Search Results (4)

This study investigates a symmetric fractional-order epidemic model with time delays and non-monotonic incidence rates, considering two viral strains. By confirming the existence, uniqueness, and boundedness of the system’s solutions, the research ensures the model’s well-posedness, guaranteeing its mathematical soundness and practical relevance. The study calculates and evaluates the equilibrium points and the basic reproduction numbers $R_0^1$ and $R_0^2$ to understand the dynamic behavior of the model under different parameter settings. Through the application of the Lyapunov method, the research examines the asymptotic global stability of the system, determining whether it will converge to a particular equilibrium state over time. Furthermore, Hopf bifurcation theory is employed to investigate potential periodic solutions and bifurcation scenarios, highlighting how the system might shift from stability to periodic oscillations under certain conditions. By utilizing the Adams-Bashforth-Moulton numerical simulation method, the theoretical results are validated, reinforcing the conclusions and demonstrating the model’s applicability in real-world contexts. It emphasizes the importance of fractional-order models in addressing epidemiological issues related to time delays ($\tau$), individual heterogeneity (m, k), and memory effects ($\theta$), offering greater accuracy compared with traditional integer-order models. In summary, this research provides a theoretical foundation and practical insights, enhancing the understanding and management of epidemic dynamics through fractional-order epidemic models. Full article

In this paper, we conducted a study on the optimal control problem of an epidemic model which consists of two strain with different types of incidence rates: bilinear and non-monotonic. We also considered use of the saturation treatment function. Two basic regeneration numbers are calculated from the epidemic model, which are denoted as $R_1$ and $R_2$. The global stability of the disease-free equilibrium point was studied by the Lyapunov method, and it was proved that the disease-free equilibrium point is globally asymptotically stable when $R_1$ and $R_2$ are less than one. Finally, we formulated a time-dependent optimal control problem by Pontryagin’s maximum principle. Numerical simulations were performed to establish the effects of model parameters for disease transmission as well as the effects of control. Full article

This paper performs a detailed analysis and explores optimal control strategies for a fractional-order SIV epidemic model, incorporating a nonmonotonic incidence rate. In this paper, the population of vaccinated individuals is included in the disease dynamics model. After proving the non-negative boundedness of the fractional-order SIV model, we focus on analyzing the equilibrium point characteristics of the model, delving into its existence, uniqueness, and stability analysis. In addition, our research includes formulating optimal control strategies specifically aimed at minimizing the number of infections while keeping costs as low as possible. To validate the theoretical findings and uncover the practical efficacy and prospects of control measures in mitigating epidemic spread, numerical simulations are performed. Full article

Few studies have focused on the potential relationship between secondhand smoke (SHS) exposure and depressive symptoms. This study aimed to explore the potential association between SHS exposure and depressive symptoms and differentiate this association in setting-specific exposure and symptom-specific outcomes. A cross-sectional study was conducted in Guangdong province of China from September to December 2010 using a multistage sampling method to randomly sample adults aged 18 years and older. SHS exposure was defined as inhalation by non-smokers of the smoke exhaled from smokers for at least 1 day a week in the past 30 days. Depressive symptoms were measured using the nine-item Patient Health Questionnaire. The zero-inflate negative binomial regression models were used to explore the associations between SHS exposure and depressive symptoms. A total of 2771 non-smokers were included in this study, with mean age of 49.6 ± 14.0 years and 70.3% of females. The prevalence of depressive symptoms was significantly higher in participants with SHS exposure than in those without exposure (incidence rate ratio (IRR) = 1.32, 95% confidence interval (CI) 1.16–1.51), and there were similar positive associations for SHS exposure in medical facilities (IRR = 1.37, 95% CI 1.17–1.61) and in schools (IRR = 1.46, 95% CI 1.20–1.77). Notably, there was a monotonically increasing dose-response relationship between frequency of SHS exposure and depressive symptoms. When differentiating this relationship by the dimensions of depressive symptoms, there were similar dose-response relationships for cognitive-affective and somatic symptoms. When differentiating this relationship by sex, only females showed a significant dose-response relationship. Our findings suggest dose-response relationships between SHS exposure and depressive symptoms in sex-specific and symptom-specific manners. Future longitudinal studies are needed to establish the biological mechanisms of the impact of SHS exposure. Full article