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Analysis of an intra-host model of malaria with a constant drug efficiency
Eddy Takoutsing,Samuel Bowong,David Yemele,Anatole Temgoua
Keywords:Malaria; Intra-host models; Drug efficiency; Stability; Sensitivity analysis.
Abstract:
      In this paper, we investigate the dynamics of an intra-host model of malaria with a constant drug efficiency, a logistic red blood growth and immune response. We provide a theoretical study of the model. We derive the basic reproduction number Rf which determines the extinction and the persistence of malaria within the body of a host. We compute equilibria and study their stability. More precisely, we show that there exists a threshold parameter zeta such that if Rf1, there exist two malaria infection equilibria which are locally asymptotically stable: one malaria infection equilibrium without immune response and one malaria infection equilibrium with immune response. The sensitivity analysis of the model has been performed in order to determine the impact of related parameters on outbreak severity. The theory is supported by numerical simulations. We also derive a spatio-temporal model, using Diffusion-Reaction equations to model parasites dispersal. We provide numerical simulations for parasites spreading, and test different treatment scenarios.