Mathematical Analysis of Dynamics of Chlamydia trachomatis
Sharomi, Oluwaseun Yusuf
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Chlamydia, caused by the bacterium Chlamydia trachomatis, is one of the most important sexually-transmitted infections globally. In addition to accounting for millions of cases every year, the disease causes numerous irreversible complications such as chronic pelvic pain, infertility in females and pelvic inflammatory disease. This thesis presents a number of mathematical models, of the form of deterministic systems of non-linear differential equations, for gaining qualitative insight into the transmission dynamics and control of Chlamydia within an infected host (in vivo) and in a population. The models designed address numerous important issues relating to the transmission dynamics of Chlamydia trachomatis, such as the roles of immune response, sex structure, time delay (in modelling the latency period) and risk structure (i.e., risk of acquiring or transmitting infection). The in-host model is shown to have a globally-asymptotically stable Chlamydia-free equilibrium whenever a certain biological threshold is less than unity. It has a unique Chlamydia-present equilibrium when the threshold exceeds unity. Unlike the in-host model, the two-group (males and females) population-level model undergoes a backward bifurcation, where a stable disease-free equilibrium co-exists with one or more stable endemic equilibria when the associated reproduction number is less than unity. This phenomenon, which is shown to be caused by the re-infection of recovered individuals, makes the effort to eliminate the disease from the population more difficult. Extending the two-group model to incorporate risk structure shows that the backward bifurcation phenomenon persists even when recovered individuals do not acquire re-infection. In other words, it is shown that stratifying the sexually-active population in terms of risk of acquiring or transmitting infection guarantees the presence of backward bifurcation in the transmission dynamics of Chlamydia in a population. Finally, it is shown (via numerical simulations) that a future Chlamydia vaccine that boosts cell-mediated immune response will be more effective in curtailing Chlamydia burden in vivo than a vaccine that enhances humoral immune response. The population-level impact of various targeted treatment strategies, in controlling the spread of Chlamydia in a population, are compared. In particular, it is shown that the use of treatment could have positive or negative population-level impact (depending on the sign of a certain epidemiological threshold).