# Modelling of the invasion dynamics of plasmodium falciparum merozoites into red blood cells

Thesis (MSc)--Stellenbosch University, 2016

Thesis

ENGLISH ABSTRACT : BACKGROUND The physiological symptoms of P. falciparum infection are associated with a 48 hour replication cycle whereby parasites (merozoites) invade susceptible red blood cells (RBCs), develop and multiply within these now infected RBCs and eventually rupture them, releasing 8 to 32 daughter merozoites which are free to di use through their environment and may subsequently invade other available RBCs and begin a new replication cycle. OBJECTIVES: To develop a novel, parameterised mechanistic mathematical model which describes the dynamics of merozoite invasion during the initial stages of malarial infection. Furthermore, to determine if the dispersal of daughter merozoites can be modelled by a random walk model and extrapolated to a di usion process. APPROACH: Two novel mathematical models were constructed to describe the dynamics of the aforementioned invasion process { a deterministic model consisting of four coupled ordinary di erential equations and a stochastic, random walk model. In addition, several forms of the mechanistic model were built to accommodate multiply-invaded RBCs. These parasitised RBCs are those which have been invaded by more than one merozoite; a phenomenon largely absent from modelling exercises seen in the literature. The novelty of the models pertains to the inclusion of a "merozoite-erythrocyte complex" or MEC. This is an unstable, intermediary species which forms after the initial interaction between a free merozoite and susceptible RBC but before successful invasion may occur. CONCLUSION: The most signi cant conclusion gained from this research was that while the mathe- matical models were constructed in a theoretically sound manner in which all interactions were based on observable phenomena, the data required to robustly validate these models and acquire accurate estimates for the parameters was not available.

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