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Personal responsibility, one of the basic principles of modern law, requires one to be responsible for what he did. However, personal responsibility is far from the only norm ruling human interactions, especially in social and economic activities. In many collective communities such as among enterprise colleagues and family members, ones personal interests are often bound to others -- once one member breaks the rule, a group of people have to bear the punishment or sanction. Such a mechanism is termed joint liability. Although many real-world cases have demonstrated that joint liability helps to maintain collective collaboration, a deep and systematic theoretical analysis on how and when joint liability promotes cooperation is lacking. Here we use evolutionary game theory to model an interacting system with joint liability, where ones losing credit could deteriorate the reputation of the whole group. We provide the analytical condition to predict when cooperation evolves in the presence of joint liability, which is verified by simulations. We also analytically prove that joint liability can greatly promote cooperation. Our work stresses that joint liability is of great significance in promoting the current economic propensity.
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Systems with simultaneous cooperation and competition among the elements are ubiquitous. In spite of their practical importance, knowledge on the evolution mechanism of this class of complex system is still very limit. In this work, by conducting extensive empirical survey to a large number of cooperation-competition systems which cover wide categories and contain the information of network topology, cooperation-competition gain, and the evolution time, we try to get some insights to the universal mechanism of their evolutions. Empirical investigations show that the distributions of the cooperation-competition gain interpolates between power law function and exponential function. Particularly, we found that the cooperation-competition systems with longer evolution durations tend to have more heterogeneous distributions of the cooperation-competition gain. Such an empirical observation can be well explained by an analytic model in which the evolution of the systems are mainly controlled by the Matthew effect, and the marginal heterogeneity of the initial distribution is amplified by the Matthew effect with similar speed in spite of the diversity of the investigated systems.
In this paper, we investigate the effect of heterogeneity of link weight, heterogeneity of the frequency or amount of interactions among individuals, on the evolution of cooperation. Based on an analysis of the evolutionary prisoners dilemma game on a weighted one-dimensional lattice network with intra-individual heterogeneity, we confirm that moderate level of link-weight heterogeneity can facilitate cooperation. Furthermore, we identify two key mechanisms by which link-weight heterogeneity promotes the evolution of cooperation: mechanisms for spread and maintenance of cooperation. We also derive the corresponding conditions under which the mechanisms can work through evolutionary dynamics.
In this study, we develop the mathematical model to understand the coupling between the spreading dynamics of infectious diseases and the mobility dynamics through urban transportation systems. We first describe the mobility dynamics of the urban population as the process of leaving from home, traveling to and from the activity locations, and engaging in activities. We then embed the susceptible-exposed-infectious-recovered (SEIR) process over the mobility dynamics and develops the spatial SEIR model with travel contagion (Trans-SEIR), which explicitly accounts for contagions both during travel and during daily activities. We investigate the theoretical properties of the proposed model and show how activity contagion and travel contagion contribute to the average number of secondary infections. In the numerical experiments, we explore how the urban transportation system may alter the fundamental dynamics of the infectious disease, change the number of secondary infections, promote the synchronization of the disease across the city, and affect the peak of the disease outbreaks. The Trans-SEIR model is further applied to the understand the disease dynamics during the COVID-19 outbreak in New York City, where we show how the activity and travel contagion may be distributed and how effective travel control can be implemented with only limited resources. The Trans-SEIR model along with the findings in our study may have significant contributions to improving our understanding of the coupling between urban transportation and disease dynamics, the development of quarantine and control measures of disease system, and promoting the idea of disease-resilient urban transportation networks.
We describe the population-based SEIR (susceptible, exposed, infected, removed) model developed by the Irish Epidemiological Modelling Advisory Group (IEMAG), which advises the Irish government on COVID-19 responses. The model assumes a time-varying effective contact rate (equivalently, a time-varying reproduction number) to model the effect of non-pharmaceutical interventions. A crucial technical challenge in applying such models is their accurate calibration to observed data, e.g., to the daily number of confirmed new cases, as the past history of the disease strongly affects predictions of future scenarios. We demonstrate an approach based on inversion of the SEIR equations in conjunction with statistical modelling and spline-fitting of the data, to produce a robust methodology for calibration of a wide class of models of this type.
A simplified method to compute $R_t$, the Effective Reproduction Number, is presented. The method relates the value of $R_t$ to the estimation of the doubling time performed with a local exponential fit. The condition $R_t = 1$ corresponds to a growth rate equal to zero or equivalently an infinite doubling time. Different assumptions on the probability distribution of the generation time are considered. A simple analytical solution is presented in case the generation time follows a gamma distribution.
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