Optimal control of rotavirus infection in breastfed and non-breastfed children

According to the World Health Organization’s guidelines, a two-year mandatory breastfeeding period is strongly recommended, supported by research demonstrating its significant benefits in reducing childhood illnesses and mortality rates. The present study is designed to address this recommendation by focusing on a specific infection, namely rotavirus. Acknowledging this evidence, researchers recognize the need for a deeper understanding of the dynamics of rotavirus disease. In response, our study focuses on constructing and analyzing an SIR epidemic model uniquely designed for transmitting rotavirus in children. The model partitions the children population into three compartments: susceptible, infected, and recovered. To enhance precision, we further categorize susceptible children based on breastfeeding status and infected individuals based on infectious or non-infectious nature. This detailed categorization enables a thorough examination of rotavirus transmission dynamics. The proposed model analyzes two equilibria, disease-free and endemic, revealing local and global stability conditions determined by the basic reproduction number ($R_0$). Our exploration extends to local stability analysis for the endemic equilibrium when $R_0>1$ and global stability assessment using the Lyapunov theory under specific conditions. Subsequently, we employ optimal control theory through Pontryagin’s maximum principle to minimize the cost burden associated with disease control in children. Then, our work provides a sensitivity analysis of different parameters for the basic reproduction number to enhance our understanding of model dynamics. Finally, numerical simulations conducted with MATLAB and Python software validate our analytical findings, offering a comprehensive and practical assessment of the proposed model’s implications for controlling rotavirus transmission in children.