Mathematical modelling of multiple target cells with delay

Abstract

Target cells contagion has sparked the necessity of a multiple target cell model with chronic infection and intracellular delay (MTC-CI-ID). This paper seeks to advance a viral dynamical model with multiple target cells and corroborate the global stability of their steady states. Hence, the affiliation of the virus with two classes of target cells, CD4 + Tcells and macrophage. The time delay amidst viral entry and the output of virions were intimated and the basic reproductive number was procured, as the long term behavior of the model and less than unity. The contagious free equilibrium E0 was unveiled as locally and globally asymptotically stable. The conditions of an infected CD4 + Tcell and macrophage on viral production were engaged. It was ascertained that CD4 + Tcell accounts for larger amounts of virions in the blood as per macrophage cells. Hence, varying time delay has no impact on peak viral levels, but only shelves the viral peaking time. The adopted model has unrestrained bearing on HIV-1 therapy.

Keywords

• Multiple target cell
• Intracellular delay
• Chronic infection
• Disease free equilibrium
• Lyapunov function
• Reproduction number