Dynamical properties and thresholds of an HIV model with super-infection.


Malunguza, NJ; Hove-Musekwa, SD; Dube, S; Mukandavire, Z; (2016) Dynamical properties and thresholds of an HIV model with super-infection. Mathematical medicine and biology. ISSN 1477-8599 DOI: https://doi.org/10.1093/imammb/dqw014

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Abstract

: Super-infection by multiple HIV-1 subtypes, previously thought restricted to high risk groups, has now been reported in the general heterosexual populations at relatively the same incidence rate as in high risk groups. We present a simple deterministic HIV model with super-infection by two HIV-1 subtypes. Mathematical characteristics including the basic reproductive number [Formula: see text], invasion threshold [Formula: see text] and conditions for asymptotic stability are derived. In the absence of super-infection the model exhibits competitive exclusion, and all equilibria are globally attracting if they exist except for the disease free which is a saddle for [Formula: see text] The results show that the subtype with the dominant reproductive number exceeding unity dominates the weaker subtype forcing it to extinction regardless of the size of the reproductive number. On the other end, super-infection may promote subtype co-existence whenever the minimum of the subtype specific reproductive numbers [Formula: see text] and the invasion reproductive numbers [Formula: see text] exceed unity. Our results demonstrate that if the partial reproductive numbers [Formula: see text] and the invasion reproductive number for the weaker subtype [Formula: see text] satisfy [Formula: see text] then primary infection by subtype [Formula: see text] may stay the extinction of subtype [Formula: see text] despite its relatively low reproductive fitness. For certain parameter ranges, hysteresis (including backward bifurcation) occurs with possible differences in the asymptotic level of disease prevalence. Super-infection may thus facilitate the continued re-generation of reproductively noncompetent subtypes whose subtype specific reproductive numbers will be less than unity while at the same time allowing for the mutual coexistence and persistence of multiple strains. Persistence and co-existence of multiple strains has detrimental effect on vaccine design and development and administration of ART where one or more of the strains are drug resistant.<br/>

Item Type: Article
Faculty and Department: Faculty of Public Health and Policy > Dept of Global Health and Development
Research Centre: Social and Mathematical Epidemiology (SaME)
SaME Modelling & Economics
PubMed ID: 27672183
URI: http://researchonline.lshtm.ac.uk/id/eprint/2997179

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