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Network-based epidemic models have been extensively employed to understandthe spread of infectious diseases, but have generally overlooked the fact thatmost realistic networks are dynamical rather than static. In this paper, westudy a susceptible-infected-susceptible epidemic model with vaccination in adynamical contact network of moving individuals, where we regard mobileindividuals as random walkers that are allowed to perform long-range jumps.Different from previous studies of epidemics in a random walk network with aconstant interaction radius, we consider the scenario where the individualshave a heterogeneous distribution of interaction radius $r$ and infectedindividuals are vaccinated with a probability depending on the interactionradius 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 ofindividual interaction radius has significant effects on the basic reproductionnumber and the epidemic prevalence. In general, the disease will break out morereadily in the population with a more heterogeneous radius distribution;however resulting in a lower epidemic prevalence. Interestingly, the resultssuggest that an optimal vaccination intervention for disease prevention andcontrol is achievable regardless of the radius distribution. Furthermore, someinteresting results on the structure of the underlying contact network areshown to have strong correlation with the epidemic dynamics. This studyprovides potential implications for developing efficient containment measuresagainst infectious disease while considering the spatial constraints of movingindividuals.

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