Dynamics of an intra-host model of malaria with a constant drug efficiency |
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Authors: | Eddy Takoutsing Samuel Bowong David Yemele Anatole Temgoua |
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Affiliation: | Department of Physics, Faculty of Science, University of Dschang, PO Box 63 Dschang, Cameroon,Department of Mathematics and Computer Science, Faculty of Science, Uni- versity of Douala, PO Box 24157 Douala, Cameroon,Department of Physics, Faculty of Science, University of Dschang, PO Box 63 Dschang, Cameroon and Department of Mathematics and Computer Science, Faculty of Science, Uni- versity of Douala, PO Box 24157 Douala, Cameroon |
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Abstract: | In this paper, we investigate the dynamics of an intra-host model of malaria with logistic red blood growth, treatment and immune response. We provide a theoretical study of the model. We derive the basic reproduction number $mathcal R_f$ 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 $mathcal R_fleqzetaleq1$, the disease-free equilibrium is globally asymptotically stable. However, if $mathcal R_f>1$, 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. Finally, we provide numerical simulations for parasites spreading, and test different treatment scenarios. |
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Keywords: | Malaria intra-host models drug efficiency stability sensitivity analysis. |
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