Susceptible-Infected-Susceptible type COVID-19 spread with collective effects

Many models developed to forecast and attempt to understand the COVID-19 pandemic are highly complex, and few take collective behavior into account. As the pandemic progressed individual recurrent infection was observed and simpler susceptible-infected type models were introduced. However, these do not include mechanisms to model collective behavior. Here, we introduce an extension of the SIS model that accounts for collective behavior and show that it has four equilibria. Two of the equilibria are the standard SIS model equilibria, a third is always unstable, and a fourth where collective behavior and infection prevalence interact to produce either node-like or oscillatory dynamics. We then parameterized the model using estimates of the transmission and recovery rates for COVID-19 and present phase diagrams for fixed recovery rate and free transmission rate, and both rates fixed. We observe that regions of oscillatory dynamics exist in both cases and that the collective behavior parameter regulates their extent. Finally, we show that the system exhibits hysteresis when the collective behavior parameter varies over time. This model provides a minimal framework for explaining oscillatory phenomena such as recurring waves of infection and hysteresis effects observed in COVID-19, and other SIS-type epidemics, in terms of collective behavior.