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Kapitanov, G., Alvey, C., Vogt-Geisse, K., & Feng, Z. L. (2015). An Age-Structured Model For The Coupled Dynamics Of Hiv And Hsv-2. Math. Biosci. Eng., 12(4), 803–840.
Abstract: Evidence suggests a strong correlation between the prevalence of HSV-2 (genital herpes) and the perseverance of the HIV epidemic. HSV-2 is an incurable viral infection, characterized by periodic reactivation. We construct a model of the co-infection dynamics between the two diseases by incorporating a time-since-infection variable to track the alternating periods of infectiousness of HSV-2. The model considers only heterosexual relationships and distinguishes three population groups: males, general population females, and female sex workers. We calculate the basic reproduction numbers for each disease that provide threshold conditions, which determine whether a disease dies out or becomes endemic in the absence of the other disease. We also derive the invasion reproduction numbers that determine whether or not a disease can invade into a population in which the other disease is endemic. The calculations of the invasion reproduction numbers suggest a new aspect in their interpretation – the class from which the initial disease carrier arises is important for understanding the invasion dynamics and biological interpretation of the expressions of the reproduction numbers. Sensitivity analysis is conducted to examine the role of model parameters in influencing the model outcomes. The results are discussed in the last section.
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Vogt-Geisse, K., Lorenzo, C., & Feng, Z. L. (2013). Impact Of Age-Dependent Relapse And Immunity On Malaria Dynamics. J. Biol. Syst., 21(4), 49 pp.
Abstract: An age-structured mathematical model for malaria is presented. The model explicitly includes the human and mosquito populations, structured by chronological age of humans. The infected human population is divided into symptomatic infectious, asymptomatic infectious and asymptomatic chronic infected individuals. The original partial differential equation (PDE) model is reduced to an ordinary differential equation (ODE) model with multiple age groups coupled by aging. The basic reproduction number R-0 is derived for the PDE model and the age group model in the case of general n age groups. We assume that infectiousness of chronic infected individuals gets triggered by bites of even susceptible mosquitoes. Our analysis points out that this assumption contributes greatly to the R0 expression and therefore needs to be further studied and understood. Numerical simulations for n = 2 age groups and a sensitivity/uncertainty analysis are presented. Results suggest that it is important not only to consider asymptomatic infectious individuals as a hidden cause for malaria transmission, but also asymptomatic chronic infections (>60%), which often get neglected due to undetectable parasite loads. These individuals represent an important reservoir for future human infectiousness. By considering age-dependent immunity types, the model helps generate insight into effective control measures, by targeting age groups in an optimal way.
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