BackgroundMumps, an infectious viral disease, classically manifested by inflammation of salivary glands and is best known as a common childhood viral disease with no specific treatment. Although it can be protected by vaccine, there are more than 100,000 reported mumps cases according to the Chinese Center for Disease Control and Prevention. However, the factors and mechanisms behind the persistence and prevalence of mumps have not been well understood.MethodsA mumps model with seasonal fluctuation is formulated and investigated. We evaluate the basic reproduction number ℛ0 and analyze the dynamical behavior of the model. We also use the model to simulate the monthly data of mumps cases and carry out some sensitivity analysis of ℛ0 in terms of various model parameters.ResultsIt is shown that there exists only disease-free solution which is globally asymptotically stable if ℛ0 < 1, and there exists a positive periodic solution if ℛ0 > 1. ℛ0 is a threshold parameter, and its magnitude determines the extinction or persistence of the disease.ConclusionOur analysis shows that vaccination rate and invalid vaccination rate play important roles in the spread of mumps. Hence, Our study suggests to increase the vaccine coverage and make two doses of MMR (Measles, mumps and rubella vaccine) vaccine freely available in China.

Due to the limitations of data transfer technologies, existing studies on urban traffic control mainly focused on isolated dimension control such as traffic signal control or vehicle route guidance to alleviate traffic congestion. However, in real traffic, the distribution of traffic flow is the result of multiple dimensions whose future state is influenced by each dimension’s decisions. Presently, the development of the Internet of Vehicles enables an integrated intelligent transportation system. This paper proposes an integrated intelligent transportation model that can optimize predictive traffic signal control and predictive vehicle route guidance simultaneously to alleviate traffic congestion based on their feedback regulation relationship. The challenges of this model lie in that the formulation of the nonlinear feedback relationship between various dimensions is hard to describe and the design of a corresponding solving algorithm that can obtain Pareto optimality for multi-dimension control is complex. In the integrated model, we introduce two medium variables—predictive traffic flow and the predictive waiting time—to two-way link the traffic signal control and vehicle route guidance. Inspired by game theory, an asymmetric information exchange framework-based updating distributed algorithm is designed to solve the integrated model. Finally, an experimental study in two typical traffic scenarios shows that more than 73.33% of the considered cases adopting the integrated model achieve Pareto optimality.

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In this paper, an asymmetrical congestion game is used to build a fairness concern‐based coordinated route guidance model for alleviating traffic congestion. Coordinated vehicle route guidance is commonly recognized as an effective way to alleviate the “route flapping” phenomenon, where a new congestion appears since numerous vehicles obey the same guidance in selfish route diversion. The existing studies mainly use the classic (symmetrical) congestion games, whose payoff depends only on the number of chosen players, to calculate the flow proportion for the alternative roads. This mechanism may make some front vehicles receive the worse payoffs than the rear ones, which further results in the front vehicles being unwilling to execute the recommended paths due to their unfair psychology. Players' fairness concern in game theory has been noted in some fields (such as supply chain) but not traffic route guidance. In this work, to fill the above gap, the concept of vehicular fairness concern is introduced and the corresponding mathematical expression is formulated. An asymmetrical congestion game‐based coordination route model is built, which can improve the fairness coefficient of vehicles. Moreover, a reinforcement learning‐based approximated solving algorithm is designed since the existing solving theorems are not necessarily valid for the asymmetrical congestion game. An experimental study shows that (1) the Nash equilibrium coefficients generated by the approximated solving algorithm all converge to 1.00, and (2) the averaged fairness coefficient is increased from 0.92 to 0.96 on the basis of equal travel time due to the improved payoff functions.