Optimal Allocation of Resources for Suppressing Epidemic Spreading on Networks

Abstract

Efficient allocation of limited medical resources is crucial for controlling epidemic spreading on networks. Based on the susceptible-infected-susceptible model, we solve an optimization problem as how best to allocate the limited resources so as to minimize the prevalence, providing that the curing rate of each node is positively correlated to its medical resource. By quenched mean-field theory and heterogeneous mean-field (HMF) theory, we prove that epidemic outbreak will be suppressed to the greatest extent if the curing rate of each node is directly proportional to its degree, under which the effective infection rate $\lambda$ has a maximal threshold ${\lambda }_c^{opt}=1/⟨k⟩$ where $⟨k⟩$ is average degree of the underlying network. For weak infection region ($\lambda \gtrsim {\lambda }_c^{opt}$), we combine a perturbation theory with Lagrange multiplier method (LMM) to derive the analytical expression of optimal allocation of the curing rates and the corresponding minimized prevalence. For general infection region ($\lambda >{\lambda }_c^{opt}$), the high-dimensional optimization problem is converted into numerically solving low-dimensional nonlinear equations by the HMF theory and LMM. Counterintuitively, in the strong infection region the low-degree nodes should be allocated more medical resources than the high-degree nodes to minimize the prevalence. Finally, we use simulated annealing to validate the theoretical results.

7 pages for two columns, 2 figures

References in corpus (7)

• Statistical physics of social dynamics
• Efficient Immunization Strategies for Computer Networks and Populations
• Efficient local strategies for vaccination and network attack
• Immunization and targeted destruction of networks using explosive percolation
• Solving the Dynamic Correlation Problem of the Susceptible-Infected-Susceptible Model on Networks
• Immunization of Real Complex Communication Networks
• An efficient strategy to suppress epidemic explosion in heterogeneous metapopulation networks

Cited by in corpus (5)

• Coevolution spreading in complex networks
• The Epidemic-Driven Collapse in a System with Limited Economic Resource
• Modeling and Controlling the Spread of Epidemic with Various Social and Economic Scenarios
• Weights Adaptation Optimization of Heterogeneous Epidemic Spreading Networks: A Constrained Cooperative Coevolution Strategy
• The effect of role-based resource allocation on epidemic dynamics