Exploring the Multi-scale character of infectious disease dynamics

Abstract

This research study characterised multiscale models of infectious disease dynamics. This was achieved by establishing when it is appropriate to implement particular mathematical methods for different multiscale models. The study of infectious disease systems has been elucidated ever since the discovery of mathematical modelling. Due to the vast complexities in the dynamics of infectious disease systems, modellers are increasingly gravitating towards multiscale modelling approach as a favourable alternative. Among the diseases that have persistently plagued most developing countries are vector-borne diseases like Malaria and directly transmitted diseases like Foot-and-Mouth disease (FMD). Globally, FMD has caused major losses in the economic sector (particularly agriculture) as well as tourism. On the other hand, Malaria remains amongst the most severe public health problems worldwide with millions of people estimated to live in permanent risk of contracting the disease. We developed multiscale models that can describe both local transmission and global transmission of infectious disease systems at any hierarchical level of organization using FMD and Malaria disease as paradigms. The first stage in formulating the multiscale models in this study was to integrate two submodels namely: (i) the between-host submodel and (ii) within-host submodel of an infectious disease system using the nested approach. The outcome was a system of nonlinear ordinary differential equations which described the local transmission mechanism of the infectious disease system. The next step was to incorporate graph theoretic methods to the system of differential equations. This approach enabled modelling the migration of humans/animals between communities (also called patches or geographical distant locations) thereby describing the global transmission mechanism of infectious disease systems. At whole organism-level we considered the organs in a host as patches and the transmission within-organ scale as direct transmission represented by ordinary differential equations. However, at between-organ scale there was movement of pathogen between the organs through the blood. This transmission mechanism called global transmission was represented by graph-theoretic methods. At macrocommunity-level we considered communities as patches and established that at withincommunity scale there was direct transmission of pathogen represented by ordinary differental equations and at between-community scale there was movement of infected individuals. Furthermore, the systems of differential equations were extended to stochastic differential equations in order to incorporate randomness in the infectious disease dynamics. By adopting a cocktail of computational and analytical tools we sufficiently analyzed the impact of the transmission mechanisms in the different multiscale models. We established that once we used a graph-theoretic method at host level it would be difficult to extend this to community level. However, when we used different methods then it was easy to extend to community level. This was the main aspect of the characterization of multiscale models that we investigated in this thesis which has not been done before. We also established distinctions between local transmission and global transmission mechanisms which enable us to implement intervention strategies targeted torwards both local transmission such as vaccination and global transmission such as travel restrictions. In spite of the fact that the results collected in this study are restricted to FMD and Malaria, the multiscale modelling frameworks established are suitable for other directly transmitted diseases and vector-borne diseases.