Abstract
This article focuses on the study of an age-structured two-strain model with super-infection. The explicit expression of basic reproduction numbers and the invasion reproduction numbers corresponding to strain one and strain two are obtained. It is shown that the infection-free steady state is globally stable if the basic reproductive number R(0) is below one. Existence of strain one and strain two exclusive equilibria is established. Conditions for local stability or instability of the exclusive equilibria of the strain one and strain two are established. Existence of coexistence equilibrium is also obtained under the condition that both invasion reproduction numbers are larger than one.
Highlights
Understanding pathogens’ ability to respond to selective pressures and change their genetic make-up is the key to combating numerous infectious diseases
Super-infection [23, 20], co-infection [21], cross-immunity [8, 9], mutation [4], host density-dependent mortality [3] have all been identified to support coexistence of pathogen variants
The disease-free equilibrium is globally stable in the case when super-infection is less likely than an original infection with strain one: 0 ≤ δ ≤ 1
Summary
Understanding pathogens’ ability to respond to selective pressures and change their genetic make-up is the key to combating numerous infectious diseases. The first key result establishes (using the tools of semigroup theory) that in the most basic S-I-S age-structured single-strain epidemic model the unique endemic equilibrium is globally stable and sustained oscillations do not occur [6]. Thieme and Castillo-Chavez [29, 30] showed that age-since-infection structure may destabilize the endemic equilibrium and lead to oscillations in an HIV/AIDS epidemic model Their results were numerically confirmed by Milner and Pugliese [22]. We can prove that λ∗2 is dominant real root of H(λ) It follows that the infection-free steady state is locally asymptotically stable if R0 < 1 and unstable if R0 > 1.
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