A Behavioral Multispread Epidemic Model

Carlo Graziani, Argonne National Laboratory

In qualitative epidemiological discussions, the term ``superspreader'' is used in several distinct senses: There are superspreader individuals, who shed disproportionate amounts of pathogen superspreader events, that is, occasions on which disproportionate sharing of pathogen occurs; and superspreader behaviors, i.e. regular patterns of activity that promote sharing of pathogen. In technical-mathematical epidemiology the first sense -- individuals -- dominates modeling, and there is some stochastic-process-based modeling to capture the second sense -- events.  The modeling of superspread behavior has apparently not been attempted.

I will discuss a new class of epidemic models that represent multiple spread rates in terms of discrete behavior classes, rather than in terms of compartments comprising individuals. The model is framed in terms of $D$ behavior classes, each with its own spread rate. The evolution equation is an integro-differential equation on the $D$-simplex. The model is capable of describing the ``superspreader'' phenomenon in terms of behavior-specific spread rates, as opposed to terms of individual infectivity. I will show the existence of SIR-like separable solutions and discuss their stability, and their relation to late-time evolution of the dynamical system. I will demonstrate the numeric properties of the model using a $D=3$ case featuring a ``safe'' behavior, a moderate-spread behavior, and a superspread behavior.

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