Program 4.4 - SIR model for mosquito vectors
The final example in Chapter 4 focusses on vector based transmission of infection, in particular obligate transmission via a mosquito vector between humans. In the standard formulation of this model, humans recover from infection but mosquitoes do not, and there is no within species transmission -- humans can only catch infection from mosquitoes and mosquitoes can only catch infection from humans. Transmission is governed by two factors: r, the rate at which humans are biten and TXY, the probability of transmission between the two species following a bite. Using numbers of individuals and density dependent transmission, the basic equations become:
where subscripts H and M refer to human and mosquito populations respectively.
Parameters
| r | is the rate at which humans are bitten |
| γi | is the recovery rate for host species i |
| νi | is the birth rate for host species i |
| μi | is the per capita death rate for host species i |
| Tij | is the transmission probability (following a bite) to species i from species j |
| Xi(0) | is the initial number of individuals of species i that are susceptible |
| Yi(0) | is the initial number of individuals of species i that are infectious |
All rates are specified in days.
Requirements.
All parameters must be positive.
Files
MATLAB Code , Python Program, R Code.