Abstract:
In this thesis a deterministic mathematical model for COVID-19 with double dose vac cination is developed and analyzed by using Modified 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
first 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 first order ordinary differen tial equations. The numerical results obtained by using MADM, show a good agreement
with the numerical method of ODE45 for few terms. The effect 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.
