Mathematical modeling of poliomyelitis with control measure

Abstract

Poliomyelitis, also known as polio, is a contagious viral illness that predominantly impacts young children, leading to paralysis and, in severe instances, death. Despite worldwide initiatives aimed at elimination, the spread of the poliovirus persists in various areas, highlighting the need for robust vaccination strategies. This research employed a mathematical model to explore the dynamics of poliovirus transmission, integrating vaccination as a crucial method for disease control. The model was analyzed to determine the basic reproduction number (R₀ )and the stability properties of the diseasefree and endemic equilibrium. Our findings demonstrated that the system achieves local asymptotic stability when the basic reproduction number is less than one, global asymptotic stability when it is exactly one, and maintains a stable endemic equilibrium when it is greater than one. Sensitivity analysis revealed critical parameters influencing the basic reproduction number, emphasizing the impact of vaccination coverage and disease transmission rates on polio dynamics. Numerical simulations further elucidated the effectiveness of interventions such as reducing contact rates between susceptible and infected individuals and increasing the vaccination rate. Based on our results, we proposed recommendations to mitigate the polio burden, including enhanced vaccine availability, improved sanitation practices, and targeted healthcare interventions for vulnerable populations. This study contributes to the understanding of polio transmission dynamics and provides insights for optimizing control strategies towards global eradication efforts.