Global dynamics of HIV infection with two disease transmission routes - a mathematical model

Xianbing Cao, Amit Kumar Roy, Fahad Al Basir, Priti Kumar Roy

Abstract


In this paper, we have studied the global dynamics of HIV model with two transmission paths: direct transmission through cells-to-cells contact and indirect transmission through virus. We have derived a four dimensional mathematical model including uninfected $CD_4^{+T}$ cells, infected $CD4^+{T}$ cells, virus and the CTL immune response cells. The nonnegativity and boundedness property of the solutions the proposed mathematical system have been analysed, and the basic reproduction ratio $R_0$ has been derived with the help of next generation matrix method. We also discussed the local and global stability with respect to the basic reproduction ratio of both disease-free and interior equilibrium points under certain conditions. Through numerical simulations, we have validated the all analytical findings. We have established that the disease-free equilibrium is globally stable for $R_0<1$ and endemic equilibrium is globally stable for $R_0>1$ whenever exists. It is also observed that cells-to-cells transmission rate is more effective compare to virus-to-cells infection rate.

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Published: 2020-03-02

How to Cite this Article:

Xianbing Cao, Amit Kumar Roy, Fahad Al Basir, Priti Kumar Roy, Global dynamics of HIV infection with two disease transmission routes - a mathematical model, Commun. Math. Biol. Neurosci., 2020 (2020), Article ID 8

Copyright © 2020 Xianbing Cao, Amit Kumar Roy, Fahad Al Basir, Priti Kumar Roy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Commun. Math. Biol. Neurosci.

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