BackgroundForecasting influenza outbreaks remains a significant challenge due to the complexity of disease transmission and the influence of environmental and behavioral factors. Traditional models based solely on the basic reproduction number often fall short in capturing the full scope of outbreak dynamics.MethodsIn this study, we employ a seasonally adjusted SEIRT model incorporating stochastic differential equations (SDEs), including Brownian motion and Lévy jump processes, to simulate random and abrupt fluctuations in transmission. A branching process approximation is used to evaluate the probability of an epidemic under the influence of seasonal variability and stochastic perturbations. The model is calibrated using weekly influenza case data from Mexico, with noise components estimated from publicly available CDC [1] and WHO [2] surveillance data.ResultsSimulation results show that the inclusion of stochastic effects and periodic transmission rates significantly enhances the model's accuracy in reflecting real-world epidemic dynamics. Numerical comparisons between deterministic, Brownian-based, and Lévy-based scenarios reveal that both the initial state of the exposed or infectious subpopulation and the seasonal transmission patterns are critical to determining outbreak probabilities. Results indicate that seasonal transmission rates and stochastic effects significantly alter epidemic probabilities, with Lévy processes capturing abrupt outbreak dynamics more accurately than deterministic models.ConclusionsThe findings underscore that deterministic models may underestimate epidemic risk when they overlook random and sudden changes in contact rates or disease introduction. The proposed stochastic modeling framework yields a deeper understanding of influenza transmission dynamics by incorporating uncertainty and seasonal variability, thereby supporting more informed and effective public health decision-making.

[This corrects the article DOI: 10.1016/j.idm.2024.12.010.].

Understanding and predicting real-world epidemic dynamics has consistently posed a formidable challenge. This study addresses an age-structured stochastic SIR model incorporating a general incidence rate, high-order white noise, and Lévy jump perturbations. By employing Lyapunov function method, we establish the existence and uniqueness of a global positive solution. Furthermore, we derive a stochastic threshold that delineates the conditions for disease persistence and extinction. Moreover, the existence and uniqueness of a stationary distribution are proven by applying an improved version of Hasminskii's theory. Numerical simulations based on the positivity- and boundedness-preserving Euler–Maruyama scheme corroborate the theoretical results, showing that reducing the amplitude of higher-order noise amplifies the infection burden, whereas increasing the age-structure parameters ϑ and ς markedly suppresses transmission. Finally, the efficacy of physics-informed neural network based on stochastic SIR model (PINN-SIR), is demonstrated through its application to the fitting and forecasting of COVID-19 case in Zhejiang, China. The method shows promise for extension to more complex dynamical systems and diseases.

HIV testing and contact tracing facilitate early detection of HIV/AIDS infections for interrupting the hidden transmission. In this study, a susceptible-undiagnosed-diagnosed transmission model with testing and contact tracing is proposed in heterosexual and homosexual populations. The basic reproduction number, the heterosexual-transmission and homosexual-transmission reproduction numbers of the transmission model are derived by the next generation matrix method. The optimal-fitting results present that the basic reproduction number of Fujian 2012–2022 HIV/AIDS epidemics ranges from 1.93 to 2.74 by phases, which is consistent with the heterosexual-transmission reproduction number. The optimal fittings and the global sensitivity analysis show that the transmission risk mainly originates from the heterosexual contacts. The transmission risk assessments and the 2023–2035 tendency predictions are performed for HIV/AIDS prevalence in Fujian Province by scenarios. The numerical simulation results point out that the decrease of female-to-male transmission rate, the decline of proportion of active diagnosed population, and the reduction of the awareness delay, are the main contributors for declining HIV/AIDS prevalence. The 2023–2035 tendency predictions of Fujian Province reveal that, when the awareness delay is fixed, the rising trends of the infection scales caused by the transmission rates are more significant than those caused by the proportion of active diagnosed population. According to the transmission risk assessments and the tendency prediction results, several suggestions are provided to the policymakers for curbing the HIV/AIDS transmission in Fujian Province.