Abstract
In this work we present an infection-age-structured mathematical model of AIDS disease dynamics and examine the endemic equilibrium state for stability. An explicit formula for the basic reproduction number R0 was obtained in terms of the demographic and epidemiological parameters of the model. The endemic equilibrium state was found to be locally asymptotically stable under certain conditions. Furthermore, by constructing a suitable Lyapunov functional, the endemic equilibrium state was found to be globally asymptotically stable under certain conditions prescribed on the model parameters.Keywords: Basic reproduction number, HIV/AIDS, Lyapunov functional
Highlights
This paper presents an infection-agestructured mathematical model of the AIDS disease dynamics proposed by Akinwande (2005)
In Akinwande (2005) a characteristic equation was obtained and analysed using the results of Bellman and Cooke (1963).This paper presents a variant of the model by Akinwande (2005) and we study the stability analysis of the endemic equilibrium state using the method of linearization and the Lyapunov method
Death rate due to HIV virus infection δ constant; k is the measure of the efficacy of the anti-retroviral therapy (ART); θ is the proportion of the off-springs of the infected who are virus-free at birth; 0 ≤ θ ≤ 1. t is time; τ is the infection age and T is the maximum infection age, We re-write (1)-(7) as follows dS(t) = (β − μ)S(t) +θβI (t) −αS(t)I (t) (8)
Summary
This paper presents an infection-agestructured mathematical model of the AIDS disease dynamics proposed by Akinwande (2005). INTRODUCTION This paper presents an infection-agestructured mathematical model of the AIDS disease dynamics proposed by Akinwande (2005). They assumed that while the new births in the susceptible class S(t) are born therein, the off-springs of the infected I (t) are divided between S(t) and I (t) in the proportionsθ and dS(t) = (β − μ )S(t) + θβI (t) − αS(t)I (t) (1)
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