Spatiotemporal dynamics of periodic waves in SIR model with driving factors

The world faces Covid-19 waves, and the overall pattern of confirmed cases shows periodic oscillations. In this paper, we investigate the spatiotemporal spread of Covid-19 in the network-organized SIR model with an extrinsic incubation period of the driving factors. Firstly, Our analysis shows the occurrences of Hopf bifurcation and periodic outbreaks consistent with the actual spread of Covid-19. And we investigate periodic waves on spatial scales using Turing instability, and the spread of infected individuals increases the localized hot spots. We study the effect of the incubation period, and more incubation periods generate Turing instability resulting in periodic outbreaks. There is an occurrence of bursting states at peaks of periodic waves due to small diffusion of infected and susceptible, which means stable and unstable areas try to convert each other due to high competition among nodes. Also, We note the disappearance of these bursts when infected and susceptible individuals' movements are easier; thus, the dominance of infected individuals prevails everywhere. Effective policy interventions and seasonality can cause periodic perturbations in the model, and therefore we study the impact of these perturbations on the spread of Covid-19. Periodic perturbations on the driving factors, infected individuals show co-existing spatial patterns. Chaotic outbreak becomes periodic outbreaks through alternating periodic or period-2 outbreaks as we regulate the amplitude and frequency of infected individuals. In short, regulations can erase period-2 and chaotic spread through policy interventions.