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

Alexander Kalinin; Thilo Meyer-Brandis; Annika Steibel

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arXiv · 2604.19308

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

Alexander Kalinin·Thilo Meyer-Brandis·Annika Steibel

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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 $p\geq 2$.

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BibTeX RIS

Alexander Kalinin, Thilo Meyer-Brandis, Annika Steibel. 2026-04-21. On McKean-Vlasov SDEs with polynomial drifts for SIS epidemic models. https://arxiv.org/abs/2604.19308

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