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Zbl 1223.92055
Hussaini, N.; Winter, M.; Gumel, A.B.
Qualitative assessment of the role of public health education program on HIV transmission dynamics. (English)
[J] Math. Med. Biol. 28, No. 3, 245-270 (2011). ISSN 1477-8599; ISSN 1477-8602/e

Summary: This paper presents a nonlinear deterministic model for assessing the impact of a public health education campaign on curtailing the spread of the human immunodeficiency virus (HIV) pandemic in a population. Rigorous qualitative analysis of the model reveals that it exhibits the phenomenon of backward bifurcation (BB), where a stable disease-free equilibrium coexists with a stable endemic equilibrium when a certain threshold quantity, known as the `effective reproduction number' ($\cal R_{\text {eff}}$), is less than unity. The epidemiological implication of BB is that a public health education campaign could fail to effectively control HIV even when the classical requirement of having the associated reproduction number less than unity is satisfied. Furthermore, an explicit threshold value is derived above which such an education campaign could lead to detrimental outcome (increase disease burden) and below which it would have positive population-level impact (reduce disease burden in the community). It is shown that the BB phenomenon is caused by imperfect efficacy of the public health education program. The model is used to assess the potential impact of some targeted public health education campaigns using data from numerous countries.

MSC 2000:: *92D30 Epidemiology
37N25 Dynamical systems in biology
34D20 Lyapunov stability of ODE
65C20 Models (numerical methods)

Keywords: HIV/AIDS; reproduction number; stability; equilibria; backward bifurcation

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Zentralblatt MATH Berlin [Germany]