A mathematical model for the transmission dynamics of malaria in eastern Uganda: a case study of Butaleja district
Loading...
Date
2016-05
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Kampala International University, College of Economics & Management
Abstract
A deterministic mathematical model for studying the transmission dynamics of malaria in Butaleja district was developed using ordinary differential equations (ODEs) where humans and mosquitoes interact and infect each other. The model has live non - linear differential equations with two state variables for mosquitoes (S and I,m ) and three state variables for humans (S~ I~ and A,~) The available literature on
previous work in this area was reviewed.Susceptible humans (S, ) are infected when they are bitten by in
infectious mosquitoes (Im ). They then progress through infectious and asymptomatic classes before re-entering susceptible class. Susceptible mosquitoes (Sm) become infected when they bite Infectious (1,) and
Asymptomatic (A,,) humans. They move to infectious class but (10 not recover due to their short life span.
Following ideas advanced by Ross. [Chapter 2] (ii]. the model can be applicable to other infectious diseases of humans such as yellow fever. typhoid. sleeping sickness, cholera etc: using specific model parameters.
Model Analysis was clone, equilibrium points analyzed to establish their local and global stability. The important threshold in this re search called the basic reproduction number (R0) was obtained using the method of next—generation matrix to determine whether the (us— ease dies out or persists. The rule of thumb is that: the disease— free equilibrium is locally asymptotically stable if R0 < I and the endemic equilibrium exist provided that R0 > 1. Using parameter values, R0 for Butaleja district was found to be = 0.00000315 < i; an indication that malaria will be rolled out of the district after a certain period of time. Numerical simulations show that there is a strong positive relation ship between the number (proportion) of infected mosquitoes and infected humans in the same locality. Reducing the current rate of female anopheles mosquito bites could assist Butaleja district to achieve malaria free status by the year 2030 [26], [25]. Therefore. I recommend
control methods such as ITNs and IRS the t increase mosquito death rate and reduce mosquito birth rate/mosquito bites, as well as treating asymptomatic hosts using ACTs. and IPT. Hence. the formulated model. provides a framework for studying and designing effective intervention strategies for prevention and control of malaria in the district.
Description
A thesis presented to the college of higher degrees and research Kampala International University Kampala, Uganda in partial fulfillment of the requirements for the degree of Master of Science in applied mathematics.
Keywords
Malaria transmission, Mathematical model, Butaleja district