# A Mathematical Model to Study the Effects of Breastfeeding and Vaccination on Rotavirus Epidemics

## Authors

• Sherif Eneye Shuaib Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani, 94000
• Pakwan Riyapan Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani, 94000

## Keywords:

breastfeeding, diarrhoea, mathematical model, rotavirus, vaccination

## Abstract

In this article, we formulate and analyze a mathematical model including breastfeeding and vaccination to study the transmission dynamics of rotavirus epidemics. The model is divided into five compartmental classes, namely, the susceptible compartment S(t); the breastfeeding compartment M(t); the vaccinated compartment V(t); the infected compartment I(t); and the recovered compartment R(t). To understand the threshold of infection, the basic reproduction number relating to breastfeeding and vaccination, denoted as Rvm, is computed. The results show that if Rvm<1, the disease-free equilibrium is globally asymptotically stable. Similarly, if Rvm>1, global asymptotic stability of the endemic equilibrium exists. Numerical simulations were carried out to support the model analysis and to examine the effects of breastfeeding and vaccination on rotavirus epidemics. The model fits well with real data to predict the infected population in real life. The analysis and numerical results of the model confirm that the combination of vaccination and breastfeeding is more effective in reducing the spread of rotavirus epidemics.

## Author Biographies

### Sherif Eneye Shuaib, Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani, 94000

Department of Mathematics and Computer Science

### Pakwan Riyapan, Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani, 94000

Department of Mathematics and Computer Science, Faculty of Science and Technology

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