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|Title: ||A Mathematical Model for the Spread of Malaria Case Study: Chorkor-Accra|
|Authors: ||Avordeh, Timothy King|
|Issue Date: ||5-Oct-2011|
|Abstract: ||Malaria is an infectious disease transmitted between humans through mosquito bites that kill about two million people a year. Many infectious diseases including malaria are preventable, yet they remain endemic in many communities like Chorkor in Accra due to lack of proper, adequate and timely control policies. The main goal of this thesis is to develop a mathematical model for the transmission of malaria. It has been shown that the model has unique disease-free and endemic equilibria.
A mathematical model for malaria is developed using ordinary differential equations. We analyze the existence and stability of disease-free and endemic malaria (malaria persisting in the population) equilibria. Key to our analysis is the definition of a reproductive number R_0(the number of the new infections caused by one individual in an otherwise fully susceptible population, through the duration of the infectious period. The methods for controlling any infectious disease include a rapid reduction in both the infected and susceptible populations as well as a rapid reduction in the susceptible class if a cure is available. For diseases of malaria where there are no vaccines, it is still possible to reduce the susceptible group through a variety of control measures. The disease-free equilibrium is locally asymptotically stable, if R_0≤1, and that the endemic equilibrium exist provided R_0>1.
Further simulation of the model clearly shows that, with proper combination of treatment and concerted effort aimed at prevention, malaria could be eliminated from our society. In fact, effective treatment offered to about fifty percent of the infected population together with about fifty percent prevention rate is all that is required to eliminate the diseases|
|Description: ||A Thesis Submitted to the Department of Mathematics, Kwame
Nkrumah University of Science and Technology, Kumasi, in partial
fulfillment of the requirement for the degree of
Master of Science in Industrial Mathematics,
Institute of Distance Learning, 2011|
|Appears in Collections:||Distance Learning|
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