Epidemic spreading in random walkers with heterogeneous interaction radius

Abstract

We study epidemic spreading in a random walk network where agents with heterogeneous interaction radius randomly walk in a planar space. We obtain the explicit expression of epidemic threshold which indicates that the heterogeneity of interaction radius decreases the threshold. Concretely, the greater the variance of the radius distribution is, the smaller the epidemic threshold will be. Simulation results about the epidemic threshold match well with our theoretical results. In simulation study, the infection density in steady state, which is called the final density, is investigated. When there are two dierent values of radius, a larger mean value of radius increases the final density. However, although an increasing second order origin moment of radius makes the epidemic easier to outbreak, it also lowers the final density of infected individuals.

A Differential Game Approach to Decentralized Virus-Resistant Weight Adaptation Policy Over Complex Networks

“…However, the centralized optimal control method is not practical and lack of incentive. The effect of heterogeneous weight adaptation on virus spreading has been studied by Yun et al in [18], [19]. In [18], the authors have proposed a weight adaptation rule without taking cost into consideration.…”

“…The counterpart of λ j (t), j ∈ N in the individual Hamiltonian defined for the game problem is p i j (t), j ∈ N . Due to the similar structure of the Hamiltonian of the optimal control problem and the individual Hamiltonians for the game problem, after applying maximum principle, we obtain (17)(18)(19) that are in the same structure with (9)(10)(11). An optimal point can in principle be computed centrally by network operator to achieve social optimum.…”

“…Let c i (t) = ∑ j =i f j (x j (t)). Then, the differential game with (22) is a potential differential game corresponding to the optimal control problem defined by (16), and if {u * i (t), i ∈ N } is an open-loop NE solution for new differential game with cost (22), and {x * (t), 0 ≤ t ≤ T } is the corresponding state trajectory, the relations (17) (18) and (19) Proof: See Appendix B-E. Theorem 4 indicates that with a proper choice of the penalties c i (t), i ∈ N , the necessary conditions for the openloop NE solution of the differential game is aligned with the necessary conditions for the optimal solution of the social cost optimal control problem. The counterpart of condition (11) for the penalty-based differential game can be written aṡ…”

“…Let c i (t) = ∑ j∈R i,o \{i} f j (x j ). Then, if {u * i (t), i ∈ N } is an open-loop NE solution for the new differential game, and {x * (t), 0 ≤ t ≤ T } is the corresponding state trajectory, the relations (17), (18), and (19) hold for u * and x * with u o replaced by {u * i (t), i ∈ N } and x o replaced by x * . Proof.…”

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

“…It is worth remarking that most previous mentioned works based on random walk networks [34,35,36,37] have simply assumed that all individuals have the same interaction radius in order to better include other factors such as the velocity and the direction of motion, as well as the population density. However, the interaction radius of individuals in realistic populations or networks are usually heterogeneous [50]. For example, individuals with poor personal hygiene are prone to have a larger radius of contacting infectious sources.…”