The spread of malaria with human reservoir: Effect of environmental discharges

Ghosh, M.


Abstract:

This paper proposes and analyzes an SIRS model for malaria in endemic region by incorporating the effect of human reservoir population who are immune to this disease but carry gametocytes in their blood that infect the mosquitoes biting them. It is assumed that household discharges are conducive to the growth of the mosquito population. The model is analyzed for two different cases: (i) when the rate of environmental discharge is constant; (ii) when the rate of environmental discharge is population dependent. For each case it is shown that with the increase in the parameter corresponding to environmental discharges, the equilibrium level of infective population increases. The existence and stability of equilibria of the model are discussed and threshold is determined which tells whether system will tend to disease free equilibrium or to endemic equilibrium. Numerical simulation is performed to support our analytical findings. It is found that with increased level of reservoir population, the equilibrium level of infective population increases.

Volume: 6 | Issue: 3

Pages: 79-100

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