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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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Vogt-Geisse, K., Ngonghala, C. N., & Feng, Z. L. (2020). The Impact Of Vaccination On Malaria Prevalence: A Vaccine-Age-Structured Modeling Approach. J. Biol. Syst., 28(2), 475–513.
Abstract: A deterministic model for the effects on disease prevalence of the most advanced preerythrocytic vaccine against malaria is proposed and studied. The model includes two vaccinated classes that correspond to initially vaccinated and booster dose vaccinated individuals. These two classes are structured by time-since-initial-vaccination (vaccine-age). This structure is a novelty for vector-host models; it allows us to explore the effects of parameters that describe timed and delayed delivery of a booster dose, and immunity waning on disease prevalence. Incorporating two vaccinated classes can predict more accurately threshold vaccination coverages for disease eradication under multi-dose vaccination programs. We derive a vaccine-age-structured control reproduction number R and establish conditions for the existence and stability of equilibria to the system. The model is bistable when R < 1. In particular, it exhibits a backward (sub-critical) bifurcation, indicating that R = 1 is no longer the threshold value for disease eradication. Thus, to achieve eradication we must identify and implement control measures that will reduce R to a value smaller than unity. Therefore, it is crucial to be cautious when using R to guide public health policy, although it remains a key quantity for decision making. Our results show that if the booster vaccine dose is administered with delay, individuals may not acquire its full protective effect, and that incorporating waning efficacy into the system improves the accuracy of the model outcomes. This study suggests that it is critical to follow vaccination schedules closely, and anticipate the consequences of delays in those schedules.
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