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The epidemic threshold of vector-borne diseases with seasonality. (English) Zbl 1098.92056
Summary: Cutaneous leishmaniasis is a vector-borne disease transmitted to humans by sandflies. We develop a mathematical model which takes into account the seasonality of the vector population and the distribution of the latent period from infection to symptoms in humans. Parameters are fitted to real data from the province of Chichaoua, Morocco. We also introduce a generalization of the definition of the basic reproduction number \(R_0\) which is adapted to periodic environments. This \(R_0\) is estimated numerically for the epidemic in Chichaoua; \(R_0\simeq 1.94\). The model suggests that the epidemic could be stopped if the vector population were reduced by a factor \((R_0)^2\simeq 3.76\).

MSC:
92D30 Epidemiology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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