We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Dynamic analysis of generalized epidemic models with latent period, quarantine, governmental intervention and Ornstein–Uhlenbeck process.
- Authors
Su, Tan; Zhang, Xinhong; Jiang, Daqing
- Abstract
Considering the transmission characteristics of COVID-19, we formulate a Susceptible-Exposed-Quarantine-Infected-Recovered epidemic model by five first-order differential equations to study the dynamical behaviors of diseases that have a latent period, quarantine strategy, governmental intervention and general incidence rate. After giving the basic reproduction number R 0 , conditions for the existence of equilibria and their local asymptotic stability are both investigated. However, environmental perturbations always have influence on the epidemic in the natural world. With the assumption that the transmission rate is driven by the log-normal Ornstein–Uhlenbeck process, we construct a corresponding stochastic epidemic model that incorporates environmental impacts. Based on the proof of existence and uniqueness of the global positive solution, two critical values R 0 e and R 0 s are established that can determine the extinction and persistence of disease, which are completely constituted by the basic reproduction number and random factors. By solving a changing four-dimensional Fokker–Planck equation, we calculate the exact analytical expression of the probability density function of stationary distribution near the quasi-endemic equilibrium. Finally, some numerical simulations are performed to support obtained theoretical results, and we show the sensitivity index to study the impact of each parameter on disease transmission.
- Subjects
ORNSTEIN-Uhlenbeck process; INFECTIOUS disease transmission; BASIC reproduction number; PROBABILITY density function; RANDOM numbers; EPIDEMICS; FOKKER-Planck equation
- Publication
Nonlinear Dynamics, 2024, Vol 112, Issue 9, p7749
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-024-09458-2