A computational modeling and simulation of spatial dynamics in biological systems

• Numerical simulation of a deterministic SIR model with transport and diffusion dynamics is presented.
• A controlled meshless procedure is implemented to understand finite time behavior of the reaction–convection–diffusion model.
• The simulations results are related to real life applications.
• Validation of the simulation results of the model is performed.

Most of the biological processes occurring in nature exhibit physical movements at macro and micro levels. These movements are convection–diffusion type and are studied due to the important role they play in the mathematical modeling and simulation of dynamical systems. Accurate simulation of complicated dynamical system models are quite challenging. The focus of the current work is to design an effective meshless procedure for the simulation of reaction–convection–diffusion type of epidemiological models. The simulation results of the proposed method show much realistic finite time blow-up, which occurs due to calamitous spatial movements of the susceptible class of the population. Numerical simulations obtained through the proposed method are carefully vetted and found consistent with the earlier results. In some cases, improvement in the earlier results is reported as well.