Age-Structured SIR Model for the Spread of Infectious Diseases Through Indirect Contacts

Influence of waning immunity on vaccination decision-making: A multi-strain epidemic model with an evolutionary approach analyzing cost and efficacy

In this research, we introduce a comprehensive epidemiological model that accounts for multiple strains of an infectious disease and two distinct vaccination options. Vaccination stands out as the most effective means to prevent and manage infectious diseases. However, when there are various vaccines available, each with its costs and effectiveness, the decision-making process for individuals becomes paramount. Furthermore, the factor of waning immunity following vaccination also plays a significant role in influencing these choices. To understand how individuals make decisions in the context of multiple strains and waning immunity, we employ a behavioral model, allowing an epidemiological model to be coupled with the dynamics of a decision-making process. Individuals base their choice of vaccination on factors such as the total number of infected individuals and the cost-effectiveness of the vaccine. Our findings indicate that as waning immunity increases, people tend to prioritize vaccines with higher costs and greater efficacy. Moreover, when more contagious strains are present, the equilibrium in vaccine adoption is reached more rapidly. Finally, we delve into the social dilemma inherent in our model by quantifying the social efficiency deficit (SED) under various parameter combinations.

Global stability and optimal control of an age-structured SVEIR epidemic model with waning immunity and relapses

The efficacy of vaccination, incomplete treatment and disease relapse are critical challenges that must be faced to prevent and control the spread of infectious diseases. Age heterogeneity is also a crucial factor for this study. In this paper, we investigate a new age-structured SVEIR epidemic model with the nonlinear incidence rate, waning immunity, incomplete treatment and relapse. Next, the asymptotic smoothness, the uniform persistence and the existence of interior global attractor of the solution semi-flow generated by the system are given. We define the basic reproduction number R 0 and prove the existence of the equilibria of the model. And we study the global asymptotic stability of the equilibria. Then the parameters of the model are estimated using tuberculosis data in China. The sensitivity analysis of R 0 is derived by the Partial Rank Correlation Coefficient method. These main theoretical results are applied to analyze and predict the trend of tuberculosis prevalence in China. Finally, the optimal control problem of the model is discussed. We choose to take strengthening treatment and controlling relapse as the control parameters. The necessary condition for optimal control is established.

Optimal control and stability analysis of an age-structured SEIRV model with imperfect vaccination

Vaccination programs are crucial for reducing the prevalence of infectious diseases and ultimately eradicating them. A new age-structured SEIRV (S-Susceptible, E-Exposed, I-Infected, R-Recovered, V-Vaccinated) model with imperfect vaccination is proposed. After formulating our model, we show the existence and uniqueness of the solution using semigroup of operators. For stability analysis, we obtain a threshold parameter $ R_0 $. Through rigorous analysis, we show that if $ R_0 < 1 $, then the disease-free equilibrium point is stable. The optimal control strategy is also discussed, with the vaccination rate as the control variable. We derive the optimality conditions, and the form of the optimal control is obtained using the adjoint system and sensitivity equations. We also prove the uniqueness of the optimal controller. To visually illustrate our theoretical results, we also solve the model numerically.

External intervention model with direct and indirect propagation behaviors on social media platforms

A significant distinction between the COVID-19 pandemic and previous pandemics is the significant role of social media platforms in shaping public adherence to non-pharmaceutical interventions and vaccine acceptance. However, with the recurrence of the epidemic, the conflict between epidemic prevention and production recovery has become increasingly prominent on social media. To help design effective communication strategies to guide public opinion, we propose a susceptible-forwarding-immune pseudo-environment (SFI-PE) dynamic model for understanding the environment with direct and indirect propagation behaviors. Then, we introduce a system with external interventions for direct and indirect propagation behaviors, termed the macro-controlled SFI-PE (M-SFI-PE) model. Based on the numerical analyses that were performed using actual data from the Chinese Sina microblogging platform, the data fitting results prove our models' effectiveness. The research grasps the law of the new information propagation paradigm, and our work bridges the gap between reality and theory in information interventions.