A Mathematical model for the dynamics of dengue virus disease transmission in Mandera County-Kenya
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Date
2021Author
Abdiaziz, Abdirashid
Type
ThesisLanguage
enMetadata
Show full item recordAbstract
The aim of this project is to formulate a mathematical model for the dynamics of dengue
virus disease transmission a case study of Mandera County Kenya.The compartmental
model with 5-sate variables was developed to show the relationships that exist between
the state variables.
The disease free equilibrium point was shown to be locally asymptotically stable when
the basic reproduction number is less than unity and unstable if its greater than unity, in
addition the global stability of the disease free equilibrium was determined by using the
Lyapunov function and it was discovered that the disease free was globally asymptotically
stable if the basic reproduction number is less or equal to unity.
The sensitivity index shows that the most sensitive parameters that a ect the basic reproduction
number are Nh and mv which has same degree of impact on R0. Matlab version
R2018a was used in performing the numerical simulations. We found out that the rate of
susceptible human decreases from the rate of 1 and attain equilibrium at the rate of 0.4
while the rate of infected human increased from 0 and attain the equilibrium at the rate
of 0.4.
The recovered human increased from 0 and attain equilibrium at the rate of 0.2. The
susceptible Mosquito decline from the rate 1 and attain equilibrium after attaining the
rate of 0.615 and nally the infected Mosquito increased from the rate of 0 and attain the
equilibrium upon reaching the rate of 0.36.
Publisher
University of Nairobi
Subject
A Mathematical model for the dynamics of dengue virus disease transmission in Mandera County-KenyaRights
Attribution-NonCommercial-NoDerivs 3.0 United StatesUsage Rights
http://creativecommons.org/licenses/by-nc-nd/3.0/us/Collections
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