Explaining how individual choice and government policy can appear in the same context in real society is one of the most challenging scientific problems. Controlling infectious diseases requires effective prevention and control measures, including vaccination and self-defense measures. In this context, optimal control strategies incorporating vaccination and self-defense measures have been proposed using the framework of evolutionary game theory. This approach accounts for individuals’ behavior and interactions in a population. It can provide insights into the effectiveness of different strategies for controlling the spread of infectious diseases. The optimal control strategy involves balancing the costs and benefits of vaccination, considering the dynamic interplay between the infected and susceptible populations. By combining evolutionary game theory with optimal control theory, we can identify the optimal allocation of resources for vaccination and self-defense measures, which can maximize the control of infectious diseases while minimizing costs. The model is utilized to analyze public health policies diseases, such as vaccination and self-defense strategies, to mitigate the spread of infectious in the context of delayed decision-making.

The typical framework of replicator dynamics in evolutionary game theory assumes that all mutations are equally likely, meaning that the mutation of an evolving inhabitant only contributes constantly. However, in natural systems in biological and social sciences, mutations can arise due to their repetitive regeneration. The phenomenon of changing strategies (updating), typically prolonged sequences repeated many times, is defined as a volatile mutation that has been overlooked in evolutionary game theory. Implementing a repeated time framework introduces a dynamic mutation aspect incorporated with the pairwise Fermi rule. Network structure, ubiquitous in many natural and artificial systems, has significantly affected the dynamics and outcomes of evolutionary games. We examine the evolution of the pairwise game in terms of dilemma strength. It is revealed that mutation intensity can influence evolutionary dynamics. We also demonstrated that the obtained outcomes run by the deterministic and multi-agent simulation (MAS) process present similar stability regions for both linear and non-linear dynamics, even in various game classes. In particular, the most stimulating effect is detected for the relationship between the fraction of cooperation and the fraction of the mutated individuals, as inclination tends to provide an increasing tendency and supporting defection in the opposite case. In conclusion, we identified a form of volatile mutation as a form of noise that, under certain situations, could be used to enhance cooperation in social systems and design strategies for promoting cooperation in networked environments.

Disease severity through an immunized population ensconced on a physical network topology is a key technique for preventing epidemic spreading. Its influence can be quantified by adjusting the common (basic) methodology for analyzing the percolation and connectivity of contact networks. Stochastic spreading properties are difficult to express, and physical networks significantly influence them. Visualizing physical networks is crucial for studying and intervening in disease transmission. The multi-agent simulation method is useful for measuring randomness, and this study explores stochastic characteristics of epidemic transmission in various homogeneous and heterogeneous networks. This work thoroughly explores stochastic characteristics of epidemic propagation in homogeneous and heterogeneous networks through extensive theoretical analysis (positivity and boundedness of solutions, disease-free equilibrium point, basic reproduction number, endemic equilibrium point, stability analysis) and multi-agent simulation approach using the Gilespie algorithm. Results show that Ring and Lattice networks have small stochastic variations in the ultimate epidemic size, while BA-SF networks have disease transmission starting before the threshold value. The theoretical and deterministic aftermaths strongly agree with multi-agent simulations (MAS) and could shed light on various multi-dynamic spreading process applications. The study also proposes a novel concept of void nodes, Empty nodes and disease severity, which reduces the incidence of contagious diseases through immunization and topologies.

Cholera, a highly debilitating gastrointestinal disease caused by the bacteria Vibrio cholerae, continues to be a significant public health issue in many countries and regions around the globe. Conventional epidemiological models often fail to adequately account for the strategic connections between individuals and how these interactions influence disease spread. This paper examines cholera dynamics using evolutionary game theory and proposes a novel paradigm for analyzing the impact of human behavior and strategic decision-making on cholera transmission. The model incorporates the evolutionary stability of the tactics people employ, such as vaccination, hygiene practices, and disease treatment, while accounting for diverse environmental and social variables. Results have been obtained on the factors that either encourage or impede the spread of cholera using analytical and numerical methods, underscoring the need to implement behavioral interventions alongside medical and infrastructural measures. The findings offer novel insights into public health strategies for controlling cholera outbreaks and promoting community resilience to infectious diseases.

Heatwaves pose serious risks to human health, infrastructure, and the environment, with rising frequency, intensity, and duration linked to increased morbidity and mortality – particularly among vulnerable populations. While numerous studies have analyzed heatwaves statistically, few have applied mechanistic modeling. In this study, we extend the classical SEIR framework by introducing a temperature-dependent transmission function ϕ(T) to model heatwave impacts on disease dynamics in Dhaka, Bangladesh. Seasonal forcing was incorporated via sinusoidal modulation of the reproduction number R_0, capturing oscillatory behavior driven by annual temperature cycles. Analytical derivations identified two equilibria – Heat Impacted Free Equilibrium (HIFE) and Heat-Impacted Equilibrium (HIE) – representing heatwave-free and heatwave-endemic states. To evaluate model robustness, we performed local sensitivity and Partial Rank Correlation Coefficient (PRCC) analyses, identifying transmission rate (β) and progression rate (γ) as the most influential parameters. Simulations revealed that higher β and faster progression (γ) amplified outbreak size, whereas increased recovery (α) and reduced immunity loss (σ) substantially mitigated transmission and delayed epidemic peaks. These findings underscore that if β>α, outbreaks expand rapidly, but when α≥β, the system stabilizes near equilibrium. Complementing the mechanistic approach, meteorological data (January 2014 – February 2024) were analyzed using statistical tools and machine learning models, including Logistic Regression, SVM, and ensemble regressors. Logistic Regression achieved 95.8% accuracy, while SVM yielded the highest cross-validation score (0.9311) and AUC (0.9972). XGBRegressor provided robust short-term temperature forecasts, whereas Decision Trees offered smoother long-term projections. Taken together, these results demonstrate that integrating temperature-modulated SEIR modeling with machine learning provides a comprehensive framework for predicting heat-related morbidity, identifying early-warning thresholds, and informing public health preparedness under climate variability.