ABSTRACT
2020 has witnessed a rapidly spread pandemic COVID-19 which is one of the worst in the history of mankind. Scientists believe that COVID-19 spreads mainly from a person to another. Recent researches consider bats as a vector for COVID-19. This paper suggests a variable fractional order model for COVID-19 to figure out how bats and hosts interact, and how the seafood market affect people. The proposed model assumes that infection cannot be recovered. The basic reproduction number R0 for real data on reported cases in Wuhan China was computed. Disease-free equilibrium points and proposed model stability are studied. © 2022 NSP
ABSTRACT
In this work, we generalize the multi-vaccination for COVID-19 mathematical model to the variable-order fractional derivative case by replacing the first-order derivative with the variable-order fractional Atangana-Baleanu-Caputo operator. Moreover, the parameters of the proposed model are dependent on the variable-order fractional derivative. We use an amended numerical technique to build an asymptotically stable difference scheme. The proposed scheme accurately simulates the behavior of the solution of the presented model. Some properties, boundedness, and positivity of the studied system are proved analytically. The introduced scheme preserves these properties of the analytic solutions. Numerical treatment is run out for testing the reliability, applicability, and simplicity of this scheme. Comparitive study bettween the obtained results using the discretization of Atangana-Baleanu-Caputo derivative and nonstandard finite differeance method with the results which obtained using the discretization of the operator Yang-Abdel-Cattani is given.
ABSTRACT
A novel coronavirus is a serious global issue and has a negative impact on the economy of Egypt. According to the publicly reported data, the first case of the novel corona virus in Egypt was reported on 14 February 2020. Total of 96753 cases were recorded in Egypt from the beginning of the pandemic until the eighteenth of August, where 96, 581 individuals were Egyptians and 172 were foreigners. Recently, many mathematical models have been considered to better understand coronavirus infection. Most of these models are based on classical integer-order derivatives which can not capture the fading memory and crossover behavior found in many biological phenomena. Therefore, we study the coronavirus disease in this paper by exploring the dynamics of COVID-19 infection using new variable-order fractional derivatives. This paper presents an optimal control problem of the hybrid variable-order fractional model of Coronavirus. The variable-order fractional operator is modified by an auxiliary parameter in order to satisfy the dimensional matching between the both sides of the resultant variable-order fractional equations. Existence, uniqueness, boundedness, positivity, local and global stability of the solutions are proved. Two control variables are considered to reduce the transmission of infection into healthy people. To approximate the new hybrid variable-order operator, Grünwald-Letnikov approximation is used. Finite difference method with a hybrid variable-order operator and generalized fourth order Runge-Kutta method are used to solve the optimality system. Numerical examples and comparative studies for testing the applicability of the utilized methods and to show the simplicity of these approximation approaches are presented. Moreover, by using the proposed methods we can concluded that, the model given in this paper describes well the confirmed real data given by WHO about Egypt.
ABSTRACT
In this work, a novel mathematical model of Coronavirus (2019-nCov) with general population mask use with modified parameters. The proposed model consists of fourteen fractional-order nonlinear differential equations. Grünwald-Letnikov approximation is used to approximate the new hybrid fractional operator. Compact finite difference method of six order with a new hybrid fractional operator is developed to study the proposed model. Stability analysis of the used methods are given. Comparative studies with generalized fourth order Runge–Kutta method are given. It is found that, the proposed model can be described well the real data of daily confirmed cases in Egypt. © 2021 THE AUTHORS
ABSTRACT
In this paper, a new stochastic fractional Coronavirus (2019-nCov) model with modified parameters is presented. The proposed stochastic COVID-19 model describes well the real data of daily confirmed cases in Wuhan. Moreover, a novel fractional order operator is introduced, it is a linear combination of Caputo's fractional derivative and Riemann-Liouville integral. Milstein's higher order method is constructed with the new fractional order operator to study the model problem. The mean square stability of Milstein algorithm is proved. Numerical results and comparative studies are introduced.
ABSTRACT
In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald-Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.
ABSTRACT
Introduction: Coronavirus COVID-19 pandemic is the defining global health crisis of our time and the greatest challenge we have faced since world war two. To describe this disease mathematically, we noted that COVID-19, due to uncertainties associated to the pandemic, ordinal derivatives and their associated integral operators show deficient. The fractional order differential equations models seem more consistent with this disease than the integer order models. This is due to the fact that fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes. Hence there is a growing need to study and use the fractional order differential equations. Also, optimal control theory is very important topic to control the variables in mathematical models of infectious disease. Moreover, a hybrid fractional operator which may be expressed as a linear combination of the Caputo fractional derivative and the Riemann-Liouville fractional integral is recently introduced. This new operator is more general than the operator of Caputo's fractional derivative. Numerical techniques are very important tool in this area of research because most fractional order problems do not have exact analytic solutions. Objectives: A novel fractional order Coronavirus (2019-nCov) mathematical model with modified parameters will be presented. Optimal control of the suggested model is the main objective of this work. Three control variables are presented in this model to minimize the number of infected populations. Necessary control conditions will be derived. Methods: The numerical methods used to study the fractional optimality system are the weighted average nonstandard finite difference method and the Grünwald-Letnikov nonstandard finite difference method. Results: The proposed model with a new fractional operator is presented. We have successfully applied a kind of Pontryagin's maximum principle and were able to reduce the number of infected people using the proposed numerical methods. The weighted average nonstandard finite difference method with the new operator derivative has the best results than Grünwald-Letnikov nonstandard finite difference method with the same operator. Moreover, the proposed methods with the new operator have the best results than the proposed methods with Caputo operator. Conclusions: The combination of fractional order derivative and optimal control in the Coronavirus (2019-nCov) mathematical model improves the dynamics of the model. The new operator is more general and suitable to study the optimal control of the proposed model than the Caputo operator and could be more useful for the researchers and scientists.