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Mathematical Analysis of Visceral Leishmaniasis Model | Abstract

Research in Applied Mathematics

Abstract

Mathematical Analysis of Visceral Leishmaniasis Model

Author(s): F.Boukhalfa,M.Helal,and A.Lakmeche

In this work,we consider a mathematical modelde scribing the dynamics of visceral leishmaniasis in a population of dogs?.First, we consider the case of constanttotalpopulation ?, this is the case where birth and death rates are equal, in this case transcritical bifurcation occurs when the basic reproduction number???0is equal to one, and global stability is shown by the mean of suitable Lyapunov functions. After that, we consider the case where the birth and death rates are di??erent, if the birth rate is great than death rate the total dog population increasesexponentially,whiletheinfectiousdogs?diesoutifthebasicreproductionnumberis lessthanone,ifitisgreatthanonethen?goestoin?nity.Wealsoprovethatthetotalpopulation ?willextinctforbirthratelessthandeathrate.Finallywegivenumericalsimulations

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