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Many policymakers have adopted voluntary vaccination policies to alleviate the consequences of contagious diseases. Such policies have several well-established feathers, i.e. they are seasonal, depending on an individual's decision, adaptive, and control epidemic activity. Here, we study ideas from behavioral epidemiology embedded with a vaccination game and pairwise two-player two-strategy game to represent the environmental feedback in an SVIR model by using a composite information index including disease incidence, vaccine factors and cooperative behavior on a global time scale (repeated season). In its turn, the information index's game dynamics to participate in the vaccine program (cooperation) is supposed to reflect the feedback-evolving dynamics of competitive cognitions and the environment. The assuming model is described by two different evolutionary game systems connected by an unknown external public opinion environment feedback. The embedded model is described by an inherited system showing a behavioral aspect, i.e. pairwise game indicates an individual's cooperative behavior, and a vaccine game refers to vaccine-cost influence. This is a novel attempt to stabilize the two different decision processes to pool them into a single index. Extensive simulations suggest a rich spectrum of achievable results, including epidemic control, human behavior, social dilemma, and policy suggestions. [ABSTRACT FROM AUTHOR]

Evolutionary epidemiological models have played an active part in analyzing various contagious diseases and intervention policies in the biological sciences. The design in this effort is the addition of compartments for treatment and vaccination, so the system is designated as susceptible, vaccinated, infected, treated, and recovered (SVITR) epidemic dynamic. The contact of a susceptible individual with a vaccinated or an infected individual makes the individual either immunized or infected. Inventively, the assumption that infected individuals enter the treatment and recover state at different rates after a time interval is also deliberated through the presence of behavioral aspects. The rate of change from susceptible to vaccinated and infected to treatment is studied in a comprehensive evolutionary game theory with a cyclic epidemic model. We theoretically investigate the cyclic SVITR epidemic model framework for disease-free and endemic equilibrium to show stable conditions. Then, the embedded vaccination and treatment strategies are present using extensive evolutionary game theory aspects among the individuals in society through a ridiculous phase diagram. Extensive numerical simulation suggests that effective vaccination and treatment may implicitly reduce the community risk of infection when reliable and cheap. The results exhibited the dilemma and benefitted situation, in which the interplay between vaccination and treatment evolution and coexistence are investigated by the indicators of social efficiency deficit and socially benefited individuals. [ABSTRACT FROM AUTHOR]