Allocating Resources Between Asymptomatically and Symptomatically Infected Individuals on Networks

Abstract

In the process of controlling infectious diseases, the investment of medical resources is essential. To address the allocation of medical resources between asymptomatically and symptomatically infected individuals, we propose a network-based SAIRS quench mean-field model. The stability of the disease-free equilibrium is proved and the condition for the existence and uniqueness of the endemic equilibrium is given with the help of Gerschgorin theorem. Numerical simulation results reveal that the fraction of the final infected population at steady state is an increasing function of the transmission rate and a decreasing function of the amount of medical resources. We also find the existence of threshold for the amount of medical resources, such that the disease can be well controlled if it is beyond the threshold. Moreover, the threshold will become larger as the transmission rate increases. Besides, the optimal resources allocation strategy is studied. When medical resources are less, allocating all to symptomatic infected individuals will minimize the fraction of the final infected population at steady state. However, with the amount of medical resources increases, a near-average distribution between asymptomatically and symptomatically infected individuals will result in the smallest fraction of the final infected population. Our results could have practical implications for the allocation of medical resources.

Keywords

• Quench mean-field model
• dynamics
• resources allocation strategy