Abstract
In this paper, a two-strain model that links immunological and epidemiological dynamics across scales is formulated. On the within-host scale, the two strains eliminate each other with the strain with the larger immunological reproduction persisting. However, on the population scale superinfection is possible, with the strain with larger immunological reproduction number super-infecting the strain with the smaller immunological reproduction number. The two models are linked through the age-since-infection structure of the epidemiological variables. In addition, the between-host transmission and the disease-induced death rate depend on the within-host viral load. The immunological reproduction numbers, the epidemiological reproduction numbers and invasion reproduction numbers are computed. Besides the disease-free equilibrium, there are two population-level strain one and strain two isolated equilibria, as well as a population-level coexistence equilibrium when both invasion reproduction numbers are greater than one. The single-strain population-level equilibria are locally asymptotically stable suggesting that in the absence of superinfection oscillations do not occur, a result contrasting previous studies of HIV age-since-infection structured models. Simulations suggest that the epidemiological reproduction number and HIV population prevalence are monotone functions of the within-host parameters with reciprocal trends. In particular, HIV medications that decrease within-host viral load also increase overall population prevalence. The effect of the immunological parameters on the population reproduction number and prevalence is more pronounced when the initial viral load is lower.
Highlights
Mathematical models have a long history of enriching our knowledge of immunological and epidemiological processes within their separate scales
We use the immuno-epidemiological model that we formulate to address two questions: First, an early epidemiological model of HIV structured by age-since-infection suggested that the variability of infectivity with age-since-infection which presumably follows the within-host viral load, may destabilize the epidemiological dynamics and lead to sustain oscillations [37]
We address the question: Do single-strain periodic solutions exist in the immuno-epidemiological model of HIV? As we show, for the simplest dependence of the transmission and disease-induced death rate on the dynamic within-host viral load, the single-strain equilibrium is locally asymptotically stable and Hopf bifurcation does not occur
Summary
Mathematical models have a long history of enriching our knowledge of immunological and epidemiological processes within their separate scales. We use the immuno-epidemiological model that we formulate to address two questions: First, an early epidemiological model of HIV structured by age-since-infection suggested that the variability of infectivity with age-since-infection which presumably follows the within-host viral load, may destabilize the epidemiological dynamics and lead to sustain oscillations [37]. The second question that we address is: How do the within-host parameters affect the epidemiological reproduction number, prevalence of HIV, and invasion capabilities of the two strains?. Our results imply that the sensitivities of the epidemiological reproduction number and prevalence with respect to the immunological infection parameters are decreasing functions of the initial viral load, suggesting that by decreasing the amount of virus transmitted HIV medications increase the sensitivity of the epidemiological parameters with respect to immunological parameters.
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