Prosocial behavior on testing and quarantine in an epidemic disease

Effective management of disease outbreaks requires a comprehensive understanding of the complex interplay between individual decision-making, disease dynamics, and societal objectives. We incorporate a mathematical disease model coupling with behavior-driven testing and quarantining to mitigate disease and capture the social dilemma behind the dynamics using social efficiency deficit. The results obtained from the numerical finite difference method indicate that a behavior-driven approach is more effective in controlling outbreaks and limiting disease spread compared to a constant strategy. The social dilemma reaches its peak at a critical transmission rate threshold, wherein either the proportion of symptomatic infectious individuals attains its maximum value or the rate of waning immunity surpasses a specific threshold. Furthermore, the social dilemma culminates when both the economic cost associated with the disease and the cost of quarantining symptomatic individuals reach their respective maxima, giving rise to a convergence of conflicting objectives between individual and societal interests. These findings underscore the complexity of disease management strategies and the importance of carefully balancing economic considerations with public health imperatives.