Modeling and optimal control analysis of COVID-19: Case studies from Italy and Spain

Coronavirus disease 2019 (COVID-19) is a viral disease which is declared asa pandemic by WHO. This disease is posing a global threat, and almost everycountry in the world is now affected by this disease. Currently, there is no vaccine for this disease, and because of this, containing COVID-19 is not an easytask. It is noticed that elderly people got severely affected by this disease spe-cially in Europe. In the present paper, we propose and analyze a mathematicalmodel for COVID-19 virus transmission by dividing whole population in oldand young groups. We find disease-free equilibrium and the basic reproductionnumber (R0). We estimate the parameter corresponding to rate of transmissionand rate of detection of COVID-19 using real data from Italy and Spain by leastsquare method. We also perform sensitivity analysis to identify the key parameters which influence the basic reproduction number and hence regulate thetransmission dynamics of COVID-19. Finally, we extend our proposed model tooptimal control problem to explore the best cost-effective and time-dependentcontrol strategies that can reduce the number of infectives in a specified intervalof time.