerland but I have to admit that sometimes the reality (or my Vensim skills) are to difficult to simulate that is why I choose to stop the simulation after 100 days.

Code

File:Simulation Covid-19.mdl

References

Federal Office of Public Health FOPH, https://www.bag.admin.ch/bag/en/home.html
Fismann, D. (2009), “Modellig an Influenza Pandemic: A Guide for the Perplexed”, CMAJ,August.
Madhav, N. (2017), “Pandemics: Risks, Impacts, and Mitigation”, November.
Federal Office of Public Health FOPH, https://www.bag.admin.ch/bag/en/home.html
https://www.swissinfo.ch/eng/coronavirus-crisis-_has-switzerland-got-enough-hospital-beds--/45671704
https://www.covid19.admin.ch/en/epidemiologic/case?detTime=total&detRel=abs
https://www.covid19.admin.ch/en/epidemiologic/death?detTime=total&detRel=abs

@@ Line 1: / Line 1: @@
-Introduction
 =Problem definition=
+The coronavirus pandemic is an ongoing pandemic, the first case confirmed in Switzerland  was on February 25th, 2020 and has known an exponential growth since. We know that the virus is spread from an infected person to a healthy one during close contact or via touching a contaminated surface. The aim of the simulation is to display the dynamics of the reaction time of the government to take measures and to see if the hospital capacity play a key role in the spread of the COVID-19
 =Method=
+Vensim modelling approach was selected due to dynamic behavior of the simulated system.
+the model shows the evolution of the number of people who got infected by the covid-19 virus in countries where the population have a high health care protection and where the government have decided to make a decision about the virus propagation. The model will explain how fast the virus spreads itself and how political decisions can change the number of infected people at a given point in time. The construction of the model is simple: at the beginning one person is infected and will, then, infect other people. When you are infected many possibilities are open:
+* You can be a healthy virus carrier. In that case you will not know that you have the virus and after 19 days you will be recovered.
+* After 5 days you get symptoms, but you do not have any important health problems, you will recover in the next 14 days.
+* After 5 days, you get symptoms and you are very sick and have respiratory problems, after 3 more days, still feeling bad, you decide to go to the doctor to get a diagnosis. The doctor has than two options: to send you back home, where you will recover after 11 more days or hospitalized you the next day.
+* The doctor had decided to hospitalize you, you then spend two weeks in intensive care, where you will need artificial ventilation and 24-hour nursing care. You can then recover or unfortunately die.
+The higher the hospital utilization, the greater the probability to die. Indeed, if hospitals get busier, the medical staff will be less available and health care quality might decrease. When the number of diagnosed and hospitalized people (which are the official number of cases) is greater than a certain percentage of the population, the government will take decisions to slow down the spread of the virus. This is to say that governments will take some measures, such as installing a forced lockdown of the population to decrease the number of contacts per habitant. Moreover, such a decision will have an impact on the population, which will be more aware of the situation and will be more careful to not spread or contract the virus. So, the contagion rate as the number of contacts per people will slow down. They will be less hospitalized people, that means less people in the hospital, meaning a better service and so less people who die.
 =Model=
-=Results=
+Following vensim model was developed based on the study.
+[[File:Model1.png|900px|thumb|center|COVID-19 pandemic in Switzerland Stock Flow Diagram]]
+== Variables ==
+===Initial population===
+''The Population of Switzerland can be found here: https://en.wikipedia.org/wiki/Demographics_of_Switzerland''
+=8 500 000
+===Ratio susceptible people===
+''Decrease the susceptible people by the number of deaths due to the COVID-19.''
+=Susceptible population / (Initial population-Dead)
+===Susceptible population===
+''Decrease the susceptible population by the number of new infections.''
+=-New infections
+===contact===
+'''Lockdown:''' ''Function IF THEN ELSE that bring the number of new people you meet (contact) from 5 to 0.05 if the ratio exceed 0.015%''
+=IF THEN ELSE("Ratio official cases/pop"> 0.00015, 0.05 , 5 )
+===Contagion Rate===
+'''Lockdown:''' ''contagion rate: IF THEN ELSE that bring the contagion rate from 0.1 to 0.075 if the ratio exceed 0.015%. Function of the awareness in the population (washing more often their hands if lockdown)''
+=IF THEN ELSE("Ratio official cases/pop" > 0.00015 , 0.075 , 0.1 )
+===New infections===
+''It represent the new number of people infected each day.''
+=contact*Infected*Ratio susceptible people*Contagion Rate
+===Infected===
+''It represent the stock of the new people infected. We start the model with 1 infected people.''
+=New infections-New recoveries from infected-New symptoms ///// Initial value: 1
+===New recoveries from infected===
+''It represent the number of people without symptoms and they go in the recovered stock after 19 days.''
+=((1-Ratio Symptoms)*Infected)/TTA recoveries
+===New symptoms===
+''It represent the number of new people that develop symptoms during 5 days before going to the symptomatic stock.''
+=(Infected*Ratio Symptoms)/TTA Symptoms
+===Ratio Symptoms===
+''The ratio of people who develop some symptoms.''
+=0.2
+===Symptomatic===
+''The stock of people symptomatic.''
+=New symptoms-New Diagnostic-New recoveries from symptoms
+===New recoveries from symptoms===
+''It represent the number of people that have symptoms but that were not to the doctor, after 14 they are in the recovered stock.''
+=(1-Ratio Diagnost)*Symptomatic/TTA sympt
+===New Diagnostic===
+''It represent the number of new people that are diagnosed each day, they stay 3 days before having the diagnostic.''
+=Symptomatic*Ratio Diagnost/TTA Diagnostic
+===Ratio Diagnost===
+''the ratio of people that are diagnosed by a doctor.''
+=0.4
+===Diagnosed===
+''The stock of people that are diagnosed by a doctor.''
-=Conclusion=
+=New Diagnostic-New Hospitalization-New Recovery from Diagnostic
-=Code=
+===New Recovery from Diagnostic===
+''It represent the number of people that are diagnosed and not sent to the hospital. they stay 11 days before going in the Recovered stock.''
-=Problem definition=
+=(1-Ratio Hospitalize)*Diagnosed/TTA diag
-Crop rotation is based on growing a series of different types of crops in the same area in sequential seasons. The planned rotation may vary from a growing season to a few years or even longer periods. It is one of the most effective agricultural control strategies that is used in preventing the loss of soil fertility. It also helps in reducing soil erosion and increases crop yield. Planning an effective crop rotation requires weighing fixed and fluctuating production circumstances: market, farm size, labor supply, climate, soil type, growing practices, etc.
-In this simulation I will try to find parameters which have impact on the whole process of crop rotation with goal to find model providing desired outputs (these were slightly changed from concept) - crop yields, greenhouse gas emissions (N2O, CO2, NH4), soil fertility (nitrogen levels).
+===New Hospitalization===
+''It represent the number of people that are diagnosed and sent to the hospital. they stay 1 day before being sent.''
-I will focus on four crop rotation strategies with three different crops - corn, soybean, wheat:
+=(Diagnosed*Ratio Hospitalize)/TTA Hospitalization Ratio Hospitalize
-'''CCC''' (continuous corn) - only corn will be farmed for the whole observed time period (40 years)
+===Ratio Hospitalize===
+''The ratio of people that are Hospitalized.''
-'''CS''' (corn-soybean) - rotation of corn and soybean will be used in year cycles for the whole observed time period (40 years), first year corn, second year soybean, repeat..
+=0.3
-'''SSS''' (continuous soybean) - only soybean will be farmed for the whole observed time period (40 years)
+===Hospitalized===
+''The stock of people that are hospitalized before being Recovered or Dead.''
-'''CSW''' (corn-soybean-wheat) - rotation of corn, soybean and wheat will be used in year cycles for the whole observed time period (40 years), first year corn, second year soybean, third year wheat, repeat..
+=New Hospitalization-New Death-New Recovery
-Goal of this simulation is to observe dynamic changes with yields, greenhouse gas emissions, tillage strategy and soil nitrogen levels, while changing different crop rotation strategies.
+===New Recovery===
+''The number of people that recover each day from the hospitalization. It depends on the '''Taux Mortality''' which is depend from the '''hospital utilization''' (capacity or number of beds...).''
-=Method=
+=((1-Taux Mortality)*Hospitalized)/TTA Hospitalization
-Vensim modelling approach was selected due to dynamic behavior of the simulated system.
+===New Death===
+''The number of people that die each day from the hospitalization. It depends on the '''Taux Mortality''' which is depend from the '''hospital utilization''' (capacity or number of beds...).''
-=Model=
+=(Hospitalized* Taux Mortality)/TTA Hospitalization
-Following vensim model was developed based on the study.
+===hospital bed===
-[[File:Crop_rotation_vensim_finished.png|900px|thumb|center|Crop rotation Stock Flow Diagram]]
+''The number of bed in Switzerland is 356 beds for 100k people with 8.5M people it gives that number: https://www.swissinfo.ch/eng/coronavirus-crisis-_has-switzerland-got-enough-hospital-beds--/45671704''
-== Variables ==
+=30260
-===Number of rotated crops===
+===hospital utilization===
-''Input constant variable which can be changed based on crop strategy. Range <1,3>.''
+''For the utilization of the hospital I assumed that there is already 8260 beds used for regular patient (outside the covid pandemic). The more utilization we have, the greater the probability to die. Indeed, if hospitals get busier, the medical staff will be less available and health care quality might decrease.''
-=1 (in case of CCC and SSS strategies)
+=(Hospitalized/(hospital bed - 8260))
-=2 (in case of CS strategy)
+===lookup mortality===
+''The lookup function is used to described the taux mortality.''
-=3 (in case of CSW strategy)
+[(0,0)-(1000,0.3)],(0,0.065),(0.6,0.065),(0.8,0.12),(1,0.25),(1.2,0.3),(10,0.3),(1000,0.3)
-===Corn production===
+===Taux Mortality===
-''PULSE TRAIN function ensures specific crop to be delivered by time pattern. In crop rotation strategies, if corn is present, it is always first crop, therefore it starts at time 0 (first year), duration is 1 year, repetition is based on number of crops (eg. 2 - it repeats in third year) and final time is set to fixed 40 years according to simulation setup.''
+''The mortality rate depends on the hospital utilization. For example based on the above function, if the capacity reach 100% the hospital is full and the chance to die is then 25%.''
-=Corn quantity*PULSE TRAIN(0, 1 , Number of rotated crops ,40)
+=lk mortality (hospital utilization)
-===Soybean production===
+===Dead===
-''Similar case as in Corn production variable only with difference of initial year, if sobyean is present in crop rotation strategy, it is always second crop, therefore it starts at time 1 (second year). In case of SSS strategy it starts at time 0 (first year)''
+''The stock of Dead people killed by the pandemic.''
-=Soybean quantity*PULSE TRAIN(IF THEN ELSE(Number of rotated crops=1, 0 , 1 ), 1 , Number of rotated crops , 40 )
+=New Death
-===Wheat production===
+===Recovered===
-''Similar case as in Corn production variable only with difference of initial year, if wheat is present in crop rotation strategy, it is always third crop, therefore it starts at time 2 (third year).''
+''The Total amount of people who recovered from the pandemic.''
-=Wheat quantity*PULSE TRAIN(2, 1 , Number of rotated crops , 40 )
+=New recoveries from infected+New recoveries from symptoms+New Recovery+New Recovery from Diagnostic
-===Corn quantity===
+===official active cases===
-''Input constant variable which can be changed based on crop strategy. Range <0,100>.''
+''It represent the number of people that were tested and it's this number that will be used by the government to follow the pandemic and take decision of lockdown.''
-=100 (in case of CCC, CS and CSW strategies)
+=Diagnosed+Hosptitalized
-=0 (in case of SSS strategy)
+===Ratio official cases/pop===
+''The ratio that will be used for lockdown. ''
-===Soybean quantity===
+=official active cases/ Initial population
-''Input constant variable which can be changed based on crop strategy. Range <0,40>.''
-=40 (in case of CS, SSS and CSW strategies)
+===New Diagnosed.1===
+''It's is just the same as New Diagnostic, it is used in the model to have the Total Diagnosed.''
-=0 (in case of CCC strategy)
+=New Diagnostic
-===Wheat quantity===
+===Total Diagnosed===
-''Input constant variable which can be changed based on crop strategy. Range <0,80>.''
+''Used in the model to have the official number of cases in the model.''
-=80 (in case of CSW strategy)
+=New Diagnosed.1
-=0 (in case of CCC, CS, SSS strategies)
+===TTA recoveries===
+''Time to recover after being infected and not having symptoms.''
-===increase of N2O emissions===
+=19
-''Auxiliary variable which changes based on each crop production and its emission coefficient (pattern was extracted from a study),additionaly it changes slightly according to tillage strategy and usage of extra inorganic fertilizer.''
-Corn production*Corn N2O emission coef*IF THEN ELSE(Tillage=0, 1.5 , 1.4)+
+===TTA Symptoms===
-Soybean production*Soybean N2O emission coef*IF THEN ELSE(Tillage=0, 1.5 , 1.4)+
+''The time you take to develop symptoms.''
-Wheat production*Wheat N2O emission coef*IF THEN ELSE(Tillage=0, 1.5 , 1.4)+
-Inorganic fertilizer/5
-===increase of CO2 emissions===
+=5
-''Similar auxiliary variable as increase of N20 emissions extra except zero effect with inorganic fertilizer.''
-Corn production*Corn CO2 emission coef*IF THEN ELSE(Tillage=0, 3 , 2.9)+Soybean production*Soybean CO2 emission coef*IF THEN ELSE(Tillage=0, 3 , 2.9)+Wheat production
+===TTA sympt===
-*Wheat CO2 emission coef*IF THEN ELSE(Tillage=0, 3 , 2.9)
+''The time you take for recovering after being symptomatic.''
-===increase of CH4 emissions===
+=14
-''Similar auxiliary variable as increase of N20 emissions extra except zero effect with inorganic fertilizer.''
-Corn production*Corn CH4 emission coef*IF THEN ELSE(Tillage=0, 0.3 , 0.2)+Soybean production*Soybean CH4 emission coef*IF THEN ELSE(Tillage=0, 0.3 , 0.2)+Wheat production
+===TTA Diagnostic===
-*Wheat CH4 emission coef*IF THEN ELSE(Tillage=0, 0.3 , 0.2)
+''Time to go to the doctor and have the result.''
-===Cumulative N2O emissions===
+=3
-=INTEG(increase of N2O emissions)
+===TTA diag===
+''The time you take for recovering after being diagnosed.''
-===Cumulative CO2 emissions===
+=11
-=INTEG(increase of CO2 emissions)
+===TTA Hospitalization===
+''Time to go to the Hospital.''
-===Cumulative CH4 emissions===
+=1
-=INTEG(increase of CH4 emissions)
+===TTA Hospital===
+''The time you stay at the hospital before recovering or dying.''
-===Corn N2O emission coef===
+=14
-''Constant variable extracted from study and its data, representing how much N20 emissions is produced while producing corn. Can be adjusted in the future. Further coefficients are similar just crop and emission type changes.''
-=0.5
+=Results=
+As explained in the problem definition we will focused our results on 3 cases.
+* The first one is the normal scenario, with classic lockdown and regular numbers of beds for Switzerland
+* The second is the same scenario as for the 1st one but the lockdown is delayed by 1 day,
+* The third scenario is the normal scenario with a number of hospital beds reduce by 10 000 beds.
-===Soybean N2O emission coef===
+==Normal Scenario==
-=0.07
+The first scenario take place in Switzerland with 8 500 000 peoples and a hospital capacity of 356 beds for 100k people. The first case was detected the 25 february 2019 and 20 days after the Government of Switzerland have decided to take some serious measures that is in our case represented by a lockdown.
-===Wheat N2O emission coef===
+The following table show us the official number of new cases per day:
-=0.005
+[[File:Newcases.png|500px|center]]
-===Corn CO2 emission coef===
+From the simulation we get:
-=0.3
+[[File:Yes.png|500px|center]]
-===Soybean CO2 emission coef===
+We can see that the model is reality closed to the reality with a pic of 1350 after 35 days. The simulation stopped after 100 days so we just focused on these first 100 days. The reality display a pic at 1243 days after 30 days.
-=0.2
+The true number of new death per day, and the number from the simulation is also display below:
-===Wheat CO2 emission coef===
+[[File: deat.png|500px|left]]        [[File:Deats.18.png|500px|right]]
-=0.25
-===Corn CH4 emission coef===
-=0.005
-===Soybean CH4 emission coef===
-=0.01
-===Wheat CH4 emission coef===
-=0.05
-===Inorganic fertilizer===
-''Auxiliary variable observes if soil nitrogens decrease below 20 and applies 30 units of fertilizer (which affects NO2 emissions)''
-=IF THEN ELSE(Soil nitrogen<20, 30 , 0 )
-===Soil nitrogen===
-''Level variable observes how much nitrogen in soil increase or decrease''
-=INTEG(increase of soil N-decrease of soil N)
-===increase of soil N===
-''Increase of nitrogen level in soil in this model is triggered either by application of inorganic fertilizer or soybean production (soybean and other legumes increase nitrogen level in soil by its decomposition - extracted from study and its data)''
-=Inorganic fertilizer+Soybean production/12
-===decrease of soil N===
-''Decrease of nitrogen level in soil in this model is triggered either by corn or wheat production (corn and wheat decreasing nitrogen level in soil by its farming - extracted from study and its data)''
-=Corn production/8+Wheat production/12
-===Soil nitrogen level===
-''Auxiliary variable which is dependent on soil nitrogen quantity. According to soil nitrogen levels, it affects yields based on random function with normal distribution. The less soil nitrogen level, the higher negative impact on yields.''
-IF THEN ELSE(Soil nitrogen<10, RANDOM NORMAL( 0.3 , 0.5 , 0.45 , 0.05 , 100) , 1 )*
-IF THEN ELSE(((Soil nitrogen>=10) :OR: (Soil nitrogen>20)), RANDOM NORMAL( 0.4 , 0.6 , 0.55 , 0.05 , 100) , 1 )*
-IF THEN ELSE(((Soil nitrogen>=20) :AND: (Soil nitrogen<30)), RANDOM NORMAL( 0.5 , 0.8 , 0.75 , 0.05 , 100) , 1 )*
-IF THEN ELSE(((Soil nitrogen>=30) :AND: (Soil nitrogen<40)), RANDOM NORMAL( 0.7 , 0.9 , 0.85 , 0.05 , 100) , 1 )*
-IF THEN ELSE(Soil nitrogen>=40, RANDOM NORMAL( 1 , 1.4 , 1.2 , 0.05 , 100) , 1 )
-===Temperature===
-''Auxiliary variable which is based on random function with normal distribution. Study showed that extremes in temperatures can have impacts on harvests and yields. Due to complex behavior, I decided to implement only random function.''
-=RANDOM NORMAL( 0.9 , 1.1 , 1 , 0.05 , 100)
-===Precipitation===
+We can see that the model is one more time really closed to the reality with a pic of 43 deaths after 50 days, while the reality display a pic at 44 days after 36 days.
-''Auxiliary variable, similar to Temperature variable only with different min and max parameters''
-=RANDOM NORMAL( 0.8 , 1.2 , 1 , 0.05 , 100)
+We have seen that the simulation is really closed from the data obtained for the Switzerland, but now lets go trough some special cases to see the impact of some decisions on the variables.
-===Pests===
+==Scenario 1: Late lockdown==
-''Auxiliary variable, similar to Temperature variable only with different min and max parameters''
-=RANDOM NORMAL( 0.9 , 1 , 0.98 , 0.005 , 100)
+In this scenario we will see what could have happened if the government take 1 more day to react and to set up the lockdown. To simulate such a scenario I simply increased the number of "Ratio official cases/pop" in the function IF THEN ELSE in "contact" and "contagion rate" from 0.00015 to 0.00018 and it delay the reaction of the government by 1 day.
-===Natural disasters===
+[[File: Deathz1.png|450px|left]][[File: Deathz2.png|500px|right]]
-''Auxiliary variable, similar to Temperature variable only with different min and max parameters''
-=RANDOM NORMAL( 0.01 , 1 , 0.99 , 0.05 , 100)
-===Tillage===
-''Constant variable, which affects yield and emissions. 1 = tilled, 0 = no-till. No-till suppose to be better ecological decision according to study.''
-=1 (can be changed to 0)
-===increase of C yield===
-''Corn yield calculated based on previous variables.''
-=Corn production*Soil nitrogen level*IF THEN ELSE(Tillage=0, 1, 1.05)*Temperature*Precipitation*Pests*Natural disasters
-===increase of S yield===
-''Soybean  yield calculated based on previous variables.''
-=Soybean production*Soil nitrogen level*IF THEN ELSE(Tillage=0, 1, 1.03)*Temperature*Precipitation*Pests*Natural disasters
-===increase of W yield===
-''Wheat yield calculated based on previous variables.''
-=Wheat production*Soil nitrogen level*IF THEN ELSE(Tillage=0, 1, 1.07)*Temperature*Precipitation*Pests*Natural disasters
-===Corn yield===
-=INTEG(increase of C yield)
-===Soybean yield===
-=INTEG(increase of S yield)
-===Wheat yield===
-=INTEG(increase of W yield)
-===Total yield===
-''Sum of yields''
-=Corn yield + Soybean yield + Wheat yield
-=Results=
-As explained in problem definition sections, four crop rotation strategy were observed: CCC, CS, SSS, CSW. For each strategy I changed necessary variables and did simulation run. I divided results into yields, N2O and CO2 emissions, CH4 emissions and soil nitrogen for comparsion between mentioned crop rotation strategies.
-===Yields===
+As you can see in the first graph, the total number of official cases (=total diagnosed) jump from 33 000 to 45 000 cases. An increase of 35% in the number of official cases by just delaying for 1 day the government decisions. It illustrates well the exponential effect on the model, indeed we don't have to forget that the delay is just one day but if it has been 4-5 days the number of cases would have been exponentially higher. The second graph shows the deaths jumping from 1600 to 2300, that is due to increasing number of cases and the hospital capacity reaching more than 60% utilization. Indeed due to the lookup function if the hospital capacity exceed 60% the mortality increase in the hospital. This is a very interesting scenarios that shows quite well the importance of the early lockdown and highlight the most important point in our model, '''the reaction time'''.
-CCC Yield
-[[File:CCC yield.png|400px|CCC Yield]]
-CS Yield
+==Scenario 2: Small Hospital capacity==
-[[File:CS yield.png|400px|CS Yield]]
-SSS Yield
+In this scenario the number of hospital beds goes from 356/100k people to 238/100k people, a loss of -10 000 in variable ''hospital bed'' for Switzerland. This number of beds corresponds to the number of beds for a less developing country, such as Iceland (https://www.swissinfo.ch/eng/coronavirus-crisis-_has-switzerland-got-enough-hospital-beds--/45671704).
-[[File:SSS yield.png|400px|SSS Yield]]
-CSW Yield
+[[File: Utiliz.png|500px|left]][[File: Dead.png|480px|right]]
-[[File:CSW yield.png|400px|CSW Yield]]
-===N2O and CO2 emissions===
-CCC N2O CO2
-[[File:CCC N2O CO2.png|400px|CCC N2O CO2]]
-CS N2O CO2
-[[File:CS N2O CO2.png|400px|CS N2O CO2]]
-SSS N2O CO2
-[[File:SSS N2O CO2.png|400px|SSS N2O CO2]]
-CSW N2O CO2
-[[File:CSW N2O CO2.png|400px|CSW N2O CO2]]
-===CH4 emissions===
-CCC CH4
-[[File:CCC CH4.png|400px|CCC CH4]]
-CS CH4
-[[File:CS CH4.png|400px|CS CH4]]
-SSS CH4
-[[File:SSS CH4.png|400px|SSS CH4]]
-CSW CH4
-[[File:CSW CH4.png|400px|CSW CH4]]
-===Soil nitrogen===
-CCC soil nitrogen
-[[File:CCC soil nitrogen.png|400px|CCC soil nitrogen]]
-CS soil nitrogen
-[[File:CS soil nitrogen.png|400px|CS soil nitrogen]]
-SSS soil nitrogen
-[[File:SSS soil nitrogen.png|400px|SSS soil nitrogen]]
-CSW soil nitrogen
-[[File:CSW soil nitrogen.png|400px|CSW soil nitrogen]]
-=Conclusion=
-Simulation of such complex evnironment as crop rotation in farming was challenging. Created VENSIM model of crop rotation is simplified with some parameters based on just few studies. Real world behaviour can be different because there are many variables affecting the whole process. Although with dramatic simplification, it can be used as a starting point for creating more complex models in agriculture sector. My goal to demonstrate changing of yield, greenhouse gas emissions and nitrogen level was achieved.
-Yields results could be extended with price and demand of market implementation for comparsion with different crop yields.
-N2O and CO2 emissions were highest in CCC crop strategy, providing speculation that monoculture is enviromentaly unfriendly in compare with polyculture strategies. SSS strategy was providing lowest N2O emissions, on other hand it showed highest CH4 emissions which are specific for legumes as soybean.
-Soil nitrogen levels were highly dependent on soybean in crop rotation strategy. With no soybean in crop strategy - in CCC strategy, dramaticaly more inorganic fertilization inputs were necessary
+As you can see in the first graphs, the hospital utilization reach almost 80%. Patients are not treated as well as they would if the utilization was lower, and it involves more deaths for these patients (right graph). We can see the importance of hospital capacity and for government to have a '''good amount of hospitals'''.
-Due to the scope of model, different tillage scenario (0 - no-til) was not simulated. Provided study concluded higher yield and lower emission levels with tillage sceario (1 - tillage, default for simulated model)
+=Conclusion=
-===Model extension===
+To conclude I would say that it has been quite difficult to deal with the real data because I had to find every number or to adjust some variables to fit with the reality. Another difficulty that I had to faced was all times and units to setup.
-More complexity can be implemented in the future, for example:
-Detailed description of parameteres like Temperature, Pests, Natural disasters or Precipitation.
+The model display almost the same numbers as the ones communicated by the Swiss government, what could indicate that the model are not too far from what is happening in real-life.
-More crop strategies or new crops.
+The most important variable in the simulation is the '''reaction time''' of the government in order to take some measures against the fast spread of the virus, such as bringing more awareness or imposing a lockdown.
-Market variables like demand or prices of crop seeds or harvesting costs could be also implemented.
+A further exogenous variable here is the number of hospital beds, which is a good proxy for modeling different countries. Having a smaller number of beds is a sign of vulnerability for the health care system and will impact mortality. A solution to this pandemic could therefore be to increase the number of beds in order to avoid exceeding capacity.
-Monthly changes (instead of yearly) with more detailed fluctuations during seasons (in Spring there is bigger demand for fertilizers, temperature spikes)
+A limit to this simulation would be that it is a real pandemic, for example I first tried to simulate the full pandemic with the second pic (higher) as you can see in the graph of Switzerland but I have to admit that sometimes the reality (or my Vensim skills) are to difficult to simulate that is why I choose to stop the simulation after 100 days.
 =Code=
+[[File:Simulation Covid-19.mdl]]
-[http://www.simulace.info/index.php/File:Crop_rotation_finished.mdl Crop rotation VENSIM model]
 =References=
-#BEHNKE, Gevan D., Stacy M. ZUBER, Cameron M. PITTELKOW, Emerson D. NAFZIGER a María B. VILLAMIL. Long-term crop rotation and tillage effects on soil greenhouse gas emissions and crop production in Illinois, USA. Agriculture, Ecosystems & Environment [online]. 2018, 261, 62-70 [cit. 2020-01-26]. DOI: 10.1016/j.agee.2018.03.007. ISSN 01678809. Availiable: https://linkinghub.elsevier.com/retrieve/pii/S0167880918301221
+#Federal Office of Public Health FOPH, https://www.bag.admin.ch/bag/en/home.html
-#KOLLAS, Chris, Kurt Christian KERSEBAUM, Claas NENDEL, et al. Crop rotation modelling—A European model intercomparison. European Journal of Agronomy [online]. 2015, 70, 98-111 [cit. 2020-01-26]. DOI: 10.1016/j.eja.2015.06.007. ISSN 11610301. Availiable: https://linkinghub.elsevier.com/retrieve/pii/S1161030115300010
+#Fismann, D. (2009), “Modellig an Influenza Pandemic: A Guide for the Perplexed”, CMAJ,August.
-#BRANKATSCHK, Gerhard a Matthias FINKBEINER. Modeling crop rotation in agricultural LCAs — Challenges and potential solutions. Agricultural Systems [online]. 2015, 138, 66-76 [cit. 2020-01-26]. DOI: 10.1016/j.agsy.2015.05.008. ISSN 0308521X. Availiable: https://linkinghub.elsevier.com/retrieve/pii/S0308521X1500075X
+#Madhav, N. (2017), “Pandemics: Risks, Impacts, and Mitigation”, November.
+#Federal Office of Public Health FOPH, https://www.bag.admin.ch/bag/en/home.html
+#https://www.swissinfo.ch/eng/coronavirus-crisis-_has-switzerland-got-enough-hospital-beds--/45671704
+#https://www.covid19.admin.ch/en/epidemiologic/case?detTime=total&detRel=abs
+#https://www.covid19.admin.ch/en/epidemiologic/death?detTime=total&detRel=abs

Difference between revisions of "Impact of late lockdown and hospital capacity on 19-COVID spread"