Evolutionary Game Theoretic Insights on the SIRS Model of the COVID-19 Pandemic.

The effectiveness of control measures against the diffusion of the COVID-19 pandemic is grounded on the assumption that people are prepared and disposed to cooperate. From a strategic decision point of view, cooperation is the unreachable strategy of the prisoner's dilemma game, where the temptation to exploit the others and the fear to be betrayed by them drives the people behavior, which eventually results fully defective. In this work, we integrate the SIRS epidemic model with the replicator equation of evolutionary games in order to study the interplay between the infection spreading and the propensity of people to become cooperative under the pressure of the epidemic. We find that the developed model possesses several steady states, including fully or partially cooperative ones and that the presence of such states allows to take the disease under control. Moreover, assuming a seasonal variation of the infection rate, the system presents rich dynamics, including chaotic behavior and epidemic extinction.

Lumping evolutionary game dynamics on networks.

We study evolutionary game dynamics on networks (EGN), where players reside in the vertices of a graph, and games are played between neighboring vertices. The model is described by a system of ordinary differential equations which depends on players payoff functions, as well as on the adjacency matrix of the underlying graph. Since the number of differential equations increases with the number of vertices in the graph, the analysis of EGN becomes hard for large graphs. Building on the notion of lumpability for Markov chains, we identify conditions on the network structure allowing to reduce the original graph. In particular, we identify a partition of the vertex set of the graph and show that players in the same block of a lumpable partition have equivalent dynamical behaviors, whenever their payoff functions and initial conditions are equivalent. Therefore, vertices belonging to the same partition block can be merged into a single vertex, giving rise to a reduced graph and consequently to a simplified system of equations. We also introduce a tighter condition, called strong lumpability, which can be used to identify dynamical symmetries in EGN which are related to the interchangeability of players in the system.

Kinetic analysis and comparison of models of xylose metabolism by Klebsiella planticola.

A model for the degradation of xylose and ethanol production by Klebsiella planticola is proposed and compared with the exponential and Michaelis-Menten approaches. This model is based on the energy system diagrams and it is a simplified version of a previous model developed for the glucose and ethanol kinetics of the yeast Saccharomices cerevisiae. In this model the dynamics of the substrate and of the final product are strictly related by means of the cellular activity. This model shows superior performances with respect to the two alternatives, behaving better along the whole dynamics.