Intervention Serology and Interaction Substitution: Modeling the Role of 'Shield Immunity' in Reducing COVID-19 Epidemic Spread

Joshua S Weitz; Stephen J Beckett; Ashley R Coenen; David Demory; Marian Dominguez-Mirazo; Jonathan Dushoff; Chung-Yin Leung; Guanlin Li; Andreea Magalie; Sang Woo Park; Rogelio Rodriguez-Gonzalez; Shashwat Shivam; Conan Zhao

such that when α = 0 we recover the conventional SIR model. Note that the denominator of 1 + αR can be thought of as S + I + R + αR. Given that S + I + R = 1, this is equivalent to the term 1 + αR. Detailed mixing and substitution models could lead to variations of this model, e.g., in spatially explicit domains, on networks, etc [19] [20] [21] [22] . Figure 2 illustrates shield immunity impacts on an SIR epidemic with R 0 = 2.5. In this SIR model, shield immunity reduces the epidemic peak and reduces epidemic duration. In effect, shielding acts as a negative feedback loop, i.e., given that the effective reproduction number is R ef f (t)/R 0 = S(t)/(1 + αR(t)). As a result, interaction substitution increases as recovered individuals increase in number and are identified. For example, in the case of α = 20, the epidemic concludes with less than 20% infected in contrast to the final size of approximately 90% in the baseline scenario without shielding.