ABSTRACT
A Caputo fractional order mathematical model is proposed and analysed to study the dynamics of pneumonia–COVID-19 co-infection. The existence and uniqueness of solution of the model is established. Basic reproduction number is calculated for pneumonia and COVID-19 infection. The model possesses four equilibrium points, namely, disease free, pneumonia-free, COVID-19-free and endemic point where both the disease co-exists. Local stability conditions are established for disease-free, pneumonia-free and COVID-19-free equilibrium point. Also forward bifurcation is plotted where disease-free losses its stability and stable endemic equilibrium exists as R 0 > 1. In simulation, solution for each class is plotted and convergence is shown. The role of fractional order derivative is studied for different values α = 0.85,0.9,0.95 and 1; moreover, the importance of memory is analysed. It is concluded that with the increase in memory the prevalence of pneumonia– COVID-19 co-infective are decreased. An increment in recovered population is also observed when memory effect is introduced by considering fractional order model.
