An integro–ODE–PDE model for Covid-19 pandemic with vaccination and loss of immunity: well-posedness, RBF-FD numerical scheme and simulation

During an epidemic, the way individuals spread the infection can vary depending on the number of days they have been infected. Vaccination is a key factor in the control of the transmission of the pathogen. We propose an SIR-like model to simulate the propagation of a virus in a closed population. The model presents a continuous structure in age of infectivity and in age of immunity. By using a fixed point theorem, we then prove the well-posedness of the model and properties of its solution. Then we present the radial basis function-generated finite difference method, which we use to numerically solve our problem. Finally, numerical simulations are explored to witness the impact of the parameter values in the model.