MODIFIED ADOMIAN DECOMPOSITION METHOD FOR ANALYZING THE DYNAMICS OF COVID-19 WITH DOUBLE DOSE VACCINATION

Abstract

In this thesis a deterministic mathematical model for COVID-19 with double dose vac- cination is developed and analyzed by using Modi ed Adomian Decomposition Method (MADM). To conduct the objective, secondary recent data collected from Ministry of Health Ethiopia website and related literatures. The required data for the study were performed by using a MATLAB software program and the results are presented in the form of graphs. The total population in this model is sub-divided in to six compartments, namely Susceptible S(t), First dose Vaccinated V1(t), Second dose Vaccinated V2(t), In- fected I(t), Treated T(t) and Recovered R(t). The qualitative behavior, like positivity, invariant region, the existence of equilibrium point, stability and sensitivity analysis of the model were analyzed. The model reproduction number was derived, and the stabil- ity of the equilibrium point was analyzed. The results of the analysis show that, the basic reproduction number is less than one, this indicate that disease free equilibrium point is stable. I have conducted numerical experiments to analyze the collected data and obtained interesting simulation results. Which indicated decreasing susceptible and rst dose vaccinated population contact rate and increasing double dose vaccination and treatment rate have plays an important role to control and minimize the transmission rate of COVID-19 pandemic in the community. In this work, MADM was introduced for solving the mathematical model of COVID-19 system of rst order ordinary di eren- tial equations. The numerical results obtained by using MADM, show a good agreement with the numerical method of ODE45 for few terms. The e ect of Adomian polynomial terms was considered and show that, the accuracy of result increases with increasing Adomian polynomial terms. Comparing the numerical result of MADM with ODE45 method, MADM have been alternative methods for solving the mathematical model of epidemics and many functional equations as algebraic equation, ordinary and partial dierential equation, integral equation without linearization, perturbation and discretiza- tion. Therefore, MADM is reliable, powerful and promising.