Transition from susceptible-infected to susceptible-infected-recovered dynamics in a susceptible-cleric-zombie-recovered active matter model

The susceptible-infected (SI) and susceptible-infected-recovered (SIR) models provide two distinct representations of epidemic evolution, distinguished by whether or not the number of susceptibles always drops to zero at long times. Here we introduce a new active matter epidemic model, the susceptible-cleric-zombie-recovered (SCZR) model, in which spontaneous recovery is absent but zombies can recover with probability gamma via interaction with a cleric. Upon colliding with a zombie, both susceptibles and clerics enter the zombie state with probability beta and alpha, respectively. By changing the initial fraction of clerics or their healing ability rate gamma , we can tune the SCZR model between SI dynamics, in which no susceptibles or clerics remain at long times, and SIR dynamics, in which a finite number of clerics and susceptibles survive at long times. The model is relevant to certain real world diseases such as HIV where spontaneous recovery is impossible but where medical interventions by a limited number of caregivers can reduce or eliminate the spread of infection.

Automated summary

The SI and SIR models represent epidemic evolution, distinguishable by whether susceptibles always drop to zero at long times. The new SCZR model is introduced, where spontaneous recovery is absent but zombies can recover with probability gamma through interaction with a cleric. By changing the initial fraction of clerics or their healing ability rate gamma, the SCZR model can be tuned between SI dynamics and SIR dynamics.