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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.
r
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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
Python Program, MATLAB Code.
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