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On the delayed Ross-Macdonald model for malaria transmission. (English) Zbl 1142.92040
Summary: The feedback dynamics from mosquitos to humans and back to mosquitos involve considerable time delays due to the incubation periods of the parasites. In this paper, taking explicit account of the incubation periods of parasites within the humans and the mosquitos, we first propose a delayed Ross-Macdonald model [R. Ross, The prevention of malaria. 2nd ed., Murray, London (1911); G. Macdonald, The epidemiology and control of malaria. Oxford Univ. Press (1957)]. Then we calculate the basic reproduction number \(R _{0}\) and carry out some sensitivity analysis of \(R _{0}\) on the incubation periods, that is, to study the effect of time delays on the basic reproduction number. It is shown that the basic reproduction number is a decreasing function of both time delays. Thus, prolonging the incubation periods in either humans or mosquitos (via medicine or control measures) could reduce the prevalence of infection.

92D30 Epidemiology
34K60 Qualitative investigation and simulation of models involving functional-differential equations
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