The purpose of this study is to present the numerical performances and interpretations of the SEIR nonlinear system based on the Zika virus spreading by using the stochastic neural networks based intelligent computing solver. The epidemic form of the nonlinear system represents the four dynamics of the patients, susceptible patients

The coronavirus is known as one of the quickly spreading diseases. Adequate and appropriate processes and proper treatment are required to avoid its spread and control. To manage the affected population’s probability, the epidemic with the function of therapy is displayed. Prospects reveal how many individuals based on the afflicted classes have gone for the cure. Few of the traditional samples provide the treatment ratios, which are proportional to the affected number of patients [

Currently, there is no definitive treatment for the Zika virus with the exclusion of controlling the vectors by using insecticide spray along with the extinguishing habitats of the larval breeds. In recent investigations, pregnant women, particularly present vulnerable to the infection of Zika virus infection [

Moreover, the researchers considered indirect/direct transmission forms through diseased animals and environmental viruses. The best control policies are vaccination, elimination, reduction in migration, and disinfection. Xing et al. [

The performances of computations are based on the SEIR nonlinear system using the Zika virus spreading through the computational artificial neural networks (ANNs) and the scaled conjugate gradient (SCG), ANNs-SCG scheme. Recently, stochastic solvers have been famous due to the variety of stiff-natured problems [

A few motivational aspects and novel features of the SEIR nonlinear system based on the Zika virus spreading using the artificial neural networks (ANNs) enhanced by the scaled conjugate gradient (SCG), ANNs-SCG approach are presented:

The numerical representations of the SEIR nonlinear system based on the spreading of the Zika virus have been described/presented/analyzed using the ANNs-SCG stochastic solver.

Different cases and scenarios of the spreading of the Zika virus have been numerically simulated using the ANNs-SCG stochastic solver for a better understanding of the dynamics.

The stochastic solver’s exactness is authenticated by comparing the obtained reference solutions.

The values based on the absolute error for each dynamic of the SEIR nonlinear system of the Zika virus spreading have been observed in good negligible ranges by using the ANNs-SCG scheme.

The constancy of the scheme is authenticated through the values of state transitions, error histograms measures, correlation, and regression analysis.

The other paper parts are presented: Section 2 provides the mathematical model. Section 3 shows the proposed stochastic methodology. Section 4 designates the results and discussions of the model. The conclusions along with future research studies are presented in the final Section.

This section performs both forms of infection based on vector-to-human and human-to-human transmission. This model is categorized based on the total population of the human (_{H}(_{H}(_{H}(_{H}(_{H}(_{H}(_{H}(_{H}(_{H}(_{H}(_{V}(_{V}(_{V}(_{V}(_{V}(_{V}(_{V}(_{V}(

Parameters | Details |
---|---|

Susceptible humans | |

Susceptible vector | |

Exposed humans | |

Exposed vector | |

Infected humans | |

Infected vector | |

Recovered humans | |

Susceptible: Humans recruiting | |

Susceptible: Humans to infection | |

Susceptible humans to infected mosquitoes | |

Humans: Mortality rate | |

Infected human ratio to susceptible mosquitoes | |

Treatment | |

Natural rate | |

Transmission ratio of the Infected humans to susceptible vector | |

Morality rate persuaded in people | |

Natural rate of morality using the vector compartment | |

Susceptible mosquitos’ recruitment | |

Initial conditions | |

Time |

The necessary definitions of the terms in the SEIR nonlinear system (1) based on the Zika virus spreading are tabulated in

While theoretical convergence and further descriptions based on the parametric values using the global and local stability can be seen in the reported study [

The proposed computing scheme for solving the SEIR nonlinear system based on the Zika virus spreading is presented in two phases.

The process of the artificial neural networks (ANNs) and the scaled conjugate gradient (SCG), ANNs-SCG computing scheme is provided along with extensive and critical explanations.

The numerical representations through the ANNs-SCG computing scheme for the SEIR nonlinear system based on the Zika virus spreading are provided.

A suitable procedure based on the flow structure for the ANNs-SCG computing scheme for the SEIR nonlinear system using the Zika virus spreading is described in

The numerical explanations are provided for solving the SEIR nonlinear system based on the Zika virus using the stochastic scheme. The mathematical form of the SEIR nonlinear systems is presented in three cases with different sets of initial conditions:

The numerical solutions of the SEIR nonlinear system based on the Zika virus are presented by using the artificial neural networks (ANNs) and the scaled conjugate gradient (SCG), ANNs-SCG with input intervals 0 and 1. ^{−12}, 7.17372 × 10^{−11}, and 2.13257 × 10^{−12}. The gradient measures of the SEIR nonlinear system based on the Zika virus, are calculated as 7.7856 × 10^{−08}, 9.0585 × 10^{−08}, and 6.7981 × 10^{−08}. These graphical plots provide the convergence measures, exactness, and accuracy performances of the designed ANNs-SCG approach to solving the SEIR nonlinear system of the Zika virus spreading. The fitting curve performances are presented in ^{-07}, 2.27×10^{-06}, and 2.86×10^{-07}, respectively.

The correlation plots are provided in ^{2} found as 1 to solve the SEIR nonlinear system of the Zika virus spreading using the ANNs-SCG. The best plots of the training, testing, and corroboration authenticate the performances of the ANNs-SCG and are found correct for the SEIR nonlinear system of the Zika virus spreading.

Case | MSE | Performance | Gradient | Mu | Iterations | Complexity | ||
---|---|---|---|---|---|---|---|---|

Training | Confirmation | Testing | ||||||

I | 3 × 10^{−12} |
3 ×10^{−12} |
4 ×10^{−12} |
3.15 × 10^{−12} |
7.8 × 10^{−8} |
1 × 10^{−13} |
23 | 2 |

2 | 5 × 10^{−11} |
7 ×10^{−11} |
2 ×10^{−11} |
5.22 × 10^{−11} |
9.0 × 10^{−8} |
1 × 10^{−11} |
30 | 2 |

3 | 2 × 10^{−12} |
2 ×10^{−12} |
2 ×10^{−12} |
2.44 × 10^{−12} |
6.8 × 10^{−8} |
1 × 10^{−17} |
28 | 2 |

The result comparison plots and AE (obtained and reference results) to solve the SEIR nonlinear system based on the Zika virus spreading are illustrated in ^{−05} to 10^{−07}, 10^{−05} to 10^{−06} and 10^{−04} to 10^{−06} for the category ^{−06} to 10^{−08}, 10^{−05} to 10^{−06} and 10^{−06} to 10^{−07} for class ^{−06} to 10^{−07}, 10^{−05} to 10^{−06} and 10^{−05} to 10^{−07} for class ^{−07} to 10^{−09}, 10^{−05} to 10^{−07} and 10^{−06} to 10^{−08} for class ^{−06} to 10^{−09}, 10^{−05} to 10^{−07} and 10^{−06} to 10^{−07} for class ^{−05} to 10^{−07}, 10^{−04} to 10^{−06} and 10^{−05} to 10^{−06} for class ^{−06} to 10^{−07}, 10^{−05} to 10^{−07} and 10^{−07} to 10^{−08} for class

The purpose of the current work is to present the numerical performances of the SEIR nonlinear system based on the Zika virus spreading by using stochastic procedures. The epidemic form of the SEIR nonlinear system is divided into four dynamics of the patients, susceptible patients

The numerical presentations based on the SEIR nonlinear system of the Zika virus spreading have been described through the stochastic scheme.

Three variations of the Zika virus spreading have been described through the stochastic procedure and numerically stimulated using the designed computational approach.

The exactness of the scheme is verified by using the comparison procedures of the obtained reference solutions.

The default stoppage limits, step size, and tolerances are applied to label the data, training targets, and inputs, which have been accessed using the standard numerical result performances.

The AE values of each dynamic of the SEIR nonlinear system of the spreading Zika virus have been performed accurately using the proposed scheme.

The statics of the dataset has been divided into three parts, 11% for testing, 72% for measures for training and 17% for validation.

The constancy of the computing scheme has been authenticated through the different statistical performances.

In the future, the suggested schemes can be applied to propose the numerical performances of the computational dynamics based on fluidic systems, computer virus systems, fractional kinds of systems, and biological models [

This research has received funding support from the NSRF via the program anagement Unit for Human Resources & Institutional Development, Research and Innovation [Grant number B05F640183] and Chiang Mai University. Watcharaporn Cholamjiak would like to thank National Research Council of Thailand (N42A650334) and Thailand Science Research and Innovation, the University of Phayao (Grant No. FF66-UoE).

This work was supported by

The authors declare that they have no conflicts of interest to report regarding the present study.