On McKean-Vlasov SDEs with polynomial drifts for SIS epidemic models

TL;DR

This paper introduces a class of McKean-Vlasov SDEs with polynomial drifts that model SIS epidemic dynamics, providing solutions, analysis of disease extinction/persistence, and an Euler-Maruyama numerical scheme with error bounds.

Contribution

It extends SIS epidemic models using polynomial drift McKean-Vlasov equations with proven solution uniqueness and an explicit numerical error estimate.

Findings

Unique strong solutions for the proposed McKean-Vlasov equations.

Analysis of extinction and persistence scenarios in epidemic models.

An Euler-Maruyama scheme with explicit strong error bounds.

Abstract

We present a tractable class of one-dimensional McKean-Vlasov equations that allow for unique strong solutions and extend the dynamics of various SIS epidemic models that are well-established in the literature. While the distribution-dependent drift coefficients are of polynomial type, the diffusion coefficients may involve sums of power functions. Our analysis includes various scenarios of extinction and persistence of the disease and an effective Euler-Maruyama scheme, for which we derive an explicit strong error estimate in $p$th moment for $p\geq 2$.