MODELING AND ANALYSIS OF COVID-19 DYNAMICS WITH INTERVENTION

Abstract

The coronavirus disease 2019 (COVID-19) is caused by the severe acute respira- tory syndrome coronavirus-2 (SARS-CoV-2). The virus is primarily transmitted to humans through inhaling respiratory droplets produced by sneezing, coughing, and conversing closely with an infectious person (direct transmission) or indirectly through contact with contaminated surfaces (indirect transmission). To Prevent and control the fast spreading of COVID-19, health providers and governments around the world have used containment measures such as lockdown, travel bans, cessation of movement, social distancing, proper hygiene, and hand sanitization, among others. Despite these safeguards, the virus continues to spread, although at a slower rate. The disease is linked to a range of infectious periods and hu- man movement (di usion). Vaccination has proved to be e ective in minimising the severity of the disease. Most of the COVID-19 dynamics models so far done have employed a constant coe cient of transmission, whereas infectiousness of an individual varies with time. Thus, an SEIR model is developed to assess the e ect of the varying transmission coe cient in the dynamics of COVID-19. The model solutions were checked for well-posedness to ensure that they are both positive and bounded. The next generation matrix approach is applied to determine the e ective reproduction number, R!. The bifurcation analysis showed that when the trans- mission coe cient > then R! > 1 and the disease would spread, otherwise the disease will die out. The numerical simulation showed that reducing the trans- mission coe cient would curtail the spread of infection. The existing COVID-19 di usive models do not establish the minimum travelling wave speed that connects the Disease Free Equilibrium (DFE) and the Endemic Equilibrium (EE) enabling infection. Thus, a di usive COVID-19 model is developed and analyzed to assess the e ect of human movement. Existence of travelling wave solutions of the model are shown. Exact solutions to the traveling wave are computed using the Tangent hyperbolic method (Tanh Method). Faced with the inadequate supply of COVID- 19 vaccines especially in developing world, it is imperative to determine the critical mass to be vaccinated so as to attain herd immunity. Thus, a COVID-19 model in- corporating vaccination is developed and analyzed. Sensitivity analysis done with respect to key parameters of the vaccine reproduction number, RV , indicates that control strategies should target increasing the rate of vaccination with high e cacy vaccines. The study results suggest that a high rate of vaccination ( ) and high e cacy vaccine (#) are critical in achieving herd immunity also known as 'popula- tion immunity' and control disease spread within the population. Optimal control analysis shows that an optimal infection control is achieved by increasing the rate of vaccination and reducing infection by administering a high e cacy vaccine, thus reducing the probability of transmission. Numerical simulations show that when vaccination rates and vaccine e cacy are high, the number of infections fall sharply. The ndings of this study highlight the signi cance of interventions and in partic- ular the speci c targets for health care providers in mitigating the transmission of COVID-19.