Optimal resource allocation for rapid convergence to stable healthy state in epidemic spreading models

The networked Susceptible-Infected-Susceptible (SIS) model has been widely investigated as a model for the spread of epidemics within networked systems. In networks with SIS dynamics and unstable healthy states, a critical question is how to distribute compensatory curing resources (with constrained total cost) among individuals, ensuring that the network converges to a healthy state as fast as possible. This paper introduces a novel approach to this problem by developing an algorithm for the optimal allocation of compensatory curing resources required by agents in a given network. This solution approach has been made possible by reformulating the original convergence rate optimization problem and an additional constraint guaranteeing a minimum convergence rate as a standard semidefinite programming problem. The applicability of the proposed algorithm to arbitrary undirected topologies and other variations of the SIS model, including the one with a weighted cost function, has been demonstrated. In the case of symmetry preserving curing and infection rates, it has been shown that the problem over a given network with a symmetric topology can be reduced to a smaller network with each orbit acting as a node. Additionally, for networks with one or two orbits, the problem has been addressed analytically, and several examples have been included. Based on two different scenarios inspired by the SARS outbreak in Hong Kong and the COVID-19 outbreak in the USA, it is shown that the algorithm's optimal results outperform the uniform distribution of additional curing resources. The paper also explores how optimal performance metrics change with the given upper limit on the total amount of additional curing resources.