ABSTRACT
Research focus on optimal control problems brought on by fractional differential equations has been extensively applied in practice. However, because they are still open ended and challenging, a number of problems with fractional mathematical modeling and problems with optimal control require additional study. Using fractional-order derivatives defined in the Atangana–Baleanu–Caputo sense, we alter the integer-order model that has been proposed in the literature. We prove the solution's existence, uniqueness, equilibrium points, fundamental reproduction number, and local stability of the equilibrium points. The operator's numerical approach was put into practice to obtain a numerical simulation to back up the analytical conclusions. Fractional optimum controls were incorporated into the model to identify the most efficient intervention strategies for controlling the disease. Utilizing actual data from Ghana for the months of March 2020 to March 2021, the model is validated. The simulation's results show that the fractional operator significantly affected each compartment and that the incidence rate of the population rose when v≥0.6. The examination of the most effective control technique discovered that social exclusion and vaccination were both very effective methods for halting the development of the illness.
ABSTRACT
Coronavirus has become a serious global phenomenon in recent times and has negative effects on the entire world economy. In this study, a fractional mathematical model formulated in fractional conformable derivative is studied. The model hinges on the concept of mammal hosts and humans. The basic properties of the coronavirus model are investigated. The stability analysis is carried out as well as sensitivity analysis based on the reproduction number. Numerical simulation is undertaken to give impetus to the analytical results which indicate that both fractional conformable order derivative and fractional-order derivative have serious consequences in numerical result outcomes.
ABSTRACT
In this article, we investigated a deterministic model of pneumonia-meningitis coinfection. Employing the Atangana–Baleanu fractional derivative operator in the Caputo framework, we analyze a seven-component approach based on ordinary differential equations (DEs). Furthermore, the invariant domain, disease-free as well as endemic equilibria, and the validity of the model’s potential results are all investigated. According to controller design evaluation and modelling, the modulation technique devised is effective in diminishing the proportion of incidences in various compartments. A fundamental reproducing value is generated by exploiting the next generation matrix to assess the properties of the equilibrium. The system’s reliability is further evaluated. Sensitivity analysis is used to classify the impact of each component on the spread or prevention of illness. Using simulation studies, the impacts of providing therapy have been determined. Additionally, modelling the appropriate configuration demonstrated that lowering the fractional order from 1 necessitates a rapid initiation of the specified control technique at the largest intensity achievable and retaining it for the bulk of the pandemic’s duration.
ABSTRACT
This research study focuses on the analytical behavior and numerical computation of the fractional order Ebola model. In this study we have calculated the conditions for the existence, uniqueness, and stability of the solution with the help of the fixed point results. In addition to this, we calculated the numerical solution of the fractional order smoke model with the help two-step fractional Adam’s Bashforth method using the Caputo’s fractional derivative of order μ. Furthermore, the results obtained for different orders of the fractional derivative μ have been shown graphically with the help of Matlab.
ABSTRACT
This paper is devoted to answering some questions using a mathematical model by analyzing India's first and second phases of the COVID-19 pandemic. A new mathematical model is introduced with a nonmonotonic incidence rate to incorporate the psychological effect of COVID-19 in society. The paper also discusses the local stability and global stability of an endemic equilibrium and a disease-free equilibrium. The basic reproduction number is evaluated using the proposed COVID-19 model for disease spread in India based on the actual data sets. The study of nonperiodic solutions at a positive equilibrium point is also analyzed. The model is rigorously studied using MATLAB to alert the decision-making bodies to hinder the emergence of any other pandemic outbreaks or the arrival of subsequent pandemic waves. This paper shows the excellent prediction of the first wave and very commanding for the second wave. The exciting results of the paper are as follows: (i) psychological effect on the human population has an impact on propagation; (ii) lockdown is a suitable technique mathematically to control the COVID spread; (iii) different variants produce different waves; (iv) the peak value always crosses its past value.
Subject(s)
COVID-19 , COVID-19/epidemiology , COVID-19/prevention & control , Communicable Disease Control/methods , Humans , Pandemics/prevention & control , SARS-CoV-2 , VaccinationABSTRACT
[...]many discus the dynamics through immune response toward viruses [6, 7]. [...]there are some models which work on free viruses without taking immune response into a reaction of considering viruses [8–12]. Many models dealt with immune reaction as a separate model [13]. [...]the growth of tumor with undamped oscillatory cancer cells is used to transient diminution of the severity of disease. In this recent work, a model presented is considered as a special case of Dingli et al.’s model [18];in this, assumption is made on logistic growth of a tumor, and this model discussed cancer that is aggressive in nature. [...]the replication of tumors is accordingly to their size. [...]the mathematical term ( −βIV) describes the elimination of viruses included in free viruses V due to infection of uninfected cells ( I).
ABSTRACT
Most countries around the world are battling to limit the spread of severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2). As the world strives to get an effective medication to control the disease, appropriate control measures for now remains one of the effective measures to reduce the spread of the disease. In this study, a fractional optimal control model is formulated in Atangana-Baleanu-Caputo derivative sense. The reproduction number and steady state of disease free of the Coronavirus model are examined and found to be globally stable. The existence and uniqueness of solution of the fractional Coronavirus model is established by using the Banach fixed point theorem approach. Three controls are considered in the model and Pontryagins Maximum Principle is used to establish the necessary conditions for optimal control solution. The numerical solution suggests that the best strategy is found to be the utilization of all three controls at the same time.
ABSTRACT
Coronavirus, in recent times, has been noticed to be highly contagious killing a lot of people in in the world. This has attracted global attention because of its negative effect on global economy. This paper seeks to examine the disease in the light of both conformable and fractal fractional derivative in Livioullile-Caputo order sense. The bounded solution of the model is established. The steady states of the model examined and detailed numerical schemes for each method derivatives are presented. It is established that fractional orders have significant roles in the dynamics of the coronavirus spread in the communities. The numerical result suggests that each fractional derivative provides quality qualitative information on Coronavirus menace. [ABSTRACT FROM AUTHOR] Copyright of Mathematics in Engineering, Science & Aerospace (MESA) is the property of Nonlinear Studies and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)