Networked Competitive Bivirus SIS spread with Higher Order Interactions
Résumé
The paper studies the simultaneous spread of two competing viruses over a network of population nodes by also accounting for the possibility of higher-order interactions (HOI). To this end, we consider a continuous-time time-invariant competitive bivirus networked susceptible-infected-susceptible (SIS) HOI system. First, we show that, under the assumption that the hypergraph associated with the system is strongly connected, the model is strongly monotone. Subsequently, using the Parametric Transversality Theorem of differential topology, we show that, for generic
parameter choices, the system admits only a finite number of equilibria, and that the Jacobian, evaluated at any equilibrium, is a nonsingular matrix. The aforementioned two findings together guarantee that the typical behavior of the model is convergence to some stable equilibrium point. The
equilibria of this system are i) the disease-free equilibrium (DFE), ii) single-virus endemic equilibria, and iii) coexistence equilibria (where both viruses are present in separate fractions of a population node). We identify a parameter regime that admits the possibility of three equilibria (namely,
the DFE, and two single-virus endemic equilibria) being simultaneously stable. We then provide sufficient conditions for the existence of a coexistence equilibrium, both for the same parameter regime as mentioned above, and for a different one. Thereafter, we identify a necessary condition for
the existence of a coexistence equilibrium. Finally, we illustrate our results using several numerical examples.
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