Plots of the reachable region of disease incidence (

*i*_{1},

*i*_{2}) and the threshold forces of infection under various resident strategies, (

*φ̄*_{1},

*φ̄*_{2}). Each plot corresponds to the relative proportion of vaccine skeptics (

*q*_{1}=0.1, 0.3 and 0.4). The right boundary of the reachable region corresponds to

*φ̄*_{1} = 0, and the top boundary of the reachable region corresponds to

*φ̄*_{2} = 0. The threshold forces of infection are plotted as lines over the reachable regions of disease incidence. Specifically, dotted and solid lines indicate the threshold force of infection of behavioral groups 1 (

) and 2 (

), respectively. Depending on the relative size of behavioral groups and the balance between the cost of vaccination and the cost of infection, there may be various types of Nash strategies (marked by dots) for the population game, -. If the proportion of vaccine skeptics is relatively small (

*q*_{1}=0.1,

*q*_{2}=0.9), then the resulting Nash strategy is

*φ̄*_{1}=0 and

*φ̄*_{2} ∈ (0,1), marked as a dot A. If the proportion of vaccine skeptics is 30% of the population (

*q*_{1}=0.3,

*q*_{2}=0.7), then the resulting Nash strategy is

*φ̄*_{1}= 0 and

*φ̄*_{2} =1, marked as a dot B. Finally, if the proportion of vaccine skeptics is 40% of the population (

*q*_{1}=0.4,

*q*_{2}=0.6), the resulting Nash equilibrium is

*φ̄*_{1} ∈ (0,1)and

*φ̄*_{2} =1(marked as a dot C).

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