Behavioral vaccination policies and game-environment feedback in epidemic dynamics.

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.

Exploring the performance of volatile mutations on evolutionary game dynamics in complex networks.

The typical framework of replicator dynamics in evolutionary game theory assumes that all mutations are equally likely, meaning that the mutation of an evolving inhabitant only contributes constantly. However, in natural systems in biological and social sciences, mutations can arise due to their repetitive regeneration. The phenomenon of changing strategies (updating), typically prolonged sequences repeated many times, is defined as a volatile mutation that has been overlooked in evolutionary game theory. Implementing a repeated time framework introduces a dynamic mutation aspect incorporated with the pairwise Fermi rule. Network structure, ubiquitous in many natural and artificial systems, has significantly affected the dynamics and outcomes of evolutionary games. We examine the evolution of the pairwise game in terms of dilemma strength. It is revealed that mutation intensity can influence evolutionary dynamics. We also demonstrated that the obtained outcomes run by the deterministic and multi-agent simulation (MAS) process present similar stability regions for both linear and non-linear dynamics, even in various game classes. In particular, the most stimulating effect is detected for the relationship between the fraction of cooperation and the fraction of the mutated individuals, as inclination tends to provide an increasing tendency and supporting defection in the opposite case. In conclusion, we identified a form of volatile mutation as a form of noise that, under certain situations, could be used to enhance cooperation in social systems and design strategies for promoting cooperation in networked environments.

A cyclic behavioral modeling aspect to understand the effects of vaccination and treatment on epidemic transmission dynamics.

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.

Modeling the epidemic control measures in overcoming COVID-19 outbreaks: A fractional-order derivative approach.

Novel coronavirus named SARS-CoV-2 is one of the global threads and uncertain challenges worldwide faced at present. It has stroke rapidly around the globe due to viral transmissibility, new variants (strains), and human unconsciousness. Lack of adequate and reliable vaccination and proper treatment, control measures such as self-protection, physical distancing, lockdown, quarantine, and isolation policy plays an essential role in controlling and reducing the pandemic. Decisions on enforcing various control measures should be determined based on a theoretical framework and real-data evidence. We deliberate a general mathematical control measures epidemic model consisting of lockdown, self-protection, physical distancing, quarantine, and isolation compartments. Then, we investigate the proposed model through Caputo fractional order derivative. Fixed point theory has been used to analyze the Caputo fractional-order derivative model's existence and uniqueness solutions, whereas the Adams-Bashforth-Moulton numerical scheme was applied for numerical simulation. Driven by extensive theoretical analysis and numerical simulation, this work further illuminates the substantial impact of various control measures.

Analysis of individual strategies for artificial and natural immunity with imperfectness and durability of protection.

As protection against infectious disease, immunity is conferred by one of two main defense mechanisms, namely (i) resistance generated by previous infection (known as natural immunity) or (ii) by being vaccinated (known as artificial immunity). To analyze, a modified SVIRS epidemic model is established that integrates the effects of the durability of protection and imperfectness in the framework of the human decision-making process as a vaccination game. It is supposed that immunized people become susceptible again when their immunity expires, which depends on the duration of immunity. The current theory for most voluntary vaccination games assumes that seasonal diseases such as influenza are controlled by a temporal vaccine, the immunity of which lasts for only one season. Also, a novel perspective is established involving an individual's immune system combined with self-interest to take the vaccine and natural immunity obtained from infection by coupling a disease-spreading model with an evolutionary game approach over a long period. Numerical simulations show that the longer attenuation helps significantly to control the spread of disease. Also discovered is the entire mechanism of active and passive immunities, in the sense of how they coexist with natural and artificial immunity. Thus, the prospect of finding the optimal strategy for eradicating a disease could help in the design of effective vaccination campaigns and policies.

The role of advanced and late provisions in a co-evolutionary epidemic game model for assessing the social triple-dilemma aspect.

In the context of voluntary vaccination, we consider two additional provisions as well as pre-emptive vaccination for a unified model over epidemiology and evolutionary game theory to assess the extent to which advanced and late provisions restrict the spread of disease. To circumvent infection, people can be vaccinated pre-emptively before the epidemic season, but the imperfectness of vaccination or an unwillingness to be vaccinated may cause people instead to either be late-vaccinated or use self-protection. Here, self-protection corresponds to actions such as wearing a mask, washing hands, or using a mosquito net and is defined as the third strategy after pre-emptive vaccination (the first strategy) and late-vaccination (the second strategy). Our model can reproduce multiple social dilemma situations resulting from what is known as the vaccination dilemma (originating from preemptive vaccination), which works on a global time scale (i.e., repeated seasons approaching social equilibrium), and also from two other dilemmas due to late provisions, which work on a local time scale (i.e., every time step in a single season). To reproduce how an individual can acquire information for adaptation from neighbors or the society for a suitable provision, we introduce several strategy-updating rules for both global and local time scales and this behavioral feedback has a significant effect to reducing a transmissible disease. We also establish the social efficiency deficit (SED) indicator for a triple-dilemma game to quantify the existence of a social dilemma. Relying fully on a theoretical framework, our model provides a new perspective for evaluations: (i) how much more advantageous and effective pre-emptive vaccination is in eradicating a communicable disease compared with late provisions such as late vaccination and self-protection, and (ii) the extent of the social dilemma resulting from each of the three provisions, given the new idea of SED. The main effect of the triple-dilemma is that expensive provision displays no SED (no dilemma) until the efficiency or effectiveness of provisions reaches a certain level.