In this paper, we propose a novel stochastic SEIQ model of a disease with the general incidence rate and temporary immunity. We first investigate the existence and uniqueness of a global positive solution for the model by constructing a suitable Lyapunov function. Then, we discuss the extinction of the SEIQ epidemic model. Furthermore, a stationary distribution for the model is obtained and the ergodic holds by using the method of Khasminskii. Finally, the theoretical results are verified by some numerical simulations. The simulation results show that the noise intensity has a strong influence on the epidemic spreading.

The whale optimization algorithm (WOA) is a high‐performance metaheuristic algorithm that can effectively solve many practical problems and broad application prospects. However, the original algorithm has a significant improvement in space in solving speed and precision. It is easy to fall into local optimization when facing complex or high‐dimensional problems. To solve these shortcomings, an elite strategy and spiral motion from moth flame optimization are utilized to enhance the original algorithm’s efficiency, called MEWOA. Using these two methods to build a more superior population, MEWOA further balances the exploration and exploitation phases and makes it easier for the algorithm to get rid of the local optimum. To show the proposed method’s performance, MEWOA is contrasted to other superior algorithms on a series of comprehensive benchmark functions and applied to practical engineering problems. The experimental data reveal that the MEWOA is better than the contrast algorithms in convergence speed and solution quality. Hence, it can be concluded that MEWOA has great potential in global optimization.

In this paper, we establish some Hermite-Hadamard type inequalities for h- convex function on high-dimensional balls and ellipsoids, which extend some known results. Some mappings connected with these inequalities and related results are also obtained.

In this paper, with eclipse stage in consideration, we propose an HIV-1 infection model with a general incidence rate and CTL immune response. We first study the existence and local stability of equilibria, which is characterized by the basic infection reproduction number ${\mathcal{R}}_0$ and the basic immunity reproduction number ${\mathcal{R}}_1$. The local stability analysis indicates the occurrence of transcritical bifurcations of equilibria. We confirm the bifurcations at the disease-free equilibrium and the infected immune-free equilibrium with transmission rate and the decay rate of CTLs as bifurcation parameters, respectively. Then we apply the approach of Lyapunov functions to establish the global stability of the equilibria, which is determined by the two basic reproduction numbers. These theoretical results are supported with numerical simulations. Moreover, we also identify the high sensitivity parameters by carrying out the sensitivity analysis of the two basic reproduction numbers to the model parameters.

In this article, we study some Hermite-Hadamard-type inequalities for strongly h -convex functions on co-ordinates in R n , which extend some known results. Some mappings connected with these inequalities and related applications are also obtained.