Scaled Conjugate Gradient for the Numerical Simulations of the Mathematical Model-Based Monkeypox Transmission

The current study presents the numerical solutions of a fractional order monkeypox virus model. The fractional order derivatives in the sense of Caputo are applied to achieve more realistic results for the nonlinear model. The dynamics of the monkeypox virus model are categorized into eight classes, namely susceptible human, exposed human, infectious human, clinically ill human, recovered human, susceptible rodent, exposed rodent and infected rodent. Three different fractional order cases have been presented for the numerical solutions of the mathematical monkeypox virus model by applying the stochastic computing performances through the artificial intelligence-based scaled conjugate gradient neural networks. The statics for the system were selected as 83%, 10% and 7% for training, testing and validation, respectively. The exactness of the stochastic procedure is presented through the performances of the obtained results and the reference Adams results. The rationality and constancy are presented through the stochastic solutions together with simulations based on the state transition measures, regression, error histogram performances and correlation.

[1]  M. Raja,et al.  Stochastic procedures to solve the nonlinear mass and heat transfer model of Williamson nanofluid past over a stretching sheet , 2023, Annals of Nuclear Energy.

[2]  Z. Sabir,et al.  IoT technology enabled stochastic computing paradigm for numerical simulation of heterogeneous mosquito model , 2022, Multimedia Tools and Applications.

[3]  Z. Sabir,et al.  A numerical performance of the novel fractional water pollution model through the Levenberg-Marquardt backpropagation method , 2022, Arabian Journal of Chemistry.

[4]  O. J. Peter,et al.  Fractional order mathematical model of monkeypox transmission dynamics , 2022, Physica Scripta.

[5]  Mati ur Rahman,et al.  Investigation of fractional order bacteria dependent disease with the effects of different contact rates , 2022, Chaos, Solitons & Fractals.

[6]  Delfim F. M. Torres,et al.  Fractional Modelling and Optimal Control of COVID-19 Transmission in Portugal , 2022, Axioms.

[7]  Mati ur Rahman,et al.  Fractional Mathematical Modeling to the Spread of Polio with the Role of Vaccination under Non-singular Kernel , 2022, Fractals.

[8]  A. Akgül,et al.  Fractional order COVID-19 model with transmission rout infected through environment , 2022, AIMS Mathematics.

[9]  F. Lienert,et al.  The changing epidemiology of human monkeypox—A potential threat? A systematic review , 2021, medRxiv.

[10]  S. Salahshour,et al.  Fractal–fractional dynamical system of Typhoid disease including protection from infection , 2021, Engineering with Computers.

[11]  O. J. Peter,et al.  Transmission dynamics of Monkeypox virus: a mathematical modelling approach , 2021, Modeling Earth Systems and Environment.

[12]  Yongjin Li,et al.  ON ANALYSIS OF FRACTIONAL ORDER MATHEMATICAL MODEL OF HEPATITIS B USING ATANGANA–BALEANU CAPUTO (ABC) DERIVATIVE , 2021, Fractals.

[13]  Sania Qureshi,et al.  Modeling of measles epidemic with optimized fractional order under Caputo differential operator , 2021 .

[14]  O. J. Peter,et al.  A new mathematical model of COVID-19 using real data from Pakistan , 2021, Results in Physics.

[15]  Muhammad Aslam,et al.  A fractional order HIV/AIDS epidemic model with Mittag-Leffler kernel , 2021 .

[16]  Ram Singh,et al.  Numerical solution of hybrid mathematical model of dengue transmission with relapse and memory via Adam–Bashforth–Moulton predictor-corrector scheme , 2021 .

[17]  D. Baleanu,et al.  On the weighted fractional integral inequalities for Chebyshev functionals , 2021, Advances in Difference Equations.

[18]  Juan Luis García Guirao,et al.  Solving a novel designed second order nonlinear Lane-Emden delay differential model using the heuristic techniques , 2021, Appl. Soft Comput..

[19]  K. A. Abro Numerical study and chaotic oscillations for aerodynamic model of wind turbine via fractal and fractional differential operators , 2020, Numerical Methods for Partial Differential Equations.

[20]  U. Moens,et al.  Monkeypox Virus in Nigeria: Infection Biology, Epidemiology, and Evolution , 2020, Viruses.

[21]  Isa Abdullahi Baba,et al.  Fractional order epidemic model for the dynamics of novel COVID-19 , 2020, Alexandria Engineering Journal.

[22]  Zulqurnain Sabir,et al.  Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model , 2020 .

[23]  M. Khan,et al.  A new model of dengue fever in terms of fractional derivative. , 2020, Mathematical biosciences and engineering : MBE.

[24]  J. Rychtář,et al.  A game-theoretic model of Monkeypox to assess vaccination strategies , 2020, PeerJ.

[25]  Manar A. Alqudah,et al.  Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo–Febrizio fractional order derivative , 2020 .

[26]  Esin Ilhan,et al.  A generalization of truncated M-fractional derivative and applications to fractional differential equations , 2020, Applied Mathematics and Nonlinear Sciences.

[27]  B. Ghanbari,et al.  Mathematical and numerical analysis of a three‐species predator‐prey model with herd behavior and time fractional‐order derivative , 2019, Mathematical Methods in the Applied Sciences.

[28]  M. Khan,et al.  Modeling the transmission of dengue infection through fractional derivatives , 2019, Chaos, Solitons & Fractals.

[29]  Zakia Hammouch,et al.  Spatiotemporal patterns in the Belousov–Zhabotinskii reaction systems with Atangana–Baleanu fractional order derivative , 2019, Physica A: Statistical Mechanics and its Applications.

[30]  Fathalla A. Rihan,et al.  A fractional‐order model with time delay for tuberculosis with endogenous reactivation and exogenous reinfections , 2019, Mathematical Methods in the Applied Sciences.

[31]  Hang Cheng,et al.  Application of fractional-order derivative in the quantitative estimation of soil organic matter content through visible and near-infrared spectroscopy , 2019, Geoderma.

[32]  Asıf Yokuş,et al.  Numerical Solutions with Linearization Techniques of the Fractional Harry Dym Equation , 2019, Applied Mathematics and Nonlinear Sciences.

[33]  C. Cattani,et al.  A new general fractional-order derivataive with Rabotnov fractional-exponential kernel applied to model the anomalous heat transfer , 2019, Thermal Science.

[34]  Y. Nakazawa,et al.  Emergence of Monkeypox — West and Central Africa, 1970–2017 , 2018, MMWR. Morbidity and mortality weekly report.

[35]  I. Adamu,et al.  Modeling the Transmission Dynamics of the Monkeypox Virus Infection with Treatment and Vaccination Interventions , 2017 .

[36]  Margaret A Dudeck,et al.  Antimicrobial-Resistant Pathogens Associated With Healthcare-Associated Infections: Summary of Data Reported to the National Healthcare Safety Network at the Centers for Disease Control and Prevention, 2011–2014 , 2016, Infection Control & Hospital Epidemiology.

[37]  Haiyan Hu,et al.  Measuring memory with the order of fractional derivative , 2013, Scientific Reports.

[38]  Fajun Yu,et al.  Integrable coupling system of fractional soliton equation hierarchy , 2009 .

[39]  C. Bhunu,et al.  Mathematical Analysis of a Two Strain HIV/AIDS Model with Antiretroviral Treatment , 2009, Acta Biotheoretica.

[40]  Rabha W. Ibrahim,et al.  On a fractional integral equation of periodic functions involving Weyl–Riesz operator in Banach algebras , 2008 .

[41]  Rabha W. Ibrahim,et al.  On the existence and uniqueness of solutions of a class of fractional differential equations , 2007 .

[42]  Margarita Rivero,et al.  On systems of linear fractional differential equations with constant coefficients , 2007, Appl. Math. Comput..

[43]  N. Ford,et al.  Analysis of Fractional Differential Equations , 2002 .

[44]  Grab,et al.  Human monkeypox: confusion with chickenpox. , 1988, Acta tropica.