Modeling Infectious Diseases in Humans and Animals
Matt J. Keeling & Pejman Rohani

SIR model for mosquito vectors (page 136)

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.

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..
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.

All parameters must be positive.

Python ProgramMATLAB Code.

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