# An SIS epidemic model with vaccination in a dynamical contact network of mobile individuals with heterogeneous spatial constraints

## TL;DR

This paper models an SIS epidemic with vaccination in a dynamic network of moving individuals with heterogeneous interaction ranges, revealing how radius distribution affects disease spread and control strategies.

## Contribution

It introduces a novel epidemic model incorporating heterogeneous interaction radii and mobility, deriving the basic reproduction number and analyzing vaccination effects in dynamic networks.

## Key findings

- Heterogeneous radius distribution increases outbreak likelihood.
- More heterogeneity leads to lower epidemic prevalence.
- Optimal vaccination strategies are effective regardless of radius distribution.

## Abstract

Network-based epidemic models have been extensively employed to understand the spread of infectious diseases, but have generally overlooked the fact that most realistic networks are dynamical rather than static. In this paper, we study a susceptible-infected-susceptible epidemic model with vaccination in a dynamical contact network of moving individuals, where we regard mobile individuals as random walkers that are allowed to perform long-range jumps. Different from previous studies of epidemics in a random walk network with a constant interaction radius, we consider the scenario where the individuals have a heterogeneous distribution of interaction radius $r$ and infected individuals are vaccinated with a probability depending on the interaction radius distribution. We derive the basic reproduction number $\mathcal{R}_0$ and explore the stability of disease-free and endemic equilibria of the model. Both theoretical and simulation results reveal that the distribution of individual interaction radius has significant effects on the basic reproduction number and the epidemic prevalence. In general, the disease will break out more readily in the population with a more heterogeneous radius distribution; however resulting in a lower epidemic prevalence. Interestingly, the results suggest that an optimal vaccination intervention for disease prevention and control is achievable regardless of the radius distribution. Furthermore, some interesting results on the structure of the underlying contact network are shown to have strong correlation with the epidemic dynamics. This study provides potential implications for developing efficient containment measures against infectious disease while considering the spatial constraints of moving individuals.