A With-In Host Dengue Infection Model with Immune Response and Beddington-DeAngelis Incidence Rate

Abstract

A model of viral infection of monocytes population by dengue virus is formulated in a system of four ordinary differenttial equations. The model takes into account the immune response and the incidence rate of susceptible and free virus particle as Beddington-DeAngelis functional response. By constructing a block, the global stability of the unin-fected steady state is investigated. This steady state always exists. If this is the only steady state, then it is globally asymptotically stable. If any infected steady state exists, then uninfected steady state is unstable and one of the infected steady states is locally asymptotically stable. These different cases depend on the values of the basic reproduction ratio and the other parameters.

A model of viral infection of monocytes population by dengue virus is formulated in a system of four ordinary differenttial equations. The model takes into account the immune response and the incidence rate of susceptible and free virus particle as Beddington-DeAngelis functional response. By constructing a block, the global stability of the unin-fected steady state is investigated. This steady state always exists. If this is the only steady state, then it is globally asymptotically stable. If any infected steady state exists, then uninfected steady state is unstable and one of the infected steady states is locally asymptotically stable. These different cases depend on the values of the basic reproduction ratio and the other parameters.

Cite this paper

H. Ansari and M. Hesaaraki, "A With-In Host Dengue Infection Model with Immune Response and Beddington-DeAngelis Incidence Rate,"*Applied Mathematics*, Vol. 3 No. 2, 2012, pp. 177-184. doi: 10.4236/am.2012.32028.

H. Ansari and M. Hesaaraki, "A With-In Host Dengue Infection Model with Immune Response and Beddington-DeAngelis Incidence Rate,"

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