Nonequilibrium phase transitions in metapopulation models of infectious diseases on heterogeneous networks

We study two meta-population models of infectious diseases in heterogeneous networks. We distinguish between asymptomatic and symptomatic infections and these two go through the different courses of infection and recovery. We consider that asymptomatic infections are described by an SIS model and symptomatic infections by an SIR or SIRS model depending on the immunity upon recovery. By introducing the probability of being infected asymptomatically, we combine an SIS model for asymptomatic infections with an SIR or SIRS model for symptomatic infections to obtain the SIS-SIR and SIS-SIRS models. We use a heterogeneous mean-field theory and Monte Carlo simulations to analyze two models and find that both models undergo nonequilibrium continuous phase transitions from the endemic phase to the disease-free phase at certain critical thresholds as we vary the proportion of asymptomatic infections. It suggests that it may be possible to maintain the population in the disease-free phase by controlling the proportion of asymptomatic infections. The SIS-SIRS model shows that asymptomatic infection drives symptomatic infection and vice versa. In addition, the spreading of infections eventually ceases as the population decreases even at a fixed proportion of asymptomatic infections corresponding to the endemic phase. The results provide a theoretical basis for understanding the epidemiological facts that social distancing and reducing asymptomatic infections are important factors in optimizing quarantine measures to prevent the epidemic outbreaks of infectious diseases.