![]() ![]() Motivated by the above literature, in the present investigation, the standard epidemic model is modified for the analysis of COVID-19 viral disease with the impact of vaccination in a spatially heterogeneous environment. 10 studied both the numerical and analytic solutions of space-temporal compartmental models, analyzing multiple stages of a disease. 9 implemented a non-standard finite difference splitting scheme with structure-preserving property to investigate the numerical solution of a reaction–diffusion transmission model. 8 presented approximate solutions of two similar epidemic models via meshless and finite difference techniques. 7 utilized operator-splitting-based finite difference and meshless procedures for solving spatio-temporal compartmental models. Following a similar approach, the works of Haider et al. 4, an efficient numerical scheme is derived to demonstrate the graphical dynamics of the whooping cough transmission model. They proposed a non-standard finite difference numerical scheme for the numerical solution of the model due to its ability to preserve positivity. 3 have investigated the transmission dynamics and control of HIV/AIDS using a mathematical spatio-temporal epidemic model. 2 formulated a diffusive transmission model to analyze the dynamics of influenza with spatial and temporal effects. The authors solved the developed model by using a finite-difference scheme. 1 formulated a new compartmental model to investigate the dynamical behavior of influenza with the spatial and temporal effects. For this purpose, many researchers around the globe developed spatio-temporal epidemic models and discussed their approximate solutions via various iterative schemes to explore the dynamical behavior of infectious diseases. Using this information to make some useful control strategies that help in the eradication and control of infection. In this regard, the most important thing is the numerical treatment of such models, since one might be interested in obtaining the projected information based on reported data. Epidemiological models remain an effective tool to understand the geographical spreading pattern and the impact of those factors that are responsible for the spread and control of infection. One of the major factors that rapid the transmission of COVID-19 viral disease is social contact and public gathering. Despite the availability of various vaccines, it is still dangerous to public health. It caused public health burden and create an economic crisis around the globe. The disease initially originated in December 2019 in China and has spread to the rest of the world rapidly. The disease transmission occurs between individuals through respiratory droplets generated when an infected person coughs or sneezes. The simulation results conclude that the random motion of individuals has a significant impact on the disease dynamics and helps in setting a better control strategy for disease eradication.ĬOVID-19 is a viral disease caused by a variant of coronavirus named as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Furthermore, the impact of the aforementioned interventions is investigated with and without diffusion on the incidence of disease. The impact of diffusion as well as some pharmaceutical and non-pharmaceutical control measures, i.e., reducing an effective contact causing infection transmission, vaccination rate and vaccine waning rate on the disease dynamics is presented in a spatially heterogeneous environment. Two different numerical schemes named: finite difference operator-splitting and mesh-free operator-splitting based on multi-quadratic radial basis functions are implemented in the numerical study. Further, the model is solved numerically based on uniform and non-uniform initial conditions. Moreover, a suitable nonlinear Lyapunov functional is constructed for the global asymptotical stability of the spatio-temporal model. Local asymptotical stability of the diffusive COVID-19 model at steady state is carried out using well-known criteria. The existence, uniqueness, positivity, and boundedness of the model solution are investigated. Initially, a detailed qualitative analysis of the spatio-temporal model is presented. In this paper, a new spatio-temporal model is formulated to study the spread of coronavirus infection (COVID-19) in a spatially heterogeneous environment with the impact of vaccination. ![]()
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