Mathematical modelling of cholera tbreaks in Dar es Salaam with optimal control
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Date
2017
Authors
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Publisher
University of Dar es Salaam
Abstract
Cholera is a water born disease that affects the small intestine by strain of bacteria known as V. cholera. Since its first outbreak in 1817 in India, cholera epidemics has been a great concern in developing countries. Following 2015 cholera outbreaks in Dar es Salaam, researchers have shown relentless effort in finding the optimal control in the disease transmission. In this research we adopt and analyse Mukandavire et al. (2011) model which was used to study cholera transmission dynamics. Mathematical analysis reveals that the disease free equilibrium point is both asymptotically and globally stable when the reproduction number is less than one. Also, the analysis shows that the endemic equilibrium point is both asymptotically and globally stable when the reproduction number is less than one. Also, the analysis shows that the endemic equilibrium point is asymptotically stable when the reproduction number is greater than one. The model was then extended by including five time dependent controls with the aim of minimizing the total number of infected individuals. Results from numerical simulation of optimal control shows that simultaneous application of vaccination, antibiotic treatments, water treatments, water treatments and provision of clean water can effectively eliminate cholera in Dar es Salaam. With a combination of these controls, the epidemic period was found to take fifteen days with more than fifty percent averted infection cases. Based on the results found we recommend that, health institutions should consider a combination of these controls as a solution to future cholera outbreaks in Dar es Salaam.
Description
Available in print form, East Africana Collection, Dr. Wilbert Chagula Library, (THS EAF RA644.C3.T34M83)
Keywords
Public services, Information services, Decision making, Municipal services, Information technology, Computer networks, Dar es Salaam Regional Secretariat
Citation
Mugendi, M (2017). Mathematical modelling of cholera tbreaks in Dar es Salaam with optimal control. Masters dissertation, university of Dar es Salaam, Dar es Salaam