Philosophiae Doctor - PhD (Mathematics)
http://hdl.handle.net/11394/3210
2024-03-29T14:47:54ZMathematical epidemiology of malaria disease transmission and its optimal control analyses
http://hdl.handle.net/11394/10334
Mathematical epidemiology of malaria disease transmission and its optimal control analyses
Oare, Okosun Kazeem
In this thesis, we present and analyse an SEIR (susceptible-exposed infectious-recovered) model for malaria disease transmission. The model consists treatment and control strategies such as the use of bed nets and spray of insecticides with the costs associated with each control measure. Firstly, we analyse the model without treatment and investigate its stability and bifurcation behaviour. Then, we incorporate treatment and investigated the effects of different control strategies on the spread of malaria. Further, we use optimal control methods to determine the necessary conditions for the optimality of the disease eradication or control. We determined the most cost-effective strategies in fighting malaria disease by carrying out a cost-effectiveness study. We found that mass action model exhibited transcritical bifurcation. The disease-free equilibrium (DFE) is globally stable whenever, basic reproductive number is less than unity, while the models with standard incidence form exhibited backward bifurcation. In examining the cost-effectiveness analysis, we found that the most cost-effective strategy is the combination of insecticides spray and treatment of infective individuals. Furthermore, we modified the SEIR model to incorporate treatment and vaccination with waning immunity and an appropriate cost function. We analyse the model and investigated its stability and bifurcation property. Also, we use optimal control theory to determine the necessary optimal conditions for the disease eradication, and when eradication of the disease is unachievable, we derived the necessary conditions for its control. Further, we carried out a cost-effectiveness analysis of the control strategies. In our findings, the mass action model exhibits a backward bifurcation phenomenon, while the standard incidence model exhibited a phenomenon of multiple endemic equilibria. We also found that the most cost-effective strategy to eliminate malaria is the combination of treatment of infective individuals and vaccination. From the analysis, we found that eradication will be possible and optimal when the community marginal cost is less than the community marginal benefits.
Doctor Scientiae
2010-01-01T00:00:00ZReliable numerical simulations of problems for pricing real estate derivatives
http://hdl.handle.net/11394/9603
Reliable numerical simulations of problems for pricing real estate derivatives
Dube, Mbakisi
The globalisation of nancial systems has presented new challenges to investing in real
estate assets. For example, any crisis occurring in one real estate market will have an
adverse e ect on other markets regardless of them being vastly geographically distant
from each other. This interconnectedness is due to the ease of acquiring property portfolios
using capital from investors coming from di erent jurisdictions who would have
pooled their capital to acquire those properties. This illustrates how capital can ow
internationally in the process creating linkages between various markets. The globalisation
of real estate markets and the amount of capital invested in them results in a
need for innovative mechanisms to manage and contain the risk of having shocks in
the real estate market destabilising and a ecting international nancial markets. Risk
management for real estate portfolios can be e ectively done through the use of real
estate index based derivatives.
Philosophiae Doctor - PhD
2022-01-01T00:00:00ZAnalysis and simulation of some ecological models describing weed-water hyacinth dynamics in Lake Tana, Ethiopia
http://hdl.handle.net/11394/9554
Analysis and simulation of some ecological models describing weed-water hyacinth dynamics in Lake Tana, Ethiopia
Belay, Yeshambel Azene
The water hyacinth plant is notorious for being the world’s worst aquatic weed. In
Ethiopia, it invades lake Tana which is the largest lake in Ethiopia. This is attracting
attention of many researchers including mathematical modellers. To this end,
in this thesis, we consider systems modelling water hyacinth effect in lake ecosystem.
Among the classes of models considered in this work includes, the refuge effect of water
hyacinth in lake ecosystem, the effect of water hyacinth in a lake eutrophication dynamics
and singularly perturbed (slow-fast) phytoplankton-zooplankton, predator-prey
systems with water hyacinth’s refuge effect.
Philosophiae Doctor - PhD
2022-01-01T00:00:00ZAnalysis and robust simulation of mathematical models of HIV and Leishmaniasis co-infection
http://hdl.handle.net/11394/9543
Analysis and robust simulation of mathematical models of HIV and Leishmaniasis co-infection
Adamu, Elias M.
The purpose of this thesis is the theoretical and numerical study of epidemiological
models of Visceral Leishmaniasis (VL) and human immunode ciency virus (HIV) coinfection.
We study these models theoretically and design and analyze robust numerical
methods to solve them. The rst sub-model describes the transmission dynamics
of VL and incorporates three populations: the human, the reservoir, and the vector
host populations. Then we study the Anthroponotic Visceral Leishmaniasis (AVL)
between the human and the vector host population. The second sub-model describes
a deterministic SIAT (Susceptible-Infected-AIDS-Treated) HIV/AIDS model that incorporates
the treatments of HIV-infected and AIDS-infected individuals.
Philosophiae Doctor - PhD
2022-01-01T00:00:00Z