<p>This paper presents a novel dual-stochastic network epidemic model of SIW type that systematically incorporates two complementary stochastic mechanisms. The first is a logarithmic Ornstein-Uhlenbeck (log-OU) process, which captures long-term, correlation-structured fluctuations in transmission rates while preserving positivity-a key advantage over standard OU processes that can yield biologically infeasible negative rates. The second is multiplicative white noise, which represents short-term, uncorrelated environmental variability. Mathematically, we first establish the existence and uniqueness of a global positive solution. We then derive a sharp extinction threshold <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathcal {R}_0^E$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="script">R</mi> <mn>0</mn> <mi>E</mi> </msubsup> </math></EquationSource> </InlineEquation> using spectral radius analysis of the next-generation matrix under stochastic perturbations, and prove the existence of a stationary distribution via Lyapunov function construction and Itô calculus, thereby characterizing the long-term persistence regime of the disease. Unlike deterministic thresholds that only depend on mean parameters, our stochastic thresholds <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathcal {R}_0^E$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="script">R</mi> <mn>0</mn> <mi>E</mi> </msubsup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mathcal {R}_0^S$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="script">R</mi> <mn>0</mn> <mi>S</mi> </msubsup> </math></EquationSource> </InlineEquation> explicitly incorporate noise intensities <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\sigma _i$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\rho _i$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ρ</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation> and reversion rates <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\kappa _i$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>κ</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation>, revealing how environmental variability can either destabilize or stabilize endemic states. Epidemiologically, the model introduces a multi-scale stochastic framework that bridges short-term random shocks with longer-term transmission trends, a feature often omitted in conventional models. Numerical simulations on scale-free networks reveal how network heterogeneity interacts with stochasticity to alter outbreak thresholds and persistence patterns. As a direct application, the model is calibrated to COVID-19 surveillance data from Ethiopia, where it outperforms deterministic equivalents and quantifies the differential influence of environmental clearance, pathogen release, and contact heterogeneity on epidemic outcomes. These results provide not only theoretical insights into stochastic epidemic dynamics but also quantitative support for targeted intervention strategies in real-world public health practice.</p>

A dual-stochastic network epidemic model with logarithmic Ornstein-Uhlenbeck process and white noise

期刊论文
发表日期：

2026年7月14日

查看全文

Yujie Wang,
Xiaohu Liu,
Hong Cao,
Linfei Nie,
Weiming Wang

摘要

This paper presents a novel dual-stochastic network epidemic model of SIW type that systematically incorporates two complementary stochastic mechanisms. The first is a logarithmic Ornstein-Uhlenbeck (log-OU) process, which captures long-term, correlation-structured fluctuations in transmission rates while preserving positivity-a key advantage over standard OU processes that can yield biologically infeasible negative rates. The second is multiplicative white noise, which represents short-term, uncorrelated environmental variability. Mathematically, we first establish the existence and uniqueness of a global positive solution. We then derive a sharp extinction threshold $\mathcal {R}_0^E$ $R_{0}^{E}$ using spectral radius analysis of the next-generation matrix under stochastic perturbations, and prove the existence of a stationary distribution via Lyapunov function construction and Itô calculus, thereby characterizing the long-term persistence regime of the disease. Unlike deterministic thresholds that only depend on mean parameters, our stochastic thresholds $\mathcal {R}_0^E$ $R_{0}^{E}$ and $\mathcal {R}_0^S$ $R_{0}^{S}$ explicitly incorporate noise intensities $\sigma _i$ $σ_{i}$ , $\rho _i$ $ρ_{i}$ and reversion rates $\kappa _i$ $κ_{i}$ , revealing how environmental variability can either destabilize or stabilize endemic states. Epidemiologically, the model introduces a multi-scale stochastic framework that bridges short-term random shocks with longer-term transmission trends, a feature often omitted in conventional models. Numerical simulations on scale-free networks reveal how network heterogeneity interacts with stochasticity to alter outbreak thresholds and persistence patterns. As a direct application, the model is calibrated to COVID-19 surveillance data from Ethiopia, where it outperforms deterministic equivalents and quantifies the differential influence of environmental clearance, pathogen release, and contact heterogeneity on epidemic outcomes. These results provide not only theoretical insights into stochastic epidemic dynamics but also quantitative support for targeted intervention strategies in real-world public health practice.