{"title":"涉及卡普托-法布里齐奥导数的 COVID-19 数学模型传输动力学的理论和数值分析。","authors":"Sabri T M Thabet, Mohammed S Abdo, Kamal Shah","doi":"10.1186/s13662-021-03316-w","DOIUrl":null,"url":null,"abstract":"<p><p>This manuscript is devoted to a study of the existence and uniqueness of solutions to a mathematical model addressing the transmission dynamics of the coronavirus-19 infectious disease (COVID-19). The mentioned model is considered with a nonsingular kernel type derivative given by Caputo-Fabrizo with fractional order. For the required results of the existence and uniqueness of solution to the proposed model, Picard's iterative method is applied. Furthermore, to investigate approximate solutions to the proposed model, we utilize the Laplace transform and Adomian's decomposition (LADM). Some graphical presentations are given for different fractional orders for various compartments of the model under consideration.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2021 1","pages":"184"},"PeriodicalIF":4.1000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7988648/pdf/","citationCount":"0","resultStr":"{\"title\":\"Theoretical and numerical analysis for transmission dynamics of COVID-19 mathematical model involving Caputo-Fabrizio derivative.\",\"authors\":\"Sabri T M Thabet, Mohammed S Abdo, Kamal Shah\",\"doi\":\"10.1186/s13662-021-03316-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>This manuscript is devoted to a study of the existence and uniqueness of solutions to a mathematical model addressing the transmission dynamics of the coronavirus-19 infectious disease (COVID-19). The mentioned model is considered with a nonsingular kernel type derivative given by Caputo-Fabrizo with fractional order. For the required results of the existence and uniqueness of solution to the proposed model, Picard's iterative method is applied. Furthermore, to investigate approximate solutions to the proposed model, we utilize the Laplace transform and Adomian's decomposition (LADM). Some graphical presentations are given for different fractional orders for various compartments of the model under consideration.</p>\",\"PeriodicalId\":53311,\"journal\":{\"name\":\"Advances in Difference Equations\",\"volume\":\"2021 1\",\"pages\":\"184\"},\"PeriodicalIF\":4.1000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7988648/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Difference Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1186/s13662-021-03316-w\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2021/3/24 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Difference Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13662-021-03316-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2021/3/24 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Theoretical and numerical analysis for transmission dynamics of COVID-19 mathematical model involving Caputo-Fabrizio derivative.
This manuscript is devoted to a study of the existence and uniqueness of solutions to a mathematical model addressing the transmission dynamics of the coronavirus-19 infectious disease (COVID-19). The mentioned model is considered with a nonsingular kernel type derivative given by Caputo-Fabrizo with fractional order. For the required results of the existence and uniqueness of solution to the proposed model, Picard's iterative method is applied. Furthermore, to investigate approximate solutions to the proposed model, we utilize the Laplace transform and Adomian's decomposition (LADM). Some graphical presentations are given for different fractional orders for various compartments of the model under consideration.
期刊介绍：
The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions.
The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between.
The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations.
Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.
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