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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 dogs𝐷.First, we consider the case of constanttotalpopulation 𝐷, this is the case where birth and death rates are equal, in this case transcritical bifurcation occurs when the basic reproduction numberℛ0is 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 different, if the birth rate is great than death rate the total dog population increasesexponentially,whiletheinfectiousdogs𝐼diesoutifthebasicreproductionnumberis lessthanone,ifitisgreatthanonethen𝐷goestoinfinity.Wealsoprovethatthetotalpopulation 𝐷willextinctforbirthratelessthandeathrate.Finallywegivenumericalsimulations

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