The design of evolutionary approaches has a vital role in the recent development of scientific literature. To tackle highly nonlinear complex problems, nonlinear ordinary differential equations, partial differential equations, stochastic differential equations, and many more may called computational algorithms. The rotavirus causes may include severe diarrhea, vomiting, and fever leading to rapid dehydration. By the report of the World Health Organization (WHO), approximately 600,000 children die worldwide each year, 80 percent of whom live in developing countries. Two million children are hospitalized each year. In Asia, up to 45 percent of the children hospitalized for diarrhea may be infected with rotavirus. The rotavirus model is categorized into five-compartment like susceptible (S), breastfeeding (M), vaccinated (V), infected (I), and recovered children (R). Positivity, boundedness, equilibria, reproduction number, and stability results are part of the qualitative analysis of the model. After that, the design of the evolutionary approaches on the model predicts the efficiency, visualization, long-term behavior of the disease, and best results of the rotavirus disease. In the end, evolutionary computations are an appropriate tool for double-checking the qualitative examination of the model.

Rotavirus is a double-stranded RNA virus. Rotavirus is the most common cause of diarrhea. Its spread is contagious and affects every child before the age of five. Rotavirus is round in shape when observed under a microscope. Rotavirus produces inflammation in the small bowel, especially in the stomach and intestine. Diarrhea is most common in South Asia and Africa. In 2004, 2.5 billion cases of diarrhea were reported, resulting in 1.5 million deaths. More than half of the patients were from South Asia and Africa. Diarrhea is still a problem in the developing world. In America, the death rate from diarrhea is 10% merely while in South Asia and Africa, the death rate is 31.3%. In Pakistan, many children suffering from diarrhea are 27.7% in 2018. All the children were under five years of age. Burnett et al. presented a cost-effective vaccine to prevent the rotavirus disease [

For any time, the whole population

The fixed ratios of the model are presented as follows:

Here, we can observe from the system

And

Similarly, for

For large t

The system

rotavirus endemic equilibrium (REE-

By using the next-generation matrix method, we calculate two types of matrices one is transition matrix, and the second is transmission matrix as follows:

After substituting the rotavirus free equilibrium, so we have

Where

The spectral radius of the

By applying Routh-Hurwitz Criterion for 3^{rd} order,

By applying Routh-Hurwitz Criterion for 4^{th} order, if

To analyze the behavior of the continuous model

The system

The system

Stage 1

Stage 2

Stage 3

Stage 4

Final stage

The system

By using the parameters’ values presented in

Parameters | Values (per day) |
---|---|

Λ | 0.5 |

0.5 | |

0.3 | |

0.00049 | |

0.0015 | |

0.00042 | |

DFE(0.5), EE(1.5) | |

0.0013 | |

0.0054 | |

0.62 | |

0.71 | |

0–1.5 | |

0.01–0.5 | |

k | 0.083 |

We analyze the dynamics of rotavirus disease via evolutionary approaches.

Thanks, our families and colleagues who supported us morally.