Abstract:
Mosquitoes are long-legged, two winged flies that are responsible for the transmission
of many diseases such as Zika fever, malaria, yellow fever, chikungunya and dengue
hemorrhagic fever. Mosquito borne diseases account for substantial amount of para-
sitic and infectious diseases, they have profound effects on economic growth of many
developing countries. There have been continuous efforts to optimize and improve on
existing mosquito control strategies, as well as to develop new tools aimed at reducing
burden of mosquito borne diseases. Control strategies are either applied alone or in
combination depending on available resources, education, health risk and burden of
the disease.
The main aim of this thesis is to mathematically study three mosquito borne dis-
eases in the presence of control, the diseases are Zika fever (this is because, in addition
to the disease being transmitted vertically, it is the first mosquito borne disease known
to be transmitted sexually), yellow fever (because despite having effective vaccine for
the disease, it has continue to pose sporadic challenges in different regions of the
world), and malaria (because it has the highest global burden among mosquito borne
diseases despite continuous efforts to eradicate it).
Some major highlights of the thesis include: Roles of mosquito vertical transmission
in the transmission dynamics of mosquito borne diseases, and effects of incorporating
human-human transmission are evaluated. Assessment of impact of using different
control measures both in human and mosquito populations, and effects of controlling
population of adult male (non-disease transmitting) mosquitoes through sterilization
are conducted. Implication of incorporating aquatic stage of mosquito development in
models for the transmission of mosquito borne diseases, as well as effect of temperature
variation in the transmission dynamics of malaria are also studied.
In Chapter 1, brief introduction to the epidemiology of mosquito borne diseases
is presented. Basic results and definitions in mathematical epidemiology are also dis-
cussed. In addition, some important mathematical theories and definitions used in
subsequent chapters are also presented. A Zika model that incorporates vectorial ver-
tical transmission, human-human horizontal transmission, as well as human-mosquito
and mosquito-human transmissions is studied in Chapter 2. Another Zika model is
considered in Chapter 3, the model incorporated human-human transmission in the
presence of mosquito sterilization. In Chapter 4, a yellow fever model with vaccina-
tion, use of bed nets and mosquito control at both aquatic and non-aquatic stages
is constructed and analysed. Chapter 5 considered a temperature dependent malaria
model in the presence of control. General conclusion is given in Chapter 6.
