Mathématiques en biologie et médecine
A model for the dynamic transmission of leishmaniasis in Kabylie, Algeria
Benferhat, Leila and Schehrazad Selmane
Faculty of Mathematics. University of Sciences and Technology Houari Boumediene. Algiers, Algeria

We present a compartmental model for the dynamics of transmission of leishmaniasis that includes incidental hosts for humans which act only as sinks of infection, primary reservoir hosts for animals which act as sources and sinks of infection, and secondary reservoir hosts for sandflies which act as the liaison between primary reservoirs and incidental hosts. The stability analysis of equilibria of the model shows that the threshold conditions for disease persistence, are completely determined by the reproduction number, and do not explicitly include parameters relating to the dynamics transmission in the incidental hosts, which means that the disease becomes endemic if it persists endemically in the primary reservoir hosts, and therefore the control measures should be directed towards reservoir hosts. This is illustrated via numerical simulations of the model using parameters generated from data from Kabylie, Algeria.

Mercredi, 19 juin, 15h00
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