Advances in Difference Equations最新文献

With the rapid development of information society, rumor plays an increasingly crucial part in social communication, and its spreading has a significant impact on human life. In this paper, a stochastic rumor-spreading model with Holling II functional response function considering the existence of time delay and the disturbance of white noise is proposed. Firstly, the existence of a unique global positive solution of the model is studied. Then the asymptotic behavior of the global solution around the rumor-free and rumor-local equilibrium nodes of the deterministic system is discussed. Finally, through some numerical results, the validity and availability of theoretical analysis is verified powerfully, and it shows that some factors such as the transmission rate, the intensity of white noise, and the time delay have significant relationship with the dynamical behavior of rumor spreading.

A disastrous coronavirus, which infects a normal person through droplets of infected person, has a route that is usually by mouth, eyes, nose or hands. These contact routes make it very dangerous as no one can get rid of it. The significant factor of increasing trend in COVID19 cases is the crowding factor, which we named "crowding effects". Modeling of this effect is highly necessary as it will help to predict the possible impact on the overall population. The nonlinear incidence rate is the best approach to modeling this effect. At the first step, the model is formulated by using a nonlinear incidence rate with inclusion of the crowding effect, then its positivity and proposed boundedness will be addressed leading to model dynamics using the reproductive number. Then to get the graphical results a nonstandard finite difference (NSFD) scheme and fourth order Runge-Kutta (RK4) method are applied.

Humans are always exposed to the threat of infectious diseases. It has been proven that there is a direct link between the strength or weakness of the immune system and the spread of infectious diseases such as tuberculosis, hepatitis, AIDS, and Covid-19 as soon as the immune system has no the power to fight infections and infectious diseases. Moreover, it has been proven that mathematical modeling is a great tool to accurately describe complex biological phenomena. In the recent literature, we can easily find that these effective tools provide important contributions to our understanding and analysis of such problems such as tumor growth. This is indeed one of the main reasons for the need to study computational models of how the immune system interacts with other factors involved. To this end, in this paper, we present some new approximate solutions to a computational formulation that models the interaction between tumor growth and the immune system with several fractional and fractal operators. The operators used in this model are the Liouville-Caputo, Caputo-Fabrizio, and Atangana-Baleanu-Caputo in both fractional and fractal-fractional senses. The existence and uniqueness of the solution in each of these cases is also verified. To complete our analysis, we include numerous numerical simulations to show the behavior of tumors. These diagrams help us explain mathematical results and better describe related biological concepts. In many cases the approximate results obtained have a chaotic structure, which justifies the complexity of unpredictable and uncontrollable behavior of cancerous tumors. As a result, the newly implemented operators certainly open new research windows in further computational models arising in the modeling of different diseases. It is confirmed that similar problems in the field can be also be modeled by the approaches employed in this paper.

In this research work, we present a mathematical model for novel coronavirus-19 infectious disease which consists of three different compartments: susceptible, infected, and recovered under convex incident rate involving immigration rate. We first derive the formulation of the model. Also, we give some qualitative aspects for the model including existence of equilibriums and its stability results by using various tools of nonlinear analysis. Then, by means of the nonstandard finite difference scheme (NSFD), we simulate the results for the data of Wuhan city against two different sets of values of immigration parameter. By means of simulation, we show how protection, exposure, death, and cure rates affect the susceptible, infected, and recovered population with the passage of time involving immigration. On the basis of simulation, we observe the dynamical behavior due to immigration of susceptible and infected classes or one of these two.

Acknowledging many effects on humans, which are ignored in deterministic models for COVID-19, in this paper, we consider stochastic mathematical model for COVID-19. Firstly, the formulation of a stochastic susceptible-infected-recovered model is presented. Secondly, we devote with full strength our concentrated attention to sufficient conditions for extinction and persistence. Thirdly, we examine the threshold of the proposed stochastic COVID-19 model, when noise is small or large. Finally, we show the numerical simulations graphically using MATLAB.

In this work, we investigate the stability of an SIR epidemic model with a generalized nonlinear incidence rate and distributed delay. The model also includes vaccination term and general treatment function, which are the two principal control measurements to reduce the disease burden. Using the Lyapunov functions, we show that the disease-free equilibrium state is globally asymptotically stable if $R_0\le 1$ , where $R_0$ is the basic reproduction number. On the other hand, the disease-endemic equilibrium is globally asymptotically stable when $R_0>1$ . For a specific type of treatment and incidence functions, our analysis shows the success of the vaccination strategy, as well as the treatment depends on the initial size of the susceptible population. Moreover, we discuss, numerically, the behavior of the basic reproduction number with respect to vaccination and treatment parameters.

In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker-Cusa-Huygens type.

In this paper, we analyze a delayed SEIR epidemic model in which the latent and infected states are infective. The model has a globally asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number $R_0$ , is less than or equal to unity. We investigate the effect of the time delay on the stability of endemic equilibrium when $R_0>1$ . We give criteria that ensure that endemic equilibrium is asymptotically stable for all time delays and a Hopf bifurcation occurs as time delay exceeds the critical value. We give formulae for the direction of Hopf bifurcations and the stability of bifurcated periodic solutions by applying the normal form theory and the center manifold reduction for functional differential equations. Numerical simulations are presented to illustrate the analytical results.

We establish analogues of the mean value theorem and Taylor's theorem for fractional differential operators defined using a Mittag-Leffler kernel. We formulate a new model for the fractional Boussinesq equation by using this new Taylor series expansion.

This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov-Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results.