Modeling the Transmission Dynamics of COVID-19 Pandemic in Caputo Type Fractional Derivative

COVID-19 disease, a deadly pandemic ravaging virtually throughout the world today, is undoubtedly a great calamity to human existence. There exists no complete curative medicine or successful vaccines that could be used for the complete control of this deadly pandemic at the moment. Consequently, the study of the trends of this pandemic is critical and of great importance for disease control and risk management. Computation of the basic reproduction number by means of mathematical modeling can be helpful in estimating the potential and severity of an outbreak and providing insightful information which is useful to identify disease intensity and necessary interventions. Considering the enormity of the challenge and the burdens which the spread of this COVID-19 disease placed on healthcare system, the present paper attempts to study the pattern and the trend of spread of this disease and prescribes a mathematical model which governs COVID-19 pandemic using Caputo type derivative. Local stability of the equilibria is also discussed in the paper. Some numerical simulations are given to illustrate the analytical results. The obtained results shows that applied numerical technique is computationally strong for modeling COVID-19 pandemic.

[1]  Abdon Atangana,et al.  Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative , 2020, Alexandria Engineering Journal.

[2]  Mehmet Yavuz,et al.  Stability Analysis and Numerical Computation of the Fractional Predator–Prey Model with the Harvesting Rate , 2020, Fractal and Fractional.

[3]  Saeid Abbasbandy,et al.  Valid implementation of Sinc-collocation method to solve the fuzzy Fredholm integral equation , 2020, J. Comput. Appl. Math..

[4]  K. M. Owolabi.  Mathematical modelling and analysis of love dynamics: A fractional approach , 2019, Physica A: Statistical Mechanics and its Applications.

[5]  Parvaiz Ahmad Naik,et al.  Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control , 2020, Chaos, Solitons & Fractals.

[6]  Jian Zu,et al.  A novel evolutionary model for constructing gene coexpression networks with comprehensive features , 2019, BMC Bioinformatics.

[7]  Jian Zu,et al.  The role of prostitution on HIV transmission with memory: A modeling approach , 2020 .

[8]  Tian-mu Chen,et al.  A mathematical model for simulating the phase-based transmissibility of a novel coronavirus , 2020, Infectious Diseases of Poverty.

[9]  T. Abdeljawad,et al.  Nonlinear regularized long-wave models with a new integral transformation applied to the fractional derivative with power and Mittag-Leffler kernel , 2020 .

[10]  Mehmet Yavuz,et al.  Characterizations of two different fractional operators without singular kernel , 2019, Mathematical Modelling of Natural Phenomena.

[11]  Saeid Abbasbandy,et al.  Finding optimal convergence control parameter in the homotopy analysis method to solve integral equations based on the stochastic arithmetic , 2018, Numerical Algorithms.

[12]  Abdon Atangana,et al.  Mathematical analysis of dengue fever outbreak by novel fractional operators with field data , 2019, Physica A: Statistical Mechanics and its Applications.

[13]  José Francisco Gómez-Aguilar,et al.  Modelling, analysis and simulations of some chaotic systems using derivative with Mittag–Leffler kernel , 2019, Chaos, Solitons & Fractals.

[14]  Parvaiz Ahmad Naik,et al.  Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells , 2020 .

[16]  Ebenezer Bonyah,et al.  New approaches to the fractional dynamics of schistosomiasis disease model , 2019, Physica A: Statistical Mechanics and its Applications.

[17]  A. Atangana,et al.  Fractal-fractional differentiation for the modeling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data , 2020 .

[18]  Y. Hayashi,et al.  An Overview of Severe Acute Respiratory Syndrome–Coronavirus (SARS-CoV) 3CL Protease Inhibitors: Peptidomimetics and Small Molecule Chemotherapy , 2016, Journal of medicinal chemistry.

[19]  K. M. Owolabi,et al.  Fractional operator method on a multi-mutation and intrinsic resistance model , 2020 .

[20]  Ning Wang,et al.  Serological Evidence of Bat SARS-Related Coronavirus Infection in Humans, China , 2018, Virologica Sinica.

[21]  A. Atangana,et al.  Numerical Methods for Fractional Differentiation , 2019, Springer Series in Computational Mathematics.

[22]  P. Daszak,et al.  Human-animal interactions and bat coronavirus spillover potential among rural residents in Southern China , 2019, Biosafety and Health.

[23]  Abdon Atangana,et al.  Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination? , 2020, Chaos, Solitons & Fractals.

[24]  Parvaiz Ahmad Naik,et al.  Modeling the mechanics of viral kinetics under immune control during primary infection of HIV-1 with treatment in fractional order , 2020 .

[25]  Jianhong Wu,et al.  Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions , 2020, Journal of clinical medicine.

[26]  Samad Noeiaghdam.  A novel technique to solve the modified epidemiological model of computer viruses , 2019 .

[27]  Abdon Atangana,et al.  Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative , 2019, Chaos, Solitons & Fractals.

[28]  J. Zu,et al.  Transmission patterns of COVID-19 in the mainland of China and the efficacy of different control strategies: a data- and model-driven study , 2020, Infectious Diseases of Poverty.