Understanding the Impact of Vaccination and Self-Defense Measures on Epidemic Dynamics Using an Embedded Optimization and Evolutionary Game Theory Methodology

Evolutionary analysis of a coupled epidemic-voluntary vaccination behavior model with immunity waning on complex networks

Vaccination is the most effective method of preventing and controlling the transmission of infectious diseases within populations. However, the phenomenon of waning immunity can induce periodic fluctuations in epidemic spreading. This study proposes a coupled epidemic-vaccination dynamic model to analyze the influence of immunity waning on the epidemic spreading within the context of voluntary vaccination. First, we establish an SIRSV (susceptible-infected-recovered-susceptible-vaccinated) compartment model to describe the transmission mechanism of infectious diseases based on the mean-field theory. Within this model, we incorporate a nonlinear infection rate with network topology and consider the waning natural and vaccine-induced immunity at the individual level. The evolutionary model of voluntary vaccination strategy is integrated into the SIRSV model to characterize the impact of vaccination behavior on the infectious disease transmission. We also consider two individual risk assessment methods, namely, the individual-based risk assessment (IB-RA) method and the society-based risk assessment (SB-RA) method, originating from local and global perspectives, respectively. Then, utilizing the next-generation matrix method, we derive the time-varying effective reproduction numbers of the model. Also, the theoretical analysis of optimal strategy thresholds in the individual decision-making process is also conducted. The results indicate that the thresholds obtained from the agent-based model (ABM) simulation method are consistent with the theoretical analysis, demonstrating the effectiveness of our model. Finally, we apply the coupled model to the COVID-19 pandemic in France, Germany, Italy, and the United Kingdom. This study analyzes the impact of waning immunity and provides early warning for the outbreak of the epidemics.

The optimal spatially-dependent control measures to effectively and economically eliminate emerging infectious diseases

Non-pharmaceutical interventions (NPIs) are effective in mitigating infections during the early stages of an infectious disease outbreak. However, these measures incur significant economic and livelihood costs. To address this, we developed an optimal control framework aimed at identifying strategies that minimize such costs while ensuring full control of a cross-regional outbreak of emerging infectious diseases. Our approach uses a spatial SEIR model with interventions for the epidemic process, and incorporates population flow in a gravity model dependent on gross domestic product (GDP) and geographical distance. We applied this framework to identify an optimal control strategy for the COVID-19 outbreak caused by the Delta variant in Xi'an City, Shaanxi, China, between December 2021 and January 2022. The model was parameterized by fitting it to daily case data from each district of Xi'an City. Our findings indicate that an increase in the basic reproduction number, the latent period or the infectious period leads to a prolonged outbreak and a larger final size. This indicates that diseases with greater transmissibility are more challenging and costly to control, and so it is important for governments to quickly identify cases and implement control strategies. Indeed, the optimal control strategy we identified suggests that more costly control measures should be implemented as soon as they are deemed necessary. Our results demonstrate that optimal control regimes exhibit spatial, economic, and population heterogeneity. More populated and economically developed regions require a robust regular surveillance mechanism to ensure timely detection and control of imported infections. Regions with higher GDP tend to experience larger-scale epidemics and, consequently, require higher control costs. Notably, our proposed optimal strategy significantly reduced costs compared to the actual expenditures for the Xi'an outbreak.

Mathematical analysis and prediction of future outbreak of dengue on time-varying contact rate using machine learning approach

This article introduces a novel mathematical model analyzing the dynamics of Dengue in the recent past, specifically focusing on the 2023 outbreak of this disease. The model explores the patterns and behaviors of dengue fever in Bangladesh. Incorporating a sinusoidal function reveals significant mid-May to Late October outbreak predictions, aligning with the government's exposed data in our simulation. For different amplitudes (A) within a sequence of values (A = 0.1 to 0.5), the highest number of infected mosquitoes occurs in July. However, simulations project that when βM = 0.5 and A = 0.1, the peak of human infections occurs in late September. Not only the next-generation matrix approach along with the stability of disease-free and endemic equilibrium points are observed, but also a cutting-edge Machine learning (ML) approach such as the Prophet model is explored for forecasting future Dengue outbreaks in Bangladesh. Remarkably, we have fitted our solution curve of infection with the reported data by the government of Bangladesh. We can predict the outcome of 2024 based on the ML Prophet model situation of Dengue will be detrimental and proliferate 25 % compared to 2023. Finally, the study marks a significant milestone in understanding and managing Dengue outbreaks in Bangladesh.

Behavioral game of quarantine during the monkeypox epidemic: Analysis of deterministic and fractional order approach

This work concerns the epidemiology of infectious diseases like monkeypox (mpox) in humans and animals. Our models examine transmission scenarios, including transmission dynamics between humans, animals, and both. We approach this using evolutionary game theory, specifically the intervention game-theoretical (IGT) framework, to study how human behavior can mitigate disease transmission without perfect vaccines and treatments. To do this, we use non-pharmaceutical intervention, namely the quarantine policy, which demonstrates the delayed effect of the epidemic. Additionally, we contemplate quarantine-based behavioral intervention policies in deterministic and fractional-order models to show behavioral impact in the context of the memory effect. Firstly, we extensively analyzed the model's positivity and boundness of the solution, reproduction number, disease-free and endemic equilibrium, possible stability, existence, concavity, and Ulam-Hyers stability for the fractional order. Subsequently, we proceeded to present a numerical analysis that effectively illustrates the repercussions of varying quarantine-related factors, information probability, and protection probability. We aimed to comprehensively examine the effects of non-pharmaceutical interventions on disease control, which we conveyed through line graphs and 2D heat maps. Our findings underscored the significant influence of strict quarantine measures and the protection of both humans and animals in mitigating disease outbreaks. These measures not only significantly curtailed the spread of the disease but also delayed the occurrence of the epidemic's peak. Conversely, when quarantine maintenance policies were implemented at lower rates and protection levels diminished, we observed contrasting outcomes that exacerbated the situation. Eventually, our analysis revealed the emergence of animal reservoirs in cases involving disease transmission between humans and animals.