MODELLING COVID-19 DYNAMICS (SPREAD AND CONTROL) AND THE EFFECTS OF A PREVENTIVE VACCINE

Abstract

Corona virus 2019 (COVID-19) have been pandemic both in Africa and the whole world. This work formulated and analyzed mathematical model of COVID-19 that monitors the temporal dynamics of the disease in the presence of preventive vaccine. The most effective ways of controlling the transmission of infectious disease is through vaccination and treatment. Due to transmission characteristics of COVID-19 , the population was divided into six classes. That is; susceptible(S), vaccinated (V), infective (I), hospitalized (H), home based care (𝐻𝐵) and recovery(R). In this thesis, non-linear system of differential equations governing the model was formulated to compute and were solved using quantitative analysis. Feasibility region and positivity of model variable was worked out in which the model is bounded so as to obtain the feasibility solution of the set and positivity of variables. The disease free equilibrium, local and global stability of the disease free equilibrium are discussed. The endemic equilibrium , local and global endemic equilibrium are determined. The model monitor reproduction number 𝑅𝑂 using next generation matrix method which describe the dynamics of the COVID-19.The disease free equilibrium is local asymptotically stable when basic reproduction number 𝑅𝑜<1 and unstable when basic reproduction number 𝑅𝑜>1. The numeric results obtained are determined graphically by use of MAPLE simulation method. The solution has been computed using numerical classical fourth order Runge Kutta integration method to gauge its effectiveness . The results indicated that; high vaccination coverage of 𝜑 =0.9 leads to high number of individuals recovering and low vaccination coverage of 𝜑=0.1 leads to high reproduction number hence the disease may not be eradicated .