Lassa fever is an acute viral hemorrhagic disease that affects humans and is endemic in various West African nations. In this study, a fractional-order model is constructed using the Caputo operator for SEIR-type Lassa fever transmission, including the control strategy. The proposed model examines the dynamics of Lassa fever transmission from rodents to humans and from person to person and in territories with infection in society. The model is analyzed both qualitatively and quantitatively. We examine the positively invariant area and demonstrate positive, bounded solutions to the model. We also show the equilibrium states for the occurrence and extinction of infection. The proposed nonlinear system is verified to be present, and a unique solution is shown to exist using fixed point theorems. Using the Volterra-type Lyapunov function, we investigate the global stability of the suggested system with a fractional Caputo derivative. To study the impact of the fractional operator through computational simulations, results are generated employing a two-step Lagrange polynomial in the generalized version of the power law kernel. A graphical evaluation is provided to show the simplicity and dependability of the model, and all rodents that could be source viruses are important in ecological research. The findings with a value equal to 1 are stronger, according to the comparison of outcomes with different fractional orders. The adverse effect of Lassa fever increases when all modes of transmission are taken into account, according to the study, with fractional-order findings indicating less detrimental effects on specific transmission routes.

Hub economy is a kind of emerging economic form. Developing a hub economy is essential to strengthen domestic and foreign connectivity and build a powerful country in transportation. This paper designs a two-stage analysis framework for the evaluation and impact study of the input-output efficiency of the hub economy based on the super SBM model, Malmquist model, and Tobit model. In the first stage, the Super SBM and Malmquist models are used to measure the static and dynamic efficiency of the hub economy. In the second stage, the Tobit model is used to analyze the factors influencing the efficiency of the hub economy. Among them, the explained variable in the second stage is the measurement result of technical efficiency in the first stage. The empirical results of 30 provinces and cities in China from 2012 to 2021 show that (1) the technical efficiency (TE), pure technical efficiency (PTE), and scale efficiency (SE) of China’s hub economy are 0.585, 0.740, and 0.820, respectively, which do not reach the effective state; (2) the technical efficiency change index (Effch), technical progress change index (Techch), and total factor productivity change index (Tfpch) of China’s hub economy are 0.994, 0.945, and 0.939, respectively, indicating that the corresponding efficiencies show a downward trend; and (3) industrial structure, innovation, and technology are significantly and positively correlated with the efficiency of the hub economy; policy and enterprises are significantly negatively correlated with the efficiency of the hub economy; and education does not correlate with the efficiency of the hub economy.

An implementable algorithm for solving nonsmooth nonconvex constrained optimization is proposed by combining bundle ideas, proximity control, and the exact penalty function. We construct two kinds of approximations to nonconvex objective function; these two approximations correspond to the convex and concave behaviors of the objective function at the current point, which captures precisely the characteristic of the objective function. The penalty coefficients are increased only a finite number of times under the conditions of Slater constraint qualification and the boundedness of the constrained set, which limit the unnecessary penalty growth. The given algorithm converges to an approximate stationary point of the exact penalty function for constrained nonconvex optimization with weakly semismooth objective function. We also provide the results of some preliminary numerical testing to show the validity and efficiency of the proposed method.

This study examines the discrete prey-predator model in the sense of Caputo fractional derivative by incorporating harvesting on the predator population and immigration on the prey population. We establish the topological categories of the model’s fixed points. We show analytically that a fractional order prey-predator model supports both a Neimark–Sacker (NS) bifurcation and a period-doubling (PD) bifurcation under specific parametric circumstances. Using the central manifold and bifurcation theory, we provide evidence for NS and PD bifurcations. It has been discovered that the parameter values and the initial conditions have a significant influence on the dynamical behavior of the fractional order prey-predator model. Furthermore, two chaos management strategies are applied to eliminate the chaos that objectively exists in the model. Finally, numerical simulations are used to demonstrate complicated and chaotic behavior in order to support our theoretical and analytical discussions.

Taking into account the impact of time factors on emission reductions and brand reputation, the reference carbon emission effect and dual-channel supply chain are incorporated into a unified analysis framework. We applied differential game theory to build models under centralized decision-making and decentralized decision-making. The aim of the research is to explore the strategies of a single manufacturer and a single retailer on product pricing, low-carbon production, and advertising. The research analyses the impact of reference carbon emission effects, cost coefficients, and interchannel substitutable coefficients on profits. In order to alleviate the double marginal effect brought about by decentralized decision-making, a cost-compensation coordination mechanism is proposed. The conclusions are as follows. First, centralized decision-making is the optimal decision-making mode, but further consultation is required to implement it voluntarily by both parties. Second, a cost-recovery contract occurs when the fixed fee that the retailer gives the manufacturer meets certain conditions. The contract can make the retailer’s advertising investment reach the level of centralized decision-making and improve the member’s profit under the decentralized decision-making. The coordination mechanism is effective. Third, the reference carbon emission effect can bring about an increase in the manufacturer’s low-carbon production input and profits. The retailer’s advertising investment is not affected by the reference carbon emission effect. Fourth, wholesale prices and online or offline retail prices are all positively correlated with the market share of the channel. The price-substitution coefficient between channels is positively correlated with both low-carbon inputs and profits.