A study on prosocial behavior of wearing a mask and self-quarantining to prevent the spread of diseases underpinned by evolutionary game theory

Investigating the trade-off between self-quarantine and forced quarantine provisions to control an epidemic: An evolutionary approach

“…We introduce the concept of behavior model [ 46 , 47 , 54 ] which accounts for the time-varying flux from normal acting susceptible ( S N ) to self-quarantine susceptible ( S Q ) denoted by x , which we call the individual control, and from the symptomatic infected ( I S ) to forced quarantine ( Q ) denoted by y , which we call the government control. We define the following two dynamical equations: where τ x and τ y are the effort rate by individual and government, respectively.…”

“…( I S + Q ) is the total visible infected people, C I is the diseases cost which is set as 1.0 throughout the study. Parameter w is the relative sensitivity resulting from taking self-quarantine to reduce self-quarantine due to its cost Δ Q [54] . is the cost for an individual to treat the forced quarantine people.…”

“…In the present model, final epidemic size (FES) [ 42 , 54 ] is defined as where the argument ∞ denotes a state of equilibrium (let us call it as, NE) at t = ∞ [54] .…”

“…Average social payoff, ASP NE , in the model can be defined as follows [54] : where the first term in the right-hand side indicates the total cost of committing self-quarantine, the second term indicates the total cost of the implementation of forced quarantine, and the third term indicates the individuals’ diseases cost ( C I = 1.0) who should be called as a failed free rider [54] .…”

“…Such a gap is formally called social efficiency deficit (SED) [29] , which helps us understand the existence of social dilemma as well as the control parameters to improve the system towards social optimum. SED demonstrates how to improve the system's ASP from an evolutionary final state (NE) to a social ideal situation in order to achieve the maximum ASP SO that could be realized if both the evolutionary processes for x and y are optimally controlled [54] . SED is mathematically defined as follows: …”