It is proved that the proposed model admits a unique global positive solution for any initial value in $(0,N)$ and that the numerical solution converges strongly to the exact solution with order $\alpha$.
Abstract
In this paper, we propose and analyze a diffusion time-changed susceptible-infected-susceptible (SIS) epidemic model driven by time-changed Brownian motion. We prove that the proposed model admits a unique global positive solution for any initial value in $(0,N)$. The extinction and persistence of the disease are then investigated. To approximate the diffusion time-changed SIS model, we construct a positivity-preserving logarithmic Euler-Maruyama (LEM) method. Assuming that the time-changed is given by the inverse of a standard $\alpha$-stable subordinator with $\alpha\in(0,1)$, we prove that the numerical solution converges strongly to the exact solution with order $\alpha$. Finally, numerical experiments are provided to confirm the predicted convergence rates and illustrate the positivity-preserving property of the proposed method.
In this paper, we consider a time-periodic nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with saturated incidence and Neumann boundary conditions in a spatiotemporally heterogeneous environment. First, we define the basic reproduction number for the model, which depends on dispersal rates, to...
The aim of this work is to provide a rigorous mathematical analysis of a well-known SIS epidemic model with a saturating contact rate. First, we establish the global asymptotic stability (GAS) of the model's equilibria by employing a suitable Lyapunov function in combination with the Poincar\'e--Bendixson theorem and t...
We incorporate stochastic fluctuations into an epidemic-behavior coevolution model and study its threshold dynamics and stationary distributions. By introducing the stochastic basic reproduction number R0σ, the behavioral threshold d, and two potential infection proportions RPσ,1 and RPσ,2, we establish conditions for...
Huan Yang, Sanyi Tang, Lin Wang· Journal of Theoretical Biolo...· 0 citations
This paper addresses the problem of controlling the spread of an epidemic through a multiplicatively controlled SIRS model, in which the control input modulates the infection rate in a bilinear manner. Classical approaches based on asymptotic stability only guarantee disease eradication as time tends to infinity, which...
A. Iggidr, M. Ouzahra, G. Sallet· Journal of Mathematical Biol...· 0 citations
This study proposes a susceptible-infectious-recovered (SIR) network model that incorporates a general recovery rate and a saturation treatment function, and establishes the well-posedness and global stability of the disease-free equilibrium in the model by employing semigroup theory and the standard comparison princip...
Jun-Yuan Yang, Maia Martcheva, Jun Zhang et al.· SIAM Journal on Applied Math...· 0 citations
Empirical results based on monthly influenza data from Xinjiang show that the proposed framework can capture epidemic trends, seasonal peaks, and fitting uncertainty and provide a theoretically grounded and practically applicable approach for infectious disease modeling under memory effects and stochastic perturbations...
Ge Zhang, Zhi-Hao Wang, Zhiming Li et al.· Fractal and Fractional· 0 citations
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