Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
AntonAntonov`EpidemiologicalModeling`
MalariaModel |
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Examples
(1)
Basic Examples
(1)
Make a Malaria model:
In[1]:=
m=
[t,"InitialConditions"True,"RateRules"True,"Ross"False];
 | MalariaModel |
Tabulate the model:
In[2]:=
| ModelGridTableForm |
Out[2]=
Stocks
,Rates
,Equations
,RateRules
,InitialConditions
# | Symbol | Description |
1 | HP[t] | Human Population |
2 | MP[t] | Mosquito Population |
3 | SHP[t] | Susceptible Human Population |
4 | SMP[t] | Susceptible Mosquito Population |
5 | IHP[t] | Infected Human Population |
6 | IMP[t] | Infected Mosquito Population |
# | Symbol | Description |
1 | a | Number of bites per mosquito and time unit |
2 | b | Probability that a bite generates a human infection |
3 | c | Probability that a mosquito becomes infected |
4 | aip | Average human infectious period |
5 | mls | Mosquito life span |
# | Equation |
1 | ′ SHP a b IHP[t] IMP[t] HP[0] |
2 | ′ IHP IHP[t] aip a b IHP[t] IMP[t] HP[0] |
3 | ′ SMP a c IHP[t] IMP[t] MP[0] |
4 | ′ IMP a c IHP[t] IMP[t] MP[0] IMP[t] mls |
# | Symbol | Value |
1 | HP[0] | 100000 |
2 | MP[0] | 1000000 |
3 | a | 0.5 |
4 | b | 0.35 |
5 | c | 0.5 |
6 | aip | 20 |
7 | mls | 20 |
# | Equation |
1 | SHP[0]99999 |
2 | IHP[0]1 |
3 | SMP[0]999999 |
4 | IMP[0]1 |
Here are model's equations:
In[3]:=
| ModelNDSolveEquations |
Out[3]=
[t]-1.75×(100000-IHP[t])IMP[t],[t]-+1.75×(100000-IHP[t])IMP[t],[t]-2.5×IHP[t](1000000-IMP[t]),[t]2.5×IHP[t](1000000-IMP[t])-,SHP[0]99999,IHP[0]1,SMP[0]999999,IMP[0]1
′
SHP
-6
10
′
IHP
IHP[t]
20
-6
10
′
SMP
-7
10
′
IMP
-7
10
IMP[t]
20
Simulate the model for 20 days:
In[4]:=
aSol=Association@First@
[m,{t,0,20}]
| ModelNDSolve |
Out[4]=
HPHP,MPMP,SHPInterpolatingFunction
,SMPInterpolatingFunction
,IHPInterpolatingFunction
,IMPInterpolatingFunction
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Plot the solutions:
In[5]:=
Association@KeyValueMap[#1Plot[Evaluate[#2[t]],{t,0,365},PlotLabel#1]&,aSol]
Out[5]=
HP,MP,SHP,SMP,IHP,IMP
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""