MATHEMATICAL MODELLING OF EPIDEMIC SPREAD UNDER DYNAMIC SOCIAL NETWORKS

Abstract

The transmission of infectious diseases is a complicated process that should also be dependent not only on biology but also on social behaviour and ways of interaction between people. Classical epidemic theories, e.g., Susceptible Infected Recovered (SIR) and Susceptible Exposed Infected Recovered (SEIR) models normally assume homogeneous populations that are static with respect to mixing. The social interactions in the real world, however, are dynamic, heterogeneous and change with time as mobility, social behaviour, policy interventions as well as the individual awareness changes. This weakness has inspired the application of the dynamic social network theory to mathematical epidemiological modelling. Dynamic social networks also record time-varying contacts between individuals, which can be used to better model disease transmission pathways. This paper aims at creating and examining mathematical models which consider dynamic social networks in order to better comprehend the epidemic spread. The study focuses on the effects of network structure, temporal dynamics of connectivity and adaptive behaviour on infection peaks, the rate of transmission and the duration of outbreaks. Dynamical modelling of epidemics in changing social networks is modelled using mathematical techniques like differential equations, graph theory, stochastic processes and agent-based simulations. The findings indicate that dynamic networks change epidemic thresholds and disease outcomes substantially relative to its counterparts in the form of static models. The results illustrate a need to include the time-dependent social interactions in the prediction of epidemic and decision-making in the field of public health. The research will enhance the effectiveness of epidemics modelling because it will provide the understanding of how the dynamics of social behaviour determine the spread and control considerations of the disease.