{"title":"The influence of prevention and isolation measures to control the infections of the fractional Chickenpox disease model","authors":"","doi":"10.1016/j.matcom.2024.07.028","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we propose a mathematical model using the Caputo fractional derivative (CFD) and two control signals to study the transmission dynamics and control of Chickenpox (Varicella) outbreak. The model consists of six compartments representing susceptible, vaccinated, exposed, infected with complications, infected without complications, and recovered individuals. We analyze the theoretical properties of the model, including existence, uniqueness, and boundedness of solutions, and calculate the basic reproduction number <span><math><mrow><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow></math></span>. We identify equilibrium points and establish conditions for their stability. Sensitivity analysis helps identify the most influential parameters on <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. We formulate a fractional optimal control problem (FOCP) by incorporating time-dependent prevention and isolation measures. The necessary optimality conditions are derived using Pontryagin’s maximum principle. Numerical simulations based on the Adams–Bashforth–Moulton (ABM) method illustrate the impact of control measures and fractional order on disease propagation. The results highlight the effectiveness of optimal controls and fractional order in understanding and managing epidemics, enhancing stability conditions. The study contributes to a better understanding of Chickenpox transmission dynamics and provides insights for disease control and management, aiding decision-makers and governments in taking preventive measures.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics and Computers in Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378475424002854","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we propose a mathematical model using the Caputo fractional derivative (CFD) and two control signals to study the transmission dynamics and control of Chickenpox (Varicella) outbreak. The model consists of six compartments representing susceptible, vaccinated, exposed, infected with complications, infected without complications, and recovered individuals. We analyze the theoretical properties of the model, including existence, uniqueness, and boundedness of solutions, and calculate the basic reproduction number . We identify equilibrium points and establish conditions for their stability. Sensitivity analysis helps identify the most influential parameters on . We formulate a fractional optimal control problem (FOCP) by incorporating time-dependent prevention and isolation measures. The necessary optimality conditions are derived using Pontryagin’s maximum principle. Numerical simulations based on the Adams–Bashforth–Moulton (ABM) method illustrate the impact of control measures and fractional order on disease propagation. The results highlight the effectiveness of optimal controls and fractional order in understanding and managing epidemics, enhancing stability conditions. The study contributes to a better understanding of Chickenpox transmission dynamics and provides insights for disease control and management, aiding decision-makers and governments in taking preventive measures.
期刊介绍:
The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles.
Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO.
Topics covered by the journal include mathematical tools in:
•The foundations of systems modelling
•Numerical analysis and the development of algorithms for simulation
They also include considerations about computer hardware for simulation and about special software and compilers.
The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research.
The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.