¹Department of Mathematics, Lagos State University, Lagos, Nigeria
²Department of Computer Science, Lagos State University, Lagos, Nigeria
³Department of Mathematics, Morgan State University, Maryland, USA

Abstract

Diphtheria remains a significant public health threat in regions with low vaccination coverage and limited healthcare infrastructure, such as Nigeria. This study introduces an SEIRP-H model (Susceptible, Exposed, Infectious, Recovered, Protected, and Hospitalized) to capture the complex dynamics of diphtheria transmission and control strategies. The model is designed to reflect the critical stages of disease progression, incorporating key compartments that account for hospital isolation, vaccination, and immunity post-recovery. Parameters for infection rate, hospitalization, vaccination efficacy, and immunity waning are estimated using available epidemiological data, providing a realistic foundation for simulation. Our analysis focuses on understanding the impact of hospitalization and vaccination efforts on transmission rates, while also exploring the role of immunity (both short- and long-term) in controlling outbreaks. Through sensitivity analysis, we identify the most influential parameters affecting the disease dynamics, which helps highlight priority areas for intervention. The model simulations suggest that increasing vaccination rates and enhancing hospital capacity can significantly reduce the basic reproduction number (\(R_0\)) and slow the spread of diphtheria. Our findings underscore the importance of targeted vaccination campaigns, strict isolation of infectious individuals, and robust healthcare response systems to effectively manage diphtheria outbreaks in Nigeria.