Erlang-Distributed SEIR Epidemic Models with Cross-Diffusion

We explore the effects of cross-diffusion dynamics in epidemiological models. Using reaction–diffusion models of infectious disease, we explicitly consider situations where an individual in a category will move according to the concentration of individuals in other categories. Namely, we model susceptible individuals moving away from infected and infectious individuals. Here, we show that including these cross-diffusion dynamics results in a delay in the onset of an epidemic and an increase in the total number of infectious individuals. This representation provides more realistic spatiotemporal dynamics of the disease classes in an Erlang SEIR model and allows us to study how spatial mobility, due to social behavior, can affect the spread of an epidemic. We found that tailored control measures, such as targeted testing, contact tracing, and isolation of infected individuals, can be more effective in mitigating the spread of infectious diseases while minimizing the negative impact on society and the economy.

Numerical solution of COVID-19 pandemic model via finite difference and meshless techniques.

In the present paper, a reaction-diffusion epidemic mathematical model is proposed for the analysis of the transmission mechanism of the novel coronavirus disease 2019 (COVID-19). The mathematical model contains six-time and space-dependent classes, namely; Susceptible, Exposed, Asymptomatically infected, Symptomatic infected, Quarantine, and Recovered or Removed (SEQIaIsR). The threshold number R0 is calculated by utilizing the next-generation matrix approach. Values of the parameters are estimated with the help of the least square curve fitting tools. In addition to the simple explicit procedure, the mathematical epidemiological model with diffusion is simulated through the operator splitting approach based on finite difference and meshless methods. Stability analysis of the disease free and endemic equilibrium points of the model is investigated. Simulation results of the model with and without diffusion are presented in detail. A comparison of the obtained numerical results of both the models is performed in the absence of an exact solution. The correctness of the solution is verified through mutual comparison and partly, via theoretical analysis as well.

Nonlinear Impact of Circulation-Industry Intelligentization on the Urban–Rural Income Gap: Evidence from China

Integrating informatization into the circulation industry has led to the concept of circulation-industry intelligence. By reducing transportation costs and increasing total factor productivity, the incomes of rural-area residents can be improved;a new pattern of regional economy can be established;urban, rural, social, and economic development can become more coordinated;and social sustainable development can be promoted. In this study, we used China’s provincial panel data corresponding to the 2007–2019 period to measure the intelligence index of the circulation industry in each region and determine the factors that affect the urban–rural income gap;thereafter, we conducted comparative analyses. Further, a fixed-effects model was established based on the theory of agglomeration and diffusion effects to analyze the relationship between these two variables. Our analysis identified innovation investment as a significant intermediary mechanism. The robustness of this finding was verified by substituting variables and controlling for endogeneity. Thus, the effect was shown to be regionally heterogeneous. This study innovatively integrated informatization into the circulation industry, and the results obtained provide a reference for formulating transportation infrastructure as well as informatization strategies for promoting urban–rural coordination and sustainable development globally.