MODELLING THE SPREAD OF INFECTIOUS DISEASES

Abstract

Mathematical models applied to epidemiology are useful tools that help understand how infectious diseases spread in populations, and hence support public-health decisions. Over the last 250 years, these modelling tools have have developed at an increasing rate, both on the theoretical and computational sides. This thesis explores various modelling techniques to address debated or unanswered questions about the transmission dynamics of infectious diseases, in particular sexually transmitted ones. The role of sero-discordant couples (when only one partner is infected) in the HIV epidemic in Sub-Saharan Africa is controversial. Their importance compared to other sexual transmission routes is critical when designing intervention policies. In chapter 2, I used a compartmental model with an original partnership process to show that infection of uncoupled individuals is usually the predominant route, while transmission within discordant couples is also important, but to a lesser extent. Despite the availability of inexpensive antimicrobial treatment, syphilis remains prevalent worldwide, affecting millions of individuals. Development of a syphilis vaccine would be a potentially promising step towards control, but the value of dedicating resources to vaccine development should be evaluated in the context of the anticipated benefits. In chapter 3, I explored the potential impact of a hypothetical syphilis vaccine on morbidity from both syphilis and HIV using an agent-based model. My results suggest that an efficacious vaccine has the potential to sharply reduce syphilis under a wide range of scenarios, while expanded treatment interventions are likely to be substantially less effective. General concepts in epidemic modelling, that could be applied to any disease, are still debated. In particular, a rigorous definition and analysis of the generation interval – the interval between the time that an individual is infected by an infector and the time this infector was infected – needed clarification. Indeed, the generation interval is a fundamental quantity when modelling and forecasting epidemics. Chapter 4 clarifies its theoretical framework, explains how its distribution changes as an epidemic progresses and discuss how empirical generation-interval data can be used to correctly inform mathematical models.