A Mathematical model for the dynamics of dengue virus disease transmission in Mandera County-Kenya

Abstract

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.