Mathematical model for transmission of American Tegumentar Leishmaniasis in the wild cycle considering several host mammals and one vector
DOI:
https://doi.org/10.33064/iycuaa2011534488Keywords:
mathematical model, American Tegumentar Leishmaniasis, wild cycle, seasonality, Basic Reproductive NumberAbstract
From a model with nonlinear ordinary differential equations, the dynamics of wild cycle of American Tegumentar Leishmaniasis is described qualitatively. The expression for the Basic Reproductive Number is obtained as the dominant eigenvalue of the Next Generation Operator. The model con siders n wild reservoirs. Numerical simulations are performed in order to explain endemic situations observed in localities of Hipólito Yrigoyen and San Ramón de la Nueva Orán, the province of Salta, Argentina. In addition, a refinement of the model is done, that is, the net rote of birth of the vector is allowed to vary according to sine function aiming to assess the influences of the seasonality in the population density of the Lutzomyia. Searching for suitable frequencies in the oscillatory behavior, qualitative descriptions of the epidemics observed in each year in both mentioned localities are done.
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