Dynamic analysis of modified SEIR epidemic model with time delay in geographical networks

The projection of the intensity of the epidemics based on their prolonged history remains wanting or lagging altogether. Numerous modeling techniques are being developed to forecast the future of the disease. Various mathematical models have been developed in the literature which assume the spread of infection by considering interaction among the susceptible and infected classes only. In this paper, we propose a more realistic modified SEIR (susceptible-exposed-infected-recovered) model with a time delay in which the origin of infection by interaction within the susceptible and exposed classes is also analyzed. Moreover, various stochastic characteristics, such as population migration and linkages at local levels, are also taken into account to depict more logical population dynamics. We compute the basic reproductive number and investigate the existence and stability of disease-free equilibrium and endemic equilibrium. The effect of crucial parameters influencing disease dynamics on basic reproductive numbers is also being investigated. It has been seen that the basic reproductive number increases with the increase in time delay, contrary to observations in the past. This highlights the significance of the incorporated modified interactions within susceptible and exposed classes along with their factual parameters on the disease dynamics. (c) 2023 Published by Elsevier B.V.