PhD Theses and Dissertation [CoCSE]https://dspace.nm-aist.ac.tz/handle/123456789/342020-06-03T16:59:51Z2020-06-03T16:59:51ZMathematical modeling of the effect of seasonal weather variations on the dynamics of plague diseaseNgeleja, Rigobert Charleshttps://dspace.nm-aist.ac.tz/handle/123456789/3102019-07-01T12:55:56Z2019-02-01T00:00:00ZMathematical modeling of the effect of seasonal weather variations on the dynamics of plague disease
Ngeleja, Rigobert Charles
A mathematical model to study the effect of seasonal weather variation on the dynamics of
plague disease is developed and analyzed. Apart from being historical, plague disease caused
by a gram negative bacteria called Yersinia pestis is still considered as a major threat around the
world. In this work we investigate three main forms of plague disease which are bubonic, septicemic
and pneumonic plague. It gives answers to various questions that relate to the complex
dynamics of plague disease and the effect of seasonal weather variation in its transmission and
spread. In particular we give answers to mainly four questions pertaining to the formulation
and analyses of the mathematical models of bubonic Plague, formulation and analysis of the
mathematical models of pneumonic plague, formulation and analysis of the combined mathematical
model for the dynamics of plague disease that includes all three forms of plague disease
and all major ways/modes of plague disease transmission. Lastly we formulate and analyze the
plague disease model incorporating parameters that are affected by seasonal weather variation
and study its effects on the dynamics of plague disease.
Using ordinary differential equations, we formulate a model for the dynamics of plague disease
in four settings namely: Human beings, Rodents, Fleas and Pathogens in the environment. We
compute the basic reproduction numbers and apply them to establish the conditions for local
and global stability of both disease free and endemic equilibrium points. We further assess
the effect of seasonal weather variation, in which we modify the transmission rates and take
them as sinusoidal functions. Using fundamental existence-uniqueness theorem, we were able
to prove the existence of positive periodic solutions. We then establish the conditions for local
and global stability of both Positive Periodic Solution (PPS) and Disease Free Solution (DFS).
The results show that the transmission and dynamics of bubonic plague are dictated by: the
rate at which fleas get infected; the infectious periods of fleas, rodents and human beings;
the probability that rodents and human beings survive the infected class; and the adequacy
of contact rates and the rate at which human beings and rodents become exposed to bubonic
plague disease. We also found that the environment condition, the abundance of pathogens in
the environment and the increase of the number of individuals with pneumonic plague greatly
influence the increase of pneumonic plague disease infectives. In the combined model, we
found that the variation in number of plague disease cases mainly depend on: the transmission
rate of infection from one individual to another; the incubation period of an individual and the
time that an individual remains infectious. The analysis further reveals that the effects posed
by seasonal weather variation depends on the extent to which the weather variation favours the
transmission of plague disease (amplitude of seasonality) and the duration that it remains in
favour of the increase or decrease of the rate of disease transmission and spread. Therefore the
control strategies should target these factors and parameters (the transmission rate of infection from one individual to another, the incubation period of an individual and the time that an
individual remains infectious) that according to our results stated above have shown to have a
significant effect on the dynamics of plague disease.
We thus recommend to the government, national security system and other health stake holders
that in order to have an effective way of controlling the disease we must ensure that there is
provision of education on plague disease infection, transmission and spread to raise peoples
awareness, continuous monitoring of factors that may lead to plague outbreak, easy access of
plague disease treatment for all and the strong collaboration with neighboring countries on
health related issues.
A Dissertation Submitted in Partial Fulfilment of the Requirements for the Degree of
Doctor of Philosophy in Mathematical and Computer Sciences and Engineering of the
Nelson Mandela African Institution of Science and Technology
2019-02-01T00:00:00ZModeling the dynamics, control and economic loss of newcastle disease in village chicken: a case of Pwani region in TanzaniaChuma, Furahahttps://dspace.nm-aist.ac.tz/handle/123456789/3092019-07-01T12:55:56Z2019-03-01T00:00:00ZModeling the dynamics, control and economic loss of newcastle disease in village chicken: a case of Pwani region in Tanzania
Chuma, Furaha
Newcastle disease (ND) is a highly contagious viral bird disease affecting the domestic and
other wild birds. The disease is a major threat to the farming of village chicken by small,
medium, and large scale farmers.
In this dissertation, a non-linear deterministic mathematical model of ND to study the dynamics,
control and the economic loss of the village poultry with village chicken population, wild
birds population of virus in the environment is formulated and analyzed.
The basic reproduction number(R0) which represents the number of secondary cases where one
case would produce in a completely susceptible population is derived using the Next Generation
Matrix technique. The bifurcation analysis of the equilibrium points shows that a model
exhibits the forward bifurcation meaning that the R0 less than a unit is a sufficient condition
to reduce the transmission of ND in village chicken population. The sensitivity analysis of the
parameters in R0 were computed using a normalized forward sensitivity analysis, results show
that the transmission coefficient of the Newcastle disease virus between the hosts and the environment
is found to be the most positive sensitive parameter in the model.
A model is then extended to include three time dependent variables: vaccination, culling and
the environmental hygiene and sanitation control strategies. To determine the best control strategy
to mitigate the ND burden, the optimal control techniques are applied. The existence of
the optimal control problem is proved with the necessary conditions for optimality determined
using the Pontryagin’s Maximum Principle. Numerical simulations were performed using the
forward-backward sweep iterative scheme of Runge-Kutta method of order four.
Finally, a cost-effectiveness analysis is performed using the Incremental Cost-Effective Ratio
(ICER). The results showed that the vaccination control strategy indicates the lowest cost
compared to other control measures. The economic burden of the ND to chicken farmers, is
considered as the total annual expenditure that a chicken farmer can incur to rescue the at risk
chicken population from the ND is also investigated. The economic data of the model were
collected from ten villages of Bagamoyo and Kibaha, Tanzania. Results from this study indicate
that the recurrence of the ND in the village chicken population could lead to a serious
economic loss at family level in this already financially constrained environment where small
and medium farmers operate. The results obtained shows that there was 22:5% loss from their
expected profit post Newcastle outbreaks in 2017. Also the results show that the occurrence of the ND leads to an average range of 482:89 541:30$ economic loss at family in 2017.
Therefore, for the effective control of NDV and its transmission we recommend vaccination to
be paired with regular cleaning of chicken yards.
A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy in Mathematical and Computer Sciences and Engineering of the
Nelson Mandela African Institution of Science and Technology
2019-03-01T00:00:00ZOptimization of dividend payouts and reinsurance policies under a set ruin probability targetKasumo, Christianhttps://dspace.nm-aist.ac.tz/handle/123456789/3082019-07-01T12:55:56Z2019-03-01T00:00:00ZOptimization of dividend payouts and reinsurance policies under a set ruin probability target
Kasumo, Christian
This dissertation is devoted to the mathematical investigation of the topic: Optimization of
Dividend Payouts and Reinsurance Policies under a Set Ruin Probability Target. Its purposes
are, first, to determine the optimal reinsurance and dividend policies for an insurance company
whose surplus is modelled by a diffusion-perturbed classical risk process and, second, to determine
the reinsurance and dividend strategies under a set ruin probability target. The dissertation
concerns itself with three aspects of risk theory: (a) minimization of infinite ruin probability,
which resulted in one published journal paper; (b) maximization of dividend payments, resulting
in a second published paper; and (c) computing optimal dividend barriers based on set
ruin probability targets, whose research paper is still in draft form. All three papers are based
on a diffusion-perturbed classical risk process compounded by quota-share and excess-of-loss
reinsurance. By means of the dynamic programming approach and the application of Itˆo’s
formula, the Hamilton-Jacobi-Bellman (HJB) equations for the optimization problems were
derived. Additionally, the corresponding second-order Volterra integrodifferential equations
(VIDEs) were obtained. These VIDEs were then transformed into Volterra integral equations
(VIEs) of the second kind which were subsequently solved using the fourth-order block-byblock
method based on Simpson’s Rule to determine the optimal value functions. The results
of the problem of minimizing the ruin probability show that the optimal reinsurance policy is
(k ; a ) = (0;1), where k and a are, respectively, the optimal retention levels for quotashare
and excess-of-loss reinsurance. This applies to both the Cram´er-Lundberg (CLM) and
diffusion-perturbed models (DPM). For the dividend maximization problem, results indicate
that for the CLM the optimal reinsurance policy is (k ; a ) = (1;1) for small claims and
(k ; a ) = (1; 10) for large claims. The optimal dividend barrier levels for small and large
claims in the CLM, respectively, are b = 10:27 and b = 9:35. For the DPM, the optimal
reinsurance policy is the same as for the CLM, with optimal dividend barriers b = 12:35 for small claims and b = 11:50 for large claims. This means higher optimal dividend barriers should be used for small claims than for large ones. With regard to ruin probability targets, results show that the optimal dividend barrier increases as the ruin probability reduces.
A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy in Applied Mathematics and Computational Science of the
Nelson Mandela African Institution of Science and Technology
2019-03-01T00:00:00ZA framework for enhancing sustainable access and use of agricultural market information by small-scale farmers in TanzaniaMagesa, Mawazo Mwitahttps://dspace.nm-aist.ac.tz/handle/123456789/3072019-07-01T12:55:56Z2018-08-01T00:00:00ZA framework for enhancing sustainable access and use of agricultural market information by small-scale farmers in Tanzania
Magesa, Mawazo Mwita
Agriculture in African developing countries employs majorities and contributes greatly to both human development and national economies. Despite its significance, the sector is dominated by small scale farmers living in rural areas and practising subsistence farming. Among the challenges confronting farmers include poor access to markets for their farm produce and lack of market information while selling their produce. The challenges have led to low prices of produce which also leads to low investments in agriculture, low productivity due to practising traditional farming methods, poor motivation to others to invest in agriculture, some quitting agriculture for other preferred jobs, and emergence of middlemen in the agricultural supply chain. Adequate market access and market information use can help farmers make important decision (e.g. plan what crops to plant, when to plant, and when and where to sell their farm produce).
With regards to market access and use of market information, farmers in Tanzania are challenged with unreliable and underdeveloped markets, lack of market information, poor or no infrastructure (e.g. rural roads, transporting means, and electricity), illiteracy, poor knowledge on agricultural marketing, and presence of middlemen. Based on the Capability Approach and Concepts, a framework for linking farmers to markets while providing them with market information was developed. The essence is to develop their (farmers) capabilities to become active market actors. Using a case study of farmers accessing agricultural market information from the NINAYO program, information capabilities of small scale farmers was measured.
Methods employed by the study include extensive literature review, data collection through field visits and surveys, interviews and observations, and by using questionnaires. Analyses of data were done using descriptive statistics, and regression analysis. To develop a framework, identified challenges in market access and market information use were mapped into various components of Livelihood Framework and the Empowerment Framework.
Thus, to improve access to markets and enhance use of market information by farmers, different actors (public and private) need to be involved. Different resources (education, financial, cultural, social and informational) of farmers need to be improved. The overall is to ensure farmers gain and benefit from their agricultural activities, their lives and economies improve, rural lives and economies improve and the national economies, at large, improve.
A Dissertation Submitted in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy in Information and Communication Science and Engineering of the Nelson Mandela African Institution of Science and Technology
2018-08-01T00:00:00Z