Epidemic spreading with immunization and mutations

TL;DR

This paper models epidemic spreading considering immunization and mutations, revealing how mutations can weaken immunization effects and cause a crossover from GEP to DP universality classes.

Contribution

It introduces a new stochastic model for epidemics with mutations, analyzing phase transitions and the impact of mutations on immunization effectiveness.

Findings

Mutations cause a crossover from GEP to DP universality class.

Immunization protection is significantly reduced by mutations.

The phase transition line near GEP follows predicted scaling behavior.

Abstract

The spreading of infectious diseases with and without immunization of individuals can be modeled by stochastic processes that exhibit a transition between an active phase of epidemic spreading and an absorbing phase, where the disease dies out. In nature, however, the transmitted pathogen may also mutate, weakening the effect of immunization. In order to study the influence of mutations, we introduce a model that mimics epidemic spreading with immunization and mutations. The model exhibits a line of continuous phase transitions and includes the general epidemic process (GEP) and directed percolation (DP) as special cases. Restricting to perfect immunization in two spatial dimensions we analyze the phase diagram and study the scaling behavior along the phase transition line as well as in the vicinity of the GEP point. We show that mutations lead generically to a crossover from the GEP to DP. Using standard scaling arguments we also predict the form of the phase transition line close to the GEP point. It turns out that the protection gained by immunization is vitally decreased by the occurrence of mutations.