Time delays shape the eco-evolutionary dynamics of cooperation.

We study the intricate interplay between ecological and evolutionary processes through the lens of the prisoner's dilemma game. But while previous studies on cooperation amongst selfish individuals often assume instantaneous interactions, we take into consideration delays to investigate how these might affect the causes underlying prosocial behavior. Through analytical calculations and numerical simulations, we demonstrate that delays can lead to oscillations, and by incorporating also the ecological variable of altruistic free space and the evolutionary strategy of punishment, we explore how these factors impact population and community dynamics. Depending on the parameter values and the initial fraction of each strategy, the studied eco-evolutionary model can mimic a cyclic dominance system and even exhibit chaotic behavior, thereby highlighting the importance of complex dynamics for the effective management and conservation of ecological communities. Our research thus contributes to the broader understanding of group decision-making and the emergence of moral behavior in multidimensional social systems.

Fractional order SEIQRD epidemic model of Covid-19: A case study of Italy.

The fractional order SEIQRD compartmental model of COVID-19 is explored in this manuscript with six different categories in the Caputo approach. A few findings for the new model's existence and uniqueness criterion, as well as non-negativity and boundedness of the solution, have been established. When RCovid19<1 at infection-free equilibrium, we prove that the system is locally asymptotically stable. We also observed that RCovid 19<1, the system is globally asymptotically stable in the absence of disease. The main objective of this study is to investigate the COVID-19 transmission dynamics in Italy, in which the first case of Coronavirus infection 2019 (COVID-19) was identified on January 31st in 2020. We used the fractional order SEIQRD compartmental model in a fractional order framework to account for the uncertainty caused by the lack of information regarding the Coronavirus (COVID-19). The Routh-Hurwitz consistency criteria and La-Salle invariant principle are used to analyze the dynamics of the equilibrium. In addition, the fractional-order Taylor's approach is utilized to approximate the solution to the proposed model. The model's validity is demonstrated by comparing real-world data with simulation outcomes. This study considered the consequences of wearing face masks, and it was discovered that consistent use of face masks can help reduce the propagation of the COVID-19 disease.

Eco-evolutionary dynamics of multigames with mutations.

Most environments favor defection over cooperation due to natural selection. Nonetheless, the emergence of cooperation is omnipresent in many biological, social, and economic systems, quite contrary to the well-celebrated Darwinian theory of evolution. Much research has been devoted to better understanding how and why cooperation persists among self-interested individuals despite their competition for limited resources. Here we go beyond a single social dilemma since individuals usually encounter various social challenges. In particular, we propose and study a mathematical model incorporating both the prisoner's dilemma and the snowdrift game. We further extend this model by considering ecological signatures like mutation and selfless one-sided contribution of altruist free space. The nonlinear evolutionary dynamics that results from these upgrades offer a broader range of equilibrium outcomes, and it also often favors cooperation over defection. With the help of analytical and numerical calculations, our theoretical model sheds light on the mechanisms that maintain biodiversity, and it helps to explain the evolution of social order in human societies.