Evolutionary optimized Padé approximation scheme for analysis of covid-19 model with crowding effect

This work presents a novel evolutionary computation-based Padé approximation (EPA) scheme for constructing a closed-form approximate solution of a nonlinear dynamical model of Covid-19 disease with a crowding effect that is a growing trend in epidemiological modeling. In the proposed framework of the EPA scheme, the crowding effect-driven system is transformed to an equivalent nonlinear global optimization problem by assimilating Padé rational functions. The initial conditions, boundedness, and positivity of the solution are dealt with as problem constraints. Keeping in view the complexity of formulated optimization problem, a hybrid of differential evolution (DE) and a convergent variant of the Nelder-Mead Simplex algorithm is also proposed to obtain a reliable, optimal solution. The comparison of the EPA scheme results reveals that optimization results of all formulated optimization problems for the Covid-19 model with crowding effect are better than those of several modern metaheuristics. EPA-based solutions of the Covid-19 model with crowding effect are in good agreement with those of a well-practiced nonstandard finite difference (NSFD) scheme. The proposed EPA scheme is less sensitive to step lengths and converges to true equilibrium points unconditionally.