An epidemic spread model with nonlinear recovery rates on meta-population networks

During the COVID-19 pandemic, many countries face healthcare system collapses, then leading governments to recognize the importance of rational allocation of limited medical resources. Therefore, we construct an epidemic propagation model on a meta-population network using the microscopic Markov chain method. Unlike other works, our model accounts for nonlinear recovery rates due to healthcare system collapse and resource limitations. Combining Monte Carlo simulation, we analyze the impact of medical resources on the phase transition, steady state infected density and propagation threshold of disease spread. An interesting finding is that when medical resources are severely limited, allocating resources to smaller cities can most effectively contain the epidemic. Furthermore, it is found that introducing a healthcare system collapse mechanism results in two propagation thresholds, rendering the outbreak of epidemics to be dependent on the initial proportion of infected individuals. Finally, we validate our results on the constructed real population network.