School of Mathematics and Statistics - Theses
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ItemMathematical Modelling of Plasmodium Vivax Transmission( 2023-08)Malaria is caused by Plasmodium parasites transmitted to humans by the bite of an infected Anopheles mosquito. Plasmodium vivax is distinct from other malaria species in its ability to remain dormant in the liver (as hypnozoites) and activate later to cause further infections (referred to as relapses). For this reason, P. vivax is currently the most geographically widespread malaria-causing parasite resulting in significant associated global morbidity and mortality. As around 79–96% of infections are attributed to relapses from activating hypnozoites, targeting the hypnozoite reservoir (i.e., the collection of dormant parasites) to eliminate P. vivax is crucial. Mathematical models to describe the transmission dynamics of P. vivax have been developed, but most fail to capture realistic hypnozoite dynamics. Models that capture the complexity tend to involve many governing equations, making them difficult to extend to incorporate other important factors for P. vivax, such as treatment status, age, and pregnancy. In this thesis, we have developed a multiscale model (a system of integro-differential equations) that involves a minimal set of equations at the population scale, with an embedded within-host model that captures the dynamics of the hypnozoite reservoir and accounts for superinfection and mosquito seasonality. In this way, we can gain critical insights into the dynamics of P. vivax transmission with a minimum number of equations at the population scale, making this framework readily scalable to incorporate more complexity. We use our multiscale model to study the effect of radical cure (drugs that affect hypnozoites) treatment administered via a mass drug administration (MDA) program accounting for superinfection (infectious bites and/or the activation of hypnozoites can trigger multiple infections). We explicitly model the impact of the radical cure drug on each of the hypnozoites and infections. An optimisation model with different objective functions motivated on a public health basis is constructed to obtain the MDA interval that optimally disrupts P. vivax transmission. Our work shows that the effect of MDA interventions is temporary (using the deterministic framework) and depends on the pre-intervention disease prevalence (and choice of model parameters), drug efficacy, and the number of MDA rounds under consideration. We found that prevalence alone is insufficient to determine optimal intervals between rounds of MDA in regions where seasonal variation in the mosquito population is minimal. However, when seasonal variation is present, prevalence can be considered a reliable measure for determining the optimal timing of MDAs. To study the impact of MDA with radical cure on P. vivax elimination, we re-implemented our model as a continuous time non-Markovian stochastic model, as disease fadeout is not possible with a deterministic model. We found that the more rounds of MDA, the better the chance of P. vivax elimination and up to two MDA rounds have a very minimal effect on the probability of elimination (this depends on other model parameters as well). To achieve a higher probability of elimination, MDA with a very high-efficacy drug should be considered. Furthermore, a simplified approach to MDA timings can provide similar results compared to the optimal approach. As our model captures the effect of hypnozoite dynamics on transmission and the effect of treatment on each hypnozoite, it has the potential to become a critical tool in answering public health questions related to P. vivax transmission.