Modeling and analysis of the spread of cholera disease in Nigeria with environmental controls

Cholera, a major public health problem in many developing countries in which Nigeria is not an exception. The control of deadly outbreaks remains a challenge. The main goal of this thesis is to develop and analyze a mathematical model for the control of cholera in Nigeria with vital dynamics, water hygiene, environmental sanitation and treatment as control strategies in curtailing the disease. The effective basic reproduction number RC that is used to control the trans- mission of the disease is obtained. The equilibrium points of the cholera model are determined. The disease-free equilibrium point is locally and globally asymptot- ically stable when the effective reproduction number, RC ≤1 where the disease always dies out. The endemic equilibrium exist for RC > 1. Bifurcation analysis for endemic equilibrium is also carried out using center man- ifold theory. Graphical representation of the evolution of the disease at various settings is shown for different control strategies. The model studied shows that with proper combination of control measures and rigorous effort cholera epidemic could be eradicated from our society. Numerical simulation is carried out using parameter values based on Nigeria demographic data to investigate the effect of control strategies on infected population. Simulation of the model is carried out in two categories where first we simulate the model to know the effects of each parameter at low, moderate and high level on the infected population and the results shows that treatment play a vital role in controlling the cholera infection. While in second category, we simulate the model with no control, low without treatment and low universal, moderate without treat- ment and moderate universal and lastly high without treatment and high universal. Our results show that universal strategies is an effective method for controlling cholera. In fact, model studied shows clearly that improvement in treatment, wa- ter hygiene and the environmental sanitation offered to about fifty percent is all that is required to eradicate the diseases.

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