Advances in Difference Equations最新文献

{"title":"Mathematical model of COVID-19 spread in Turkey and South Africa: theory, methods, and applications.","authors":"Abdon Atangana,&nbsp;Seda İğret Araz","doi":"10.1186/s13662-020-03095-w","DOIUrl":"https://doi.org/10.1186/s13662-020-03095-w","url":null,"abstract":"<p><p>A comprehensive study about the spread of COVID-19 cases in Turkey and South Africa has been presented in this paper. An exhaustive statistical analysis was performed using data collected from Turkey and South Africa within the period of 11 March 2020 to 3 May 2020 and 05 March and 3 of May, respectively. It was observed that in the case of Turkey, a negative Spearman correlation for the number of infected class and a positive Spearman correlation for both the number of deaths and recoveries were obtained. This implied that the daily infections could decrease, while the daily deaths and number of recovered people could increase under current conditions. In the case of South Africa, a negative Spearman correlation for both daily deaths and daily infected people were obtained, indicating that these numbers may decrease if the current conditions are maintained. The utilization of a statistical technique predicted the daily number of infected, recovered, and dead people for each country; and three results were obtained for Turkey, namely an upper boundary, a prediction from current situation and lower boundary. The histograms of the daily number of newly infected, recovered and death showed a sign of lognormal and normal distribution, which is presented using the Bell curving method parameters estimation. A new mathematical model COVID-19 comprised of nine classes was suggested; of which a formula of the reproductive number, well-poseness of the solutions and the stability analysis were presented in detail. The suggested model was further extended to the scope of nonlocal operators for each case; whereby a numerical method was used to provide numerical solutions, and simulations were performed for different non-integer numbers. Additionally, sections devoted to control optimal and others dedicated to compare cases between Turkey and South Africa with the aim to comprehend why there are less numbers of deaths and infected people in South Africa than Turkey were presented in detail.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2020 1","pages":"659"},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7758164/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38775740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence theory and numerical analysis of three species prey-predator model under Mittag-Leffler power law.","authors":"Mohammed S Abdo,&nbsp;Satish K Panchal,&nbsp;Kamal Shah,&nbsp;Thabet Abdeljawad","doi":"10.1186/s13662-020-02709-7","DOIUrl":"https://doi.org/10.1186/s13662-020-02709-7","url":null,"abstract":"<p><p>In this manuscript, the fractional Atangana-Baleanu-Caputo model of prey and predator is studied theoretically and numerically. The existence and Ulam-Hyers stability results are obtained by applying fixed point theory and nonlinear analysis. The approximation solutions for the considered model are discussed via the fractional Adams Bashforth method. Moreover, the behavior of the solution to the given model is explained by graphical representations through the numerical simulations. The obtained results play an important role in developing the theory of fractional analytical dynamic of many biological systems.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2020 1","pages":"249"},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-020-02709-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38012752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fuzzy fractional-order model of the novel coronavirus.","authors":"S Ahmad, A Ullah, K Shah, S Salahshour, A Ahmadian, T Ciano","doi":"10.1186/s13662-020-02934-0","DOIUrl":"10.1186/s13662-020-02934-0","url":null,"abstract":"<p><p>In this paper, a novel coronavirus infection system with a fuzzy fractional differential equation defined in Caputo's sense is developed. By using the fuzzy Laplace method coupled with Adomian decomposition transform, numerical results are obtained for better understanding of the dynamical structures of the physical behavior of COVID-19. Such behavior on the general properties of RNA in COVID-19 is also investigated for the governing model. The results demonstrate the efficiency of the proposed approach to address the uncertainty condition in the pandemic situation.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2020 1","pages":"472"},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7474331/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38374887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation.","authors":"Qinxu Ding, Patricia J Y Wong","doi":"10.1186/s13662-020-03021-0","DOIUrl":"10.1186/s13662-020-03021-0","url":null,"abstract":"<p><p>In this paper, we shall solve a time-fractional nonlinear Schrödinger equation by using the quintic non-polynomial spline and the <i>L</i>1 formula. The unconditional stability, unique solvability and convergence of our numerical scheme are proved by the Fourier method. It is shown that our method is sixth order accurate in the spatial dimension and <math><mo>(</mo> <mn>2</mn> <mo>-</mo> <mi>γ</mi> <mo>)</mo></math> th order accurate in the temporal dimension, where <i>γ</i> is the fractional order. The efficiency of the proposed numerical scheme is further illustrated by numerical experiments, meanwhile the simulation results indicate better performance over previous work in the literature.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2020 1","pages":"577"},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7565234/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38606596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A study on COVID-19 transmission dynamics: stability analysis of SEIR model with Hopf bifurcation for effect of time delay.","authors":"M Radha, S Balamuralitharan","doi":"10.1186/s13662-020-02958-6","DOIUrl":"10.1186/s13662-020-02958-6","url":null,"abstract":"<p><p>This paper deals with a general SEIR model for the coronavirus disease 2019 (COVID-19) with the effect of time delay proposed. We get the stability theorems for the disease-free equilibrium and provide adequate situations of the COVID-19 transmission dynamics equilibrium of present and absent cases. A Hopf bifurcation parameter <i>τ</i> concerns the effects of time delay and we demonstrate that the locally asymptotic stability holds for the present equilibrium. The reproduction number is brief in less than or greater than one, and it effectively is controlling the COVID-19 infection outbreak and subsequently reveals insight into understanding the patterns of the flare-up. We have included eight parameters and the least square method allows us to estimate the initial values for the Indian COVID-19 pandemic from real-life data. It is one of India's current pandemic models that have been studied for the time being. This Covid19 SEIR model can apply with or without delay to all country's current pandemic region, after estimating parameter values from their data. The sensitivity of seven parameters has also been explored. The paper also examines the impact of immune response time delay and the importance of determining essential parameters such as the transmission rate using sensitivity indices analysis. The numerical experiment is calculated to illustrate the theoretical results.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2020 1","pages":"523"},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7513461/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38434194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Monotonicity properties for a ratio of finite many gamma functions.","authors":"Feng Qi, Dongkyu Lim","doi":"10.1186/s13662-020-02655-4","DOIUrl":"10.1186/s13662-020-02655-4","url":null,"abstract":"<p><p>In the paper, the authors consider a ratio of finite many gamma functions and find its monotonicity properties such as complete monotonicity, the Bernstein function property, and logarithmically complete monotonicity.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2020 1","pages":"193"},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7194249/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37905254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New investigation of bats-hosts-reservoir-people coronavirus model and application to 2019-nCoV system.","authors":"Wei Gao,&nbsp;Haci Mehmet Baskonus,&nbsp;Li Shi","doi":"10.1186/s13662-020-02831-6","DOIUrl":"https://doi.org/10.1186/s13662-020-02831-6","url":null,"abstract":"<p><p>According to the report presented by the World Health Organization, a new member of viruses, namely, coronavirus, shortly 2019-nCoV, which arised in Wuhan, China, on January 7, 2020, has been introduced to the literature. The main aim of this paper is investigating and finding the optimal values for better understanding the mathematical model of the transfer of 2019-nCoV from the reservoir to people. This model, named Bats-Hosts-Reservoir-People coronavirus (BHRPC) model, is based on bats as essential animal beings. By using a powerful numerical method we obtain simulations of its spreading under suitably chosen parameters. Whereas the obtained results show the effectiveness of the theoretical method considered for the governing system, the results also present much light on the dynamic behavior of the Bats-Hosts-Reservoir-People transmission network coronavirus model.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2020 1","pages":"391"},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-020-02831-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38297076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On modeling of coronavirus-19 disease under Mittag-Leffler power law.","authors":"Samia Bushnaq,&nbsp;Kamal Shah,&nbsp;Hussam Alrabaiah","doi":"10.1186/s13662-020-02943-z","DOIUrl":"https://doi.org/10.1186/s13662-020-02943-z","url":null,"abstract":"<p><p>This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivative has been introduced by Atangana, Baleanu, and Caputo abbreviated as <math><mo>(</mo> <mi>ABC</mi> <mo>)</mo></math> . Upon utilizing fixed point theory, we first prove the existence of at least one solution for the considered model and its uniqueness. Also, some results about stability of Ulam-Hyers type are also established. By applying a numerical technique called fractional Adams-Bashforth (AB) method, we develop a scheme for the approximate solutions to the considered model. Using some real available data, we perform the concerned numerical simulation corresponding to different values of fractional order.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2020 1","pages":"487"},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-020-02943-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38386901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling the effect of delay strategy on transmission dynamics of HIV/AIDS disease.","authors":"Ali Raza,&nbsp;Ali Ahmadian,&nbsp;Muhammad Rafiq,&nbsp;Soheil Salahshour,&nbsp;Muhammad Naveed,&nbsp;Massimiliano Ferrara,&nbsp;Atif Hassan Soori","doi":"10.1186/s13662-020-03116-8","DOIUrl":"https://doi.org/10.1186/s13662-020-03116-8","url":null,"abstract":"<p><p>In this manuscript, we investigate a nonlinear delayed model to study the dynamics of human-immunodeficiency-virus in the population. For analysis, we find the equilibria of a susceptible-infectious-immune system with a delay term. The well-established tools such as the Routh-Hurwitz criterion, Volterra-Lyapunov function, and Lasalle invariance principle are presented to investigate the stability of the model. The reproduction number and sensitivity of parameters are investigated. If the delay tactics are decreased, then the disease is endemic. On the other hand, if the delay tactics are increased then the disease is controlled in the population. The effect of the delay tactics with subpopulations is investigated. More precisely, all parameters are dependent on delay terms. In the end, to give the strength to a theoretical analysis of the model, a computer simulation is presented.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2020 1","pages":"663"},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-020-03116-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38651701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative.","authors":"Dumitru Baleanu,&nbsp;Hakimeh Mohammadi,&nbsp;Shahram Rezapour","doi":"10.1186/s13662-020-02762-2","DOIUrl":"https://doi.org/10.1186/s13662-020-02762-2","url":null,"abstract":"<p><p>We present a fractional-order model for the COVID-19 transmission with Caputo-Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2020 1","pages":"299"},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-020-02762-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38073700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}