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.