Advances in Difference Equations最新文献

Lately, many studies were offered to introduce the population dynamics of COVID-19. In this investigation, we extend different physical conditions of the growth by employing fractional calculus. We study a system of coupled differential equations, which describes the dynamics of the infection spreading between infected and asymptomatic styles. The healthy population properties are measured due to the social meeting. The result is associated with a macroscopic law for the population. This dynamic system is appropriate to describe the performance of growth rate of the infection and to verify if its control is appropriately employed. A unique solution, under self-mapping possessions, is investigated. Approximate solutions are presented by utilizing fractional integral of Chebyshev polynomials. Our methodology is based on the Atangana-Baleanu calculus, which provides various activity results in the simulation. We tested the suggested system by using live data. We found positive action in the graphs.

The purpose of this work is to analytically simulate the mutual impact for the existence of both temporal and spatial Caputo fractional derivative parameters in higher-dimensional physical models. For this purpose, we employ the γ̅-Maclaurin series along with an amendment of the power series technique. To supplement our idea, we present the necessary convergence analysis regarding the γ̅-Maclaurin series. As for the application side, we solved versions of the higher-dimensional heat and wave models with spatial and temporal Caputo fractional derivatives in terms of a rapidly convergent γ̅-Maclaurin series. The method performed extremely well, and the projections of the obtained solutions into the integer space are compatible with solutions available in the literature. Finally, the graphical analysis showed a possibility that the Caputo fractional derivatives reflect some memory characteristics.

In this paper, an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on Delta-Notch pathway is proposed for the first time. The uniqueness, nonnegativity, and boundedness of solutions are studied. In a two cells model, there are two equilibriums (no-expression of Delta and normal expression of Delta). Local asymptotic stability is proved for both cases. Stability analysis shows that the orders of the fractional-order differential equation model can significantly affect the equilibriums in the two cells model. Numerical simulations are presented to illustrate the conclusions. Next, the sensitivity of model parameters is calculated, and the calculation results show that different parameters have different sensitivities. The most and least sensitive parameters in the two cells model and the 60 cells model are verified by numerical simulations. What is more, we compare the fractional-order model with the integer-order model by simulations, and the results show that the orders can significantly affect the dynamic and the phenotypes.

The aim of this work is to present a new fractional order model of novel coronavirus (nCoV-2019) under Caputo-Fabrizio derivative. We make use of fixed point theory and Picard-Lindelöf technique to explore the existence and uniqueness of solution for the proposed model. Moreover, we explore the generalized Hyers-Ulam stability of the model using Gronwall's inequality.

The novel coronavirus (SARS-CoV-2), or COVID-19, has emerged and spread at fast speed globally; the disease has become an unprecedented threat to public health worldwide. It is one of the greatest public health challenges in modern times, with no proven cure or vaccine. In this paper, our focus is on a fractional order approach to modeling and simulations of the novel COVID-19. We introduce a fractional type susceptible-exposed-infected-recovered (SEIR) model to gain insight into the ongoing pandemic. Our proposed model incorporates transmission rate, testing rates, and transition rate (from asymptomatic to symptomatic population groups) for a holistic study of the coronavirus disease. The impacts of these parameters on the dynamics of the solution profiles for the disease are simulated and discussed in detail. Furthermore, across all the different parameters, the effects of the fractional order derivative are also simulated and discussed in detail. Various simulations carried out enable us gain deep insights into the dynamics of the spread of COVID-19. The simulation results confirm that fractional calculus is an appropriate tool in modeling the spread of a complex infectious disease such as the novel COVID-19. In the absence of vaccine and treatment, our analysis strongly supports the significance reduction in the transmission rate as a valuable strategy to curb the spread of the virus. Our results suggest that tracing and moving testing up has an important benefit. It reduces the number of infected individuals in the general public and thereby reduces the spread of the pandemic. Once the infected individuals are identified and isolated, the interaction between susceptible and infected individuals diminishes and transmission reduces. Furthermore, aggressive testing is also highly recommended.

To forecast the spread tendency of the COVID-19 in China and provide effective strategies to prevent the disease, an improved SEIR model was established. The parameters of our model were estimated based on collected data that were issued by the National Health Commission of China (NHCC) from January 10 to March 3. The model was used to forecast the spread tendency of the disease. The key factors influencing the epidemic were explored through modulation of the parameters, including the removal rate, the average number of the infected contacting the susceptible per day and the average number of the exposed contacting the susceptible per day. The correlation of the infected is 99.9% between established model data in this study and issued data by NHCC from January 10 to February 15. The correlation of the removed, the death and the cured are 99.8%, 99.8% and 99.6%, respectively. The average forecasting error rates of the infected, the removed, the death and the cured are 0.78%, 0.75%, 0.35% and 0.83%, respectively, from February 16 to March 3. The peak time of the epidemic forecast by our established model coincided with the issued data by NHCC. Therefore, our study established a mathematical model with high accuracy. The aforementioned parameters significantly affected the trend of the epidemic, suggesting that the exposed and the infected population should be strictly isolated. If the removal rate increases to 0.12, the epidemic will come to an end on May 25. In conclusion, the proposed mathematical model accurately forecast the spread tendency of COVID-19 in China and the model can be applied for other countries with appropriate modifications.

This paper aims to study the impact of using an educational strategy on reducing the efforts needed to control respiratory transmitted infections represented by SIR models, taking into account heterogeneity in contacts between infected and non-infected individuals. Therefore, a new incidence function, in which the difference in contact time activity between infected and non-infected individuals is taken into account, is formulated. Equilibrium and stability analyses of the model have been carried out. The model has been extended to include the effect of herd immunity and the analysis showed that the higher the percent reduction ${\hat{P}}_r$ in the contact-activity time of infected individuals is, the lower the critical vaccination coverage level $p_c$ required to eliminate the infection is, and therefore, the lower the infection's minimum elimination effort is. Another extension of the basic model to include a control strategy based on treating infected individuals at rate α with a maximum capacity treatment $I$ has been considered. The equilibrium analysis showed the existence of multiple subcritical and supercritical endemic equilibria, while the stability analysis showed that the model exhibits a Hopf bifurcation. Simulations showed that the higher the maximum treatment capacity $I$ is, the lower the value of the critical reduction in infected individuals' time activity $P_r^{\star }$ , at which a Hopf bifurcation is generated, is. Simulations with parameter values corresponding to the case of influenza A have been carried out.

Since the first case of 2019 novel coronavirus disease (COVID-19) detected on 30 January, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April, 2020. Taking this into account, in the present work, we have analysed a Bats-Hosts-Reservoir-People transmission fractional-order COVID-19 model for simulating the potential transmission with the thought of individual response and control measures by the government. The real data available about number of infected cases from 14 March, 2000 to 26 March, 2020 is analysed and, accordingly, various parameters of the model are estimated or fitted. The Picard successive approximation technique and Banach's fixed point theory have been used for verification of the existence and stability criteria of the model. Further, we conduct stability analysis for both disease-free and endemic equilibrium states. On the basis of sensitivity analysis and dynamics of the threshold parameter, we estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies of the disease using the proposed model. Numerical computations are carried out utilising the iterative Laplace transform method and comparative study of different fractional differential operators is done. The impacts of various biological parameters on transmission dynamics of COVID-19 is investigated. Finally, we illustrate the obtained results graphically.

In the present paper, we formulate a new mathematical model for the dynamics of COVID-19 with quarantine and isolation. Initially, we provide a brief discussion on the model formulation and provide relevant mathematical results. Then, we consider the fractal-fractional derivative in Atangana-Baleanu sense, and we also generalize the model. The generalized model is used to obtain its stability results. We show that the model is locally asymptotically stable if $R_0<1$ . Further, we consider the real cases reported in China since January 11 till April 9, 2020. The reported cases have been used for obtaining the real parameters and the basic reproduction number for the given period, $R_0\approx 6.6361$ . The data of reported cases versus model for classical and fractal-factional order are presented. We show that the fractal-fractional order model provides the best fitting to the reported cases. The fractional mathematical model is solved by a novel numerical technique based on Newton approach, which is useful and reliable. A brief discussion on the graphical results using the novel numerical procedures are shown. Some key parameters that show significance in the disease elimination from the society are explored.

The current effort is devoted to investigating and exploring the stochastic nonlinear mathematical pandemic model to describe the dynamics of the novel coronavirus. The model adopts the form of a nonlinear stochastic susceptible-infected-treated-recovered system, and we investigate the stochastic reproduction dynamics, both analytically and numerically. We applied different standard and nonstandard computational numerical methods for the solution of the stochastic system. The design of a nonstandard computation method for the stochastic system is innovative. Unfortunately, standard computation numerical methods are time-dependent and violate the structure properties of models, such as positivity, boundedness, and dynamical consistency of the stochastic system. To that end, convergence analysis of nonstandard computational methods and simulation with a comparison of standard computational methods are presented.