Dynamics analysis of an SVEIR epidemic model in a patchy environment.

In this paper, we propose a multi-patch SVEIR epidemic model that incorporates vaccination of both newborns and susceptible populations. We determine the basic reproduction number $ R_{0} $ and prove that the disease-free equilibrium $ P_{0} $ is locally and globally asymptotically stable if $ R_{0} < 1, $ and it is unstable if $ R_{0} > 1. $ Moreover, we show that the disease is uniformly persistent in the population when $ R_{0} > 1. $ Numerical simulations indicate that vaccination strategies can effectively control disease spread in all patches while population migration can either intensify or prevent disease transmission within a patch.

Dynamical analysis of a heroin-cocaine epidemic model with nonlinear incidence and spatial heterogeneity.

In this paper, we investigated a new heroin-cocaine epidemic model which incorporates spatial heterogeneity and nonlinear incidence rate. The main project of this paper is to explore the threshold dynamics in terms of the basic reproduction number R0, which was defined by applying the next-generation operator. The threshold type results shown that if R0<1, then the drug-free steady state is globally asymptotically stable. If R0>1, then heroin-cocaine spread is uniformly persistent. Furthermore, the globally asymptotic stability of the drug-free steady state has been established for the critical case of R0=1 by analysing the local asymptotic stability and global attractivity.

Metriplectic Structure of a Radiation-Matter-Interaction Toy Model.

A dynamical system defined by a metriplectic structure is a dissipative model characterized by a specific pair of tensors, which defines a Leibniz bracket; and a free energy, formed by a "Hamiltonian" and an entropy, playing the role of dynamics generator. Generally, these tensors are a Poisson bracket tensor, describing the Hamiltonian part of the dynamics, and a symmetric metric tensor, that models purely dissipative dynamics. In this paper, the metriplectic system describing a simplified two-photon absorption by a two-level atom is disclosed. The Hamiltonian component is sufficient to describe the free electromagnetic radiation. The metric component encodes the radiation-matter coupling, driving the system to an asymptotically stable state in which the excited level of the atom is populated due to absorption, and the radiation has disappeared. First, a description of the system is used, based on the real-imaginary decomposition of the electromagnetic field phasor; then, the whole metriplectic system is re-written in terms of the phase-amplitude pair, named Madelung variables. This work is intended as a first result to pave the way for applying the metriplectic formalism to many other irreversible processes in nonlinear optics.

Asymptotic stabilization of underactuated surface vehicles with actuator saturation.

This paper investigates the problem of global asymptotic stabilization of underactuated surface vessels (USVs) with input saturation. A novel input transformation is presented, so that the USV system can be transformed to a cascade structure. For the obtained system, the improved fractional power control laws are proposed to ensure input signals do not exceed actuator constraints and enhance convergence rates. Finally, stabilization and parameter optimization algorithm of USVs are proposed. Simulations are given to demonstrate the effectiveness of the presented method.

Nonlinear Dynamical Analysis and Optimal Control Strategies for a New Rumor Spreading Model with Comprehensive Interventions.

In the current era, information dissemination is more convenient, the harm of rumors is more serious than ever. At the beginning of 2020, COVID-19 is a biochemical weapon made by a laboratory, which has caused a very bad impact on the world. It is very important to control the spread of these untrue statements to reduce their impact on people's lives. In this paper, a new rumor spreading model with comprehensive interventions (background detection, public education, official debunking, legal punishment) is proposed for qualitative and quantitative analysis. The basic reproduction number with important biological significance is calculated, and the stability of equilibria is proved. Through the optimal control theory, the expression of optimal control pairs is obtained. In the following numerical simulation, the optimal control under 11 control strategies are simulated. Through the data analysis of incremental cost-effectiveness ratio and infection averted ratio of all control strategies, if we consider the control problem from different perspectives, we will get different optimal control strategies. Our results provide a flexible control strategy for the security management department.

Global dynamics of COVID-19 epidemic model with recessive infection and isolation.

In this paper, we present an SEIIaHR epidemic model to study the influence of recessive infection and isolation in the spread of COVID-19. We first prove that the infection-free equilibrium is globally asymptotically stable with condition R0<1 and the positive equilibrium is uniformly persistent when the condition R0>1. By using the COVID-19 data in India, we then give numerical simulations to illustrate our results and carry out some sensitivity analysis. We know that asymptomatic infections will affect the spread of the disease when the quarantine rate is within the range of [0.3519, 0.5411]. Furthermore, isolating people with symptoms is important to control and eliminate the disease.

A 2D-FM model-based robust iterative learning model predictive control for batch processes.

The work deals with composite iterative learning model predictive control (CILMPC) for uncertain batch processes via a two dimensional Fornasini-Marchesini (2D-FM) model. A novel equivalent error system is first presented which is composed of state error and tracking error. Then an iterative learning predictive updating law is constructed by 2D state feedback control and the 'worst' case linear quadratic function is also designed. Besides, the update controller considering the input and output constraint will be optimized using the worst-case objective function along the infinite moving horizon. The solvable conditions that can be optimized online in real time are constructed using linear matrix inequalities (LMIs). The stability of the proposed control scheme can be achieved with the feasibility of the optimization problem. Compared with robust traditional MPC using one-dimensional models, the presented control approach can guarantee more degrees of tuning to achieve faster convergence of tracking error, which is of more significance since uncertainties exist inevitably in industrial batch processes. Finally, an injection molding process and a three-tank are introduced as two cases to demonstrate the feasibility and superiority of the proposed MPC strategy.

Global dynamics of a two-strain flu model with a single vaccination and general incidence rate.

Influenza remains one of the major infectious diseases that target humankind, therefore, understand transmission mechanisms and control strategies can help us obtain more accurate predictions. There are many control strategies, one of them is vaccination. In this paper, our purpose is to extend the incidence rate of a two-strain flu model with a single vaccination, which includes a wide range of incidence rates among them, some cases are not monotonic nor concave, which may be used to reflect media education or psychological effect. Our main aim is to mathematically analyze the effect of the vaccine for strain 1, the general incidence rate of strain 1 and the general incidence rate of strain 2 on the dynamics of the model. Four equilibrium points were obtained and the global dynamics of the model are completely determined via suitable Lyapunov functions. We illustrate our results by some numerical simulations. Our results showed that the vaccination is always beneficial for controlling strain 1, its impact on strain 2 depends on the force of infection of strain 2. Also, the psychological effect is always beneficial for controlling the disease.

Dynamic model with factors of polycystic ovarian syndrome in infertile women.

BACKGROUND: Previous studies present various methods for prediction disease based on statistics or neural networks.These models use statistics and results from past procedures to provide prediction through probability analysis. OBJECTIVE: In this article, the authors present a dynamic model aiming at predicting the treatment result of infertile women with the factor of polycystic ovary syndrome. MATERIALS AND METHODS: For this purpose, the authors have divided the study population into five groups: women prone to infertility, PCOS women, infertile women undergoing the treatment with Clomiphene Citrate and Gonadotropin, infertile women under IVF treatment, and improved infertile women. Therefore, the authors modeled the disease in infertile women mathematically and indicated that the free equilibrium point was asymptotically stable. Also the possibility of other equilibrium point of the system has been studied. RESULTS: The authors showed that this equilibrium point was marginally stable. Using Stoke's Theorem, the authors proved that the recurrence of the disease cycle with the factor of polycystic ovary syndrome was not intermittent in infertile women. They solved this model numerically using Rung-Kutta method and sketched the figures of the resulted solutions. CONCLUSION: It shows that with increasing age, the ovarian reserve is decreased and the treatment Clomiphene Citrate and Gonadotropin are not responsive, so IVF treatment is recommended in this group of patients considering the graphs of the model.

Resilient guaranteed cost control for uncertain T-S fuzzy systems with time-varying delays and Markov jump parameters.

This paper aims to investigate the problem of resilient guaranteed cost control for uncertain Takagi-Sugeno fuzzy systems with Markov jump parameters and time-varying delay. A resilient mode-dependent fuzzy controller is designed and a weak sufficient condition is developed to ensure that the resulting closed-loop system is robust almost surely asymptotically stable with guaranteed cost index not exceeding the specified upper bound. Subsequently, the controller gain and upper bound of the guaranteed cost index can be obtained by solving a set of linear matrix inequalities. Finally, numerical and practical examples of the single-link robot arm system are provided to demonstrate the performance of the proposed approach.

A dynamical model for the number of infertile couples.

In this paper a dynamic model is suggested in order to predict treatment results for infertility of couples. For this purpose, five basic groups of couples are examined. These groups are: susceptible couples, patient couples, couples under treatment taking medicine only, those under treatment using surgery and cured ones. The main aim is to find an asymptotically stable free equilibrium point for this model. The method benefits from scrutinizing the dynamical model deeply. We show that there is another equilibrium point that is not signed stable. In addition, we solve this model numerically via Rung-Kutta method and sketch appropriate graphs for the solutions thus obtained.

The stability of a predator-prey system with linear mass-action functional response perturbed by white noise.

The present paper deals with the problem of an ecoepidemiological model with linear mass-action functional response perturbed by white noise. The essential mathematical features are analyzed with the help of the stochastic stability, its long time behavior around the equilibrium of deterministic ecoepidemiological model, and the stochastic asymptotic stability by Lyapunov analysis methods. Numerical simulations for a hypothetical set of parameter values are presented to illustrate the analytical findings.

Epidemic dynamics on semi-directed complex networks.

In this paper an SIS model for epidemic spreading on semi-directed networks is established, which can be used to examine and compare the impact of undirected and directed contacts on disease spread. The model is analyzed for the case of uncorrelated semi-directed networks, and the basic reproduction number R0 is obtained analytically. We verify that the R0 contains the outbreak threshold on undirected networks and directed networks as special cases. It is proved that if R0<1 then the disease-free equilibrium is globally asymptotically stable, otherwise the disease-free equilibrium is unstable and the unique endemic equilibrium exists, which is globally asymptotically stable. Finally the numerical simulations holds for these analytical results are given.