Stability Analysis of COVID-19 Model with Quarantine

In this paper, A 6 (six) compartmental (S, IU, IS, IA, Q, R) model was presented to examine the dynamical behavior of disease transmission in the system with quarantine effect on the symptomatic infected, asymptomatic infected and Reproduction number R0 within a given population. The parameters model was analyzed and estimated experimentally using the real data of COVID-19 confirmed cases for Ethiopia via MATLAB 2021a. Reproduction number R0 which is a key indicator to whether a disease outbreak spread force will persist or die out within population. R0 was found using the next generation matrix with Gaussian elimination method to obtain the inverse of the transitive matrix. The model also aims at reducing R0 owning to the fact that when the basic reproduction number is less than 1 infected person, disease dies out and when the reproduction number is greater than 1 infected person, the disease persists. The facts about R0 geared us to mathematically check for the Routh-Hurwitz stability criteria and Lyapunov Functions to concisely establish the necessary and sufficient conditions for the Local and Global stability of model. results show that, when R0 - 1 and R0 > 1 the diseases free equilibrium and endemic equilibrium points are locally and globally asymptotically stable respectively. In order to interpret results and recommend possible control measure of disease, The dynamics of the Quarantine compartment in model was tested via sensitivity analysis to experimentally investigate transition/ transmission pattern. The effect of quarantine analysis on the model shows that preventive measures such as increase in quarantine with treatments during disease outbreak will significantly decrease the Reproduction number. Hence, increase in Quarantine compartment will flatten the curve of (S, IU, IS, IA, Q, R) dynamic model correspondingly.