DYNAMICS OF MULTI INFECTIONS DISEASE (MALARIA-ELEPHANTIASIS-ZIKA VIRUS) TRANSMISSION IN MOSQUITO ENDEMIC REGIONS
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Date
2019-10
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KNUST
Abstract
Mosquitoes are one of the deadliest insects in the world. Their ability to carry
and spread disease to humans cause millions of deaths every year. The
worldwide incidence of diseases caused by mosquitoes has risen 30-fold in the
past 30 years, and more countries are reporting their first outbreaks of the
mosquito caused diseases. Zika, Malaria, and Elephantiasis are all transmitted
to humans by the Aedes aegypti mosquito. More than half of the world’s
population live in areas where this mosquito species are present. Sustained
mosquito control efforts are important to prevent outbreaks from these
diseases. There are several different types of mosquitoes and some have the
ability to carry many different diseases. The study presents a multi-infections
system model to study the transmission dynamics of Malaria, Zika-Virus and
Elephantiasis in an endemic region such as Kedougou in the South Eastern part
of Senegal and other parts of the world. This makes it possible to have multiinfections of the three diseases simultaneously. The main objective of this work
was to study the dynamics of multi-infections (Malaria-Elephantiasis-Zika virus)
and transmission through the use of mathematical model, to determine the
stability of the multi-infections model, the co-infections model and also study
the single models for individual diseases including Malaria, Zika and
Elephantiasis. The disease-free equilibrium is performed and it was shown to
be globally asymptotically stable when the associated threshold number
known as the basic reproduction number for the model is R0 < 1. Investigation
on the existence and stability of equilibria was also derived, the model was
found to exhibit backward bifurcation. Thus, R0 less than unity is not sufficient
to eradicate the disease from the population and there was the need to lower
R0 below a certain threshold for effective disease control. Sensitivity analysis
was performed to determine parameters that have high influence on the basic
reproduction number. Optimal control policies was also used as measures to
eradicate the diseases from the system.
Description
Thesis submitted to the Department of Mathematics of the School of Physical
Sciences, College of Agriculture in partial fulfilment of the requirements for the award of
Doctor of Philosophy degree in Applied Mathematics