An SPR stochastic ordinary differential equation model for the spread of dengue fever

Abstract

In this thesis entitled AN SPR STOCHASTIC ORDINARY DIFFERENTIAL EQUATION MODEL FOR THE SPREAD OF DENGUE FEVER a set of differential equations was defined for the spread of dengue fever The set consists of two major parts one considering human and the other one considering mosquito Here 17 parameters and 7 states were considered The set of equations was converted to fractional quantities to eliminate the calculation difficulties The reproductive number was defined which was an important quantity for determining the spread of a disease This can be defined as the number of infections that would result from one infectious individual Either human or mosquito over the infectious period given that all the other individuals are susceptible The model was further extended to many arbitrary regions The existence of the model was discussed There existed a domain where the model was mathematically and epidemiologically well posed Existence of the disease free and endemic equilibrium points was also discussed The Jacobian is a 7 × 7 matrix of partial derivatives which was created by differentiating every equation with respect to every variable The Jacobian was evaluated at the equilibrium points and the Eigen values were found If all Eigen values were less than zero then it implied that the system was stable and if even one Eigen value was greater than zero then it the implied the system was unstable From this the asymptotic stability could be derived Bifurcation analysis is the mathematical study of changes in the solutions when changing the parameters of the equations These qualitative changes in the dynamics of the system are called bifurcations By analyzing the existence and behavior of the model in such points one can derive much about the systems properties and the same was performed for the above said model The model was analyzed by evaluating the sensitivity indices of the reproductive number and the endemic equilibrium The most important parameter for initial disease transmission is the mosquito biting rate Our analysis also shows that intervention strategies that affect the human recovery rate would be the most effective in reducing equilibrium disease The mosquito birth rate has a substantial effect on initial disease transmission The control strategies and suggestions for improvement of the above said model were also discussed