Accounting for super-spreader events and algebraic decay in SIR models

ABSTRACT

A central feature of pandemics is the emergence and decay of localized infection waves. While traditional SIR models for infectious diseases can reproduce such waves, they fail to capture two key features. First, SIR models are unable to represent short-duration super-spreader events which often trigger infection waves in a community. Second, SIR models predict exponential decay to an asymptotic state after the infection wave peaks. In contrast, observations suggest a slower algebraic decay. In this paper, we develop models for the basic reproduction number R0 to capture these features. To generate quantitative estimates for R0 during super-spreader events, we reconcile the SIR framework with the Wells-Riley model for airborne disease transmission. We also show that algebraic decay emerges naturally if models are modified to account for the behavioral tendency towards relaxing precautions as the infected fraction decreases. This approach merges for the first time behavioral with physicochemical aspects.(c) 2022 Elsevier B.V. All rights reserved.