Fig 1.
Schematic diagram of behavioral epidemiological model with social distancing and mask-wearing as infectious contact-reduction strategies.
Both detected (ID) and undetected (IU) infectious individuals are considered. Proportion of mask-wearing individuals (xM((t))) and disease transmission reduction factor due to social distancing (xd(t)) have been modelled under evolutionary game dynamics.
Table 1.
Definition of model parameters and their values used for numerical simulation.
Fig 2.
Partial rank correlation coefficients (PRCCs) of the effective reproduction number, of the model (1) with respect to the variations of the model (1) parameters.
The baseline values of the parameters are considered from Table 1. The PRCC indices for most sensitive parameters: η, β, xd(t) and q are −0.847, 0.834, 0.82 and 0.67 respectively.
Fig 3.
Heat maps of effective reproduction number () along two most sensitive parameters: effective transmission rate (β) and rate at which individuals prefer to engage in social distancing to prevent infection (xd(t)) for A: an exorbitant cost setting for both masks and social distancing with low mask efficacy and high (η = 0.1, q = 0.9, CM = 0.9 and CD = 0.9) B: η = 0.5, q = 0.5, CM = 0.5 and CD = 0.5 (a moderate cost setting for both masks and social distancing) and C: η = 0.9, q = 0.1, CM = 0.1 and CD = 0.1 (an affordable setting for both masks and social distancing). All remaining parameters remain constant and are derived from the values listed in the Table 1.
Fig 4.
Panel A: time-series of (i) total infected and (ii) benefitted from social distancing (BPD) individuals when only social distancing is considered with variations of CD and d. Panel B: time-series of (i) total infected and (ii) mask-wearing individuals when only mask-wearing is considered with variations of CM, η and q. Panel C: time-series of (i) total infected (ii) BPD individuals and (iii) mask-wearing individuals when both social distancing and mask-wearing are considered with variations of CM, CD, η, d and q.
Fig 5.
Two-dimensional phase diagram of ((a)-(b)) final epidemic size (FES), ((c)-(d)) proportion of masked individuals (PMI), ((e)-(f)) BPD individuals and ((g)-(h)) average social payoff (ASP), for parameter space η = 0.1 and 0.9 and d = 0.1 and 0.9 and q = 0.1 and 0.9 along the socio-economic cost of social distancing, CD, and the economic cost of wearing mask, CM. To construct the phase portraits, plausible parameter values from Table 1 are considered.
Fig 6.
Heat maps of (a) final epidemic size (FES) (b) effective reproduction number () and (c) BPD individuals with CD = 0.1 and 0.9 along β and d. All remaining parameters remain constant and are derived from the values listed in the Table 1.
Fig 7.
Heat maps of final epidemic size (FES) with CD = 0.1 and 0.9, CM = 0.1 and 0.9 along efficacy of face coverings, η and mask benefits to others, q.
Low maintenance of social distancing, d = 0.1 is considered for Sub-figure (a), whereas high maintenance of social distancing, d = 0.9 is considered for Sub-figure (b). Heat maps of PMI with CD = 0.1 and 0.9, CM = 0.1 and 0.9 along efficacy of face coverings, η and mask benefits to others, q. Low maintenance of social distancing, d = 0.1 is considered for Sub-figure (c), whereas high maintenance of social distancing, d = 0.9 is considered for Sub-figure (d). All remaining parameters remain constant and are derived from the values listed in the Table 1.