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

摘要

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 R-0, which is strongly related to the interaction radius distribution and is proportional to the second order moment of interaction radius r(2) in the special case of a constant vaccination rate. We argue that if R-0 1 then the disease-free equilibrium is locally asymptotically stable, whereas if R-0 1 then there is a unique endemic equilibrium which is locally asymptotically stable and uniformly persistent. In addition, we provide a sufficient condition for the global stability of the disease-free equilibrium. Both theoretical and simulation results reveal that the distribution of individual interaction radius has significant effects on the basic reproduction number and the final epidemic prevalence. In general, the disease will break out more readily in the population with a more heterogeneous radius distribution, while it will end 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. (C) 2019 Elsevier B.V. All rights reserved.