Abstract:
The purpose of this thesis is to develop coupled multi-scale dynamics of infectious disease systems. An
infectious disease system consists of three subsystems interacting, which are the host, the pathogen, and
the environment. Each level has two different interaction scales (micro-scale and macro-scale) and is
organized into hierarchical levels of an organization, from the cellular level to the macro-ecosystem level,
and is arranged into hierarchical levels of an organization. There are two main theories of infectious
diseases: (i) the transmission mechanism theory, (ii) the replication-transmission relativity theory. A
significant difference exists between these theories in that (i) the transmission mechanism theory considers
transmission to be the primary cause of infectious disease spread at the macro-scale, while (ii) replicationtransmission
relativity theory is an extension of the first theory. It is important to consider the interaction
between two scales when pathogen replication occurs within the host and transmission occurs between
hosts (macro-scale). Our research primarily focuses on the replication-transmission relativity theory of
pathogens. The main purpose of this study is to develop coupled multi-scale models of direct vectorborne
diseases using malaria as a paradigm. We have developed a basic coupled multi-scale model with
a combination of two other categories of multi-scale models, which are a nested multi-scale model in the
human host and an embedded multi-scale model in the mosquito host. The developed multi-scale model
consists of approaches of nonlinear differential equations that are employed to provide the mathematical
results to the underlying issues of the multi-scale cycle of pathogen replication and transmission of malaria
disease. Stability analyses of the models were evolved to substantiate that the infection-free equilibrium
is locally and globally asymptotically stable whenever R0 < 1, and the endemic equilibrium exists and
is globally asymptotically stable whenever R0 > 1. We applied the vaccination process as a governing
measure on the multi-scale model of malaria with mosquito life cycle by comprising the three stages of
vaccination, namely pre-erythrocyte stage vaccines, blood stage vaccines and transmission stage vaccines.
The impact of vaccination on malaria disease has been proven. Through numerical simulation, it was
found that when the comparative of vaccination efficacy is high, the community pathogen load (GH and
PV ) decreases and the reproductive number can be reduced by 89.09%, that is, the transmission of malaria
can be reduced on the dynamics of individual level and population-level.We also evolved the multi-scale
model with the human immune response on a within-human sub-model which is stimulated by the malaria
parasite. We investigated the effect of immune cells on reducing malaria infection at both the betweenhost
scale and within-host scale. We incorporate the environmental factor, such as temperature in the
multi-scale model of the malaria disease system with a mosquito life cycle. We discovered that as the
temperature enhances the mosquito population also increases which has the impact of increasing malaria
infection at the individual level and at the community-scale. We also investigated the influence of the
mosquito life cycle on the multi-scale model of the malaria disease system. The increase in eggs, larval
and pupal stages of mosquitoes result in the increase of mosquito density and malaria transmission at the
individual level and community-scale. Therefore, the suggestion is that immature and mature mosquitoes
be controlled to lessen malaria transmission. The results indicated that the combination of malaria health
interventions with the highest efficacy has the influence of reducing malaria infection at the populationlevel.
Models developed and analyzed in this study can play a significant role in preventing malaria
outbreaks. Using the coupled multi-scale models that were developed in this study, we made conclusions
about the malaria disease system based on the results obtained. It is possible to apply the multi-scale
framework in this study to other vector-borne diseases as well.