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Design of intelligent Bayesian supervised predictive networks for nonlinear delay differential systems of avian influenza model

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Abstract

Over the past two decades, avian influenza viruses have rapidly spread in poultry around the world. Both humans and industrial poultry are at risk from avian influenza virus infection because of their high levels of zoonotic transmission and pandemic potential. The goal of this study is to explore the implementation of a soft computing paradigm that incorporates artificial intelligence to numerically solve delayed-differential systems which portray the dynamical interfaces of a nonlinear delayed avian influenza (DAI-EM) employing a backpropagated Bayesian regularization neural network (BBR-NN) approach. The nonlinear DAI-EM is represented by the four classes: susceptible avian, infected avian, susceptible human and infected human populations. The Adams solver is utilized to construct the benchmark dataset for BBR-NN for the variability in the transmission rate between infected and susceptible avian, avian population natural mortality rate, avian population diseases associated mortality rate, rate of avian slaughter in the susceptible population, rate of avian slaughter in the infected population, transmission rate between infected avian and susceptible human, human population natural mortality rate, infective human population diseases associated mortality rate, infective human population recovery rate. The designed BBR-NN determined the numerical approximate solutions of the DAI-EM by arbitrarily choosing training, testing and validation sample points from the dataset and yielded promising agreements to the benchmark results. The competency, accuracy, and consistency of the design BBR-NN are assessed/evaluated further using a comprehensive simulation study that incorporates mean square error, error histogram, and regression analysis.

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Data availability statement

This paper is not associated with any data.

Abbreviations

DAI:

Delayed avian influenza

BBR-NN:

Backpropagated Bayesian regularization neural network

ODEs:

Ordinary differential equations

AIV:

Avian influenza viruses

SVEIR:

Susceptible-vaccinated-exposed class-infected class-removed

AI:

Artificial intelligence

ADS:

Adams numerical solver

S v(t), I v(t), S m(t), I m(t), and R m(t):

Susceptible avian-infective avian-susceptible human-infective human-removed human

S v(0), I v(0), S m(0), I m(0), and R m(0):

Initial values of susceptible avian-infective avian-susceptible human-infective human-removed human

AE:

Absolute error

GUI:

Graphical user interface

\(\Lambda_{v}\) :

Births and new recruits in avian populations

\(\alpha_{v}\) :

Transmission rate between infected and susceptible avian

\(\omega_{v}\) :

Avian population natural mortality rate

\(\eta_{v}\) :

Avian population diseases associated mortality rate

\(\eta_{1}\) :

Rate of avian slaughter in the susceptible population

\(\eta_{2}\) :

Rate of avian slaughter in the infected population

\(\Lambda_{m}\) :

Births and new recruits in avian populations

\(\alpha_{m}\) :

Transmission rate between infected avian and susceptible human

\(\omega_{m}\) :

Human population natural mortality rate

\(\eta_{m}\) :

Infective human population diseases associated mortality rate

\(\beta\) :

Infective human population recovery rate

\(\delta_{1}\) :

Time lag for avian incubation period

\(\delta_{2}\) :

Time lag for human incubation period

References

  1. J. Huang, K. Li, S. Xiao, J. Hu, Y. Yin, J. Zhang, S. Li, W. Wang, J. Hong, Z. Zhao, X. Chen, Global epidemiology of animal influenza infections with explicit virus subtypes until 2016: A spatio-temporal descriptive analysis. One Health 16, 100514 (2023)

    Article  Google Scholar 

  2. Y. Sun, T. Zhang, X. Zhao, J. Qian, M. Jiang, M. Jia, Y. Xu, W. Yang, L. Feng, High activity levels of avian influenza upwards 2018–2022: a global epidemiological overview of fowl and human infections. One Health 16, 100511 (2023)

    Article  Google Scholar 

  3. K.F. Shortridge, N.N. Zhou, Y. Guan, P. Gao, T. Ito, Y. Kawaoka, S. Kodihalli, S. Krauss, D. Markwell, K.G. Murti, M. Norwood, Characterization of avian H5N1 influenza viruses from poultry in Hong Kong. Virology 252(2), 331–342 (1998)

    Article  Google Scholar 

  4. L.D. Sims, T.M. Ellis, K.K. Liu, K. Dyrting, H. Wong, M. Peiris, Y. Guan, K.F. Shortridge, Avian influenza in Hong Kong 1997–2002. Avian Dis. 47(s3), 832–838 (2003)

    Article  Google Scholar 

  5. W.O. Kermack, A.G. McKendrick, Contributions to the mathematical theory of epidemics–I. 1927. Bull. Math. Biol. 53(1–2), 33–55 (1991)

    Google Scholar 

  6. Y. Zhao, L. Zhang, S. Yuan, The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model. Phys. A 512, 248–260 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Perc, N. Gorišek Miksić, M. Slavinec, A. Stožer, Forecasting covid-19. Front. Phys. 8, 127 (2020)

    Article  Google Scholar 

  8. M. Jusup, P. Holme, K. Kanazawa, M. Takayasu, I. Romić, Z. Wang, S. Geček, T. Lipić, B. Podobnik, L. Wang, W. Luo, Social physics. Phys. Rep. 948, 1–148 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  9. M. Naveed, A. Raza, A.H. Soori, M. Inc, M. Rafiq, N. Ahmed, M.S. Iqbal, A dynamical study of diarrhea delayed epidemic model: application of mathematical biology in infectious diseases. Eur. Phys. J. Plus 138(7), 664 (2023)

    Article  Google Scholar 

  10. S.M. Malakouti, Heart disease classification based on ECG using machine learning models. Biomed. Signal Process. Control 84, 104796 (2023)

    Article  Google Scholar 

  11. J. Hu, Z. Teng, Z. Li, B. Wen, The threshold dynamics in a stochastic SIS epidemic model with vaccination and nonlinear incidence under regime switching. Phys. A 529, 121555 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  12. P. Srinivas, R. Katarya, hyOPTXg: OPTUNA hyper-parameter optimization framework for predicting cardiovascular disease using XGBoost. Biomed. Signal Process. Control 73, 103456 (2022)

    Article  Google Scholar 

  13. M.A. Khan, S. Ullah, Y. Khan, M. Farhan, Modeling and scientific computing for the transmission dynamics of avian influenza with half-saturated incidence. Int. J. Model. Simul. Sci. Comput. 11(04), 2050035 (2020)

    Article  Google Scholar 

  14. C. Tadmon, B. Tsanou, A.F. Feukouo, Avian–human influenza epidemic model with diffusion, nonlocal delay and spatial homogeneous environment. Nonlinear Anal. Real World Appl. 67, 103615 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  15. Y. Chen, Z. Jin, J. Zhang, Y. Wang, J. Zhang, Global dynamical analysis of H5 subtype avian influenza model. Int. J. Biomath. 15(08), 2250058 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  16. X. Jiang, Y. Yu, F. Meng, Y. Xu, Modelling the dynamics of avian influenza with nonlinear recovery rate and psychological effect. J. Appl. Anal. Comput. 10(3), 1170–1192 (2020)

    MathSciNet  MATH  Google Scholar 

  17. G. Baggio, F. Filippini, I. Righetto, Comparative surface electrostatics and normal mode analysis of high and low pathogenic H7N7 Avian influenza viruses. Viruses 15(2), 305 (2023)

    Article  Google Scholar 

  18. X.T. Xie, A. Yitbarek, S.U. Khan, S. Sharif, Z. Poljak, A.L. Greer, A within-host mathematical model of H9N2 avian influenza infection and type-I interferon response pathways in chickens. J. Theor. Biol. 499, 110320 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  19. A. Feukouo Fossi, J. Lubuma, C. Tadmon, B. Tsanou, Mathematical modeling and nonstandard finite difference scheme analysis for the environmental and spillover transmissions of Avian Influenza A model. Dyn. Syst. 36(2), 212–255 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  20. A. Andronico, A. Courcoul, A. Bronner, A. Scoizec, S. Lebouquin-Leneveu, C. Guinat, M.C. Paul, B. Durand, S. Cauchemez, Highly pathogenic avian influenza H5N8 in south-west France 2016–2017: a modeling study of control strategies. Epidemics 28, 100340 (2019)

    Article  Google Scholar 

  21. C. Modnak, J. Wang, An avian influenza model with latency and vaccination. Dyn. Syst. 34(2), 195–217 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  22. R. Zhang, N. Li, X. Wang, B. Liu, F. Li, S. Zhang, X. Zhang, Z. Wang, Spatial analysis and mathematical modeling of human infection with avian influenza A (H7N9) virus in Zhejiang 2013–2016. Dis. Surveill. 34(1), 15–20 (2019)

    Google Scholar 

  23. A.C. Emmanuel, I.M. Olanrewaju, Mathematical modelling of the stability of highly pathogenic avian influenza with saturated contact rate. J. Math. Sci. Comput. Math. 2(2), 266–286 (2021)

    Google Scholar 

  24. T. Kang, Q. Zhang, L. Rong, A delayed avian influenza model with avian slaughter: Stability analysis and optimal control. Physica A 529, 121544 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  25. W.A. Lodwick, E.A. Untiedt, Fuzzy optimization, in Granular, Fuzzy, and Soft Computing, (Springer, New York, 2023), pp. 755–791

  26. Z. Li, J. Wang, J. Huang, M. Ding, Development and research of triangle-filter convolution neural network for fuel reloading optimization of block-type HTGRs. Appl. Soft Comput. 136, 110126 (2023)

    Article  Google Scholar 

  27. N. Anwar et al., Artificial intelligence knacks-based stochastic paradigm to study the dynamics of plant virus propagation model with impact of seasonality and delays. Eur. Phys. J. Plus 137(1), 1–47 (2022)

    Article  ADS  Google Scholar 

  28. M. Shoaib et al., Intelligent networks knacks for numerical treatment of nonlinear multi-delays SVEIR epidemic systems with vaccination. Int. J. Modern Phys. B 36, 2250100 (2022)

    Article  ADS  Google Scholar 

  29. A. Mehmood et al., Fuzzy-weighted differential evolution computing paradigm for fractional order nonlinear wiener systems. Chaos Solit. Fract. 159, 112160 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  30. N. Anwar et al., Intelligent computing networks for nonlinear influenza-A epidemic model. Int. J. Biomath. 16(04), 2250097 (2023)

    Article  MathSciNet  MATH  Google Scholar 

  31. M. Shoaib et al., Neuro-computational intelligence for numerical treatment of multiple delays SEIR model of worms propagation in wireless sensor networks. Biomed. Signal Process. Control 84, 104797 (2023)

    Article  Google Scholar 

  32. Z. Khan, S. Zuhra, S. Islam, M.A.Z. Raja, A. Ali, Modeling and simulation of Maxwell nanofluid flows in the presence of Lorentz and Darcy-Forchheimer forces: toward a new approach on Buongiorno’s model using artificial neural network (ANN). Eur. Phys. J. Plus 138(1), 107 (2023)

    Article  Google Scholar 

  33. M. Shoaib, S. Naz, K.S. Nisar, M.A.Z. Raja, S. Aslam, I. Ahmad, MHD casson nanofluid in darcy-forchheimer porous medium in the presence of heat source and Arrhenious activation energy: applications of neural networks. Int. J. Model. Simul. 43(4), 438–461 (2023)

    Article  Google Scholar 

  34. Z. Shi, X. Zhang, D. Jiang, Dynamics of an avian influenza model with half-saturated incidence. Appl. Math. Comput. 355, 399–416 (2019)

    MathSciNet  MATH  Google Scholar 

  35. X. Wei, L. Wang, Q. Jia, J. Xiao, G. Zhu, Assessing different interventions against Avian Influenza A (H7N9) infection by an epidemiological model. One Health 13, 100312 (2021)

    Article  Google Scholar 

  36. Y. Chen, H. Zhang, J. Wang, C. Li, N. Yi, Y. Wen, Analyzing an epidemic of human infections with two strains of zoonotic virus. Mathematics 10(7), 1037 (2022)

    Article  Google Scholar 

  37. M.F. Malik et al., Swarming intelligence heuristics for fractional nonlinear autoregressive exogenous noise systems. Chaos Solit. Fract. 167, 113085 (2023)

    Article  MathSciNet  Google Scholar 

  38. O.F. Benaouda, S. Kahla et al., Integration of reconfigurable fault-tolerant three-level inverter in photovoltaic power system. Int. J. Model. Simul. (2023). https://doi.org/10.1080/02286203.2023.2165786

    Article  Google Scholar 

  39. F. Almeida, M.L. Keerthi, B.J. Gireesha, P. Venkatesh, P. Kumar, B. Nagaraja, Consistent ramifications of prescribed surface temperature and prescribed heat flux boundary conditions for the slip flow of Walter B fluid in a stretching channel. Int. J. Model. Simul. (2023). https://doi.org/10.1080/02286203.2023.2237845

    Article  Google Scholar 

  40. G.C. Wu, J.L. Wei, C. Luo, L.L. Huang, Parameter estimation of fractional uncertain differential equations via Adams method. Nonlinear Anal. Model. Control 27(3), 413–427 (2022)

    MathSciNet  MATH  Google Scholar 

  41. E. Kantar, M. Ertaş, Dynamic study of a ternary trilayer Ising system with crystal field interaction. Eur. Phys. J. Plus 138(6), 509 (2023)

    Article  Google Scholar 

  42. D. Baleanu, P. Shekari, L. Torkzadeh, H. Ranjbar, A. Jajarmi, K. Nouri, Stability analysis and system properties of Nipah virus transmission: a fractional calculus case study. Chaos Solit. Fract. 166, 112990 (2023)

    Article  MathSciNet  Google Scholar 

  43. G.D. Varsamis, I.G. Karafyllidis, G.C. Sirakoulis, Quantum walks in spaces with applied potentials. Eur. Phys. J. Plus 138(4), 1–10 (2023)

    Article  Google Scholar 

  44. T.N.T. Minh, V.H. Le, N.Q.K. Le, Diffusion-tensor imaging and dynamic susceptibility contrast MRIs improve radiomics-based machine learning model of MGMT promoter methylation status in glioblastomas. Biomed. Signal Process. Control 86, 105122 (2023)

    Article  Google Scholar 

  45. T. Makayssi, M. Lamsaadi, M. Kaddiri, Y. Tizakast, Effect of an ascendant magnetic field on Rayleigh-Bénard convection for non-Newtonian power-law fluids in a horizontal rectangular cavity submitted to vertical temperature gradient. Eur. Phys. J. Plus 138(7), 650 (2023)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Narowal, Narowal, 51600, Pakistan

    Nabeela Anwar

  2. Department of Mathematics, University of Gujrat, Gujrat, 50700, Pakistan

    Iftikhar Ahmad

  3. Al-Nafees Medical College and Hospital Branch, Isra University Hyderabad, Islamabad, Pakistan

    Arooj Fatima

  4. Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin, 64002, Taiwan, R.O.C.

    Adiqa Kausar Kiani & Muhammad Asif Zahoor Raja

  5. AI Center, Yuan Ze University, Taoyuan, 320, Taiwan

    Muhammad Shoaib

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  1. Nabeela Anwar
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Correspondence to Adiqa Kausar Kiani.

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Anwar, N., Ahmad, I., Fatima, A. et al. Design of intelligent Bayesian supervised predictive networks for nonlinear delay differential systems of avian influenza model. Eur. Phys. J. Plus 138, 911 (2023). https://doi.org/10.1140/epjp/s13360-023-04533-w

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