HOMOTOPY PERTURBATION TRANSFORM METHOD FOR ANALYZING THE DYNAMICS OF DENGUE DISEASE

Abstract

In this thesis, a new deterministic model for the Dengue disease is developed and analyzed with the homotopy perturbation transform method. The model comprises six compartments namely human population susceptible class S(t), exposed class E(t), infected class I(t), recovered class R(t) and vector population namely virus-free vectors U(t) and virus-carrying vectors V(t). The qualitative behavior of this model is analyzed by a deterministic approach, invariant region, the existence of equilibrium points(disease-free and endemic equilibrium), the basic reproduction number, sensitivity analysis , and their local stability were checked. The results of the analysis showed that the basic reproduction number is less than one, then the disease free equilibrium point is stable. Some values of the parameters were estimated from data collected from Dire Dawa Dil Chora Hospital, some from related published articles, and others were assumed. Moreover, the homotopy perturbation transform method is used to solve the system of initial value problems of the developed model by using the Laplace transform, inverse Laplace, the homotopy perturbation method, and a nonlinear coupled equation decomposed by He's polynomial method. The homotopy perturbation transform method (HPTM), which competes with ODE45, enables us to obtain an approximate of the solution in a small number of iterations. This increases the number of iterations, increases convergence, and complements the solution of ODE45. The Homotopy perturbation transform method is one of alternative method to solve the system of linear and nonlinear di erential equations. Furthermore, numerical simulation was done using parameter values to taste the impact of basic parameters and the results of the simulation were displayed graphically using the MATLAB computer software program. Numerical results showed that decreasing the contact rate and exposed rate between humans and vectors helps to reduce the spread of dengue disease.