Dynamics of SEINRS deterministic epidemic model in spatio-temporal heterogeneous medium with spatially finite domain

This paper generally addresses the study of the spatial outspreading of contagious infectious diseases. A spatial deterministic mathematical model that consists of five coupled nonlinear systems of partial differential equations is introduced. The population is divided into various classes, such as susceptible, exposed, infectious, non-infectious infected, recovered, and described on a plague domain that changes with time. The space and time affect the distribution of velocity, which is unspecified in the model. The moving domain boundary describes the epidemic wavefront. Theoretical analysis has been applied to the SEINRS model and examines the existence of endemic equilibrium. The existence and termination of the disease has been determined by fundamental reproduction number which is achieved by using the next-generation matrix procedure. A numerical simulation is carried out to study the temporal and spatial dynamics of an epidemic model for various scenarios, together with a sensible epidemic setting, which shows that the system achieves endemic equilibrium after some days, with a fundamental reproduction number greater than one. Additionally, a case study on the initial COVID-19 epidemic in Italy has been carried out, allowing us to successfully apply our model to actual data and acquire essential insights into the dynamics, which predict time duration for the virus to disseminate throughout the country, nearly aligning with the actual observed. The model’s fit was confirmed with R 2 = 0.981, indicating 98.1% accuracy in predicting cumulative instances. To simulate different populations and areas, the model is very adaptable. Anticipation is that this model can exceed the spatial prediction of epidemic models.