This study presents a deterministic mathematical model for analysing the transmission dynamics and control of diphtheria using a Susceptible, Vaccinated, Latent, Infectious, and Removed (SVLIR) framework. The study was motivated by the persistent occurrence of diphtheria outbreaks in regions with inadequate vaccination coverage, weak healthcare systems, and poor public health awareness despite the availability of effective vaccines. The main aim of the study is to investigate the transmission dynamics of diphtheria and evaluate the effectiveness of vaccination and other control measures in achieving disease eradication. Specifically, the objectives were to formulate an SVLIR deterministic model, analyse the qualitative properties of the model, determine the disease-free and endemic equilibrium states, derive the basic reproduction number (R0), investigate the local and global stability of the disease-free equilibrium, and perform numerical simulations to examine the effects of epidemiological parameters on disease transmission. The total population was divided into five epidemiological compartments namely Susceptible, Vaccinated, Latent, Infectious, and Removed individuals. The model incorporated recruitment, vaccination, disease transmission, progression from latent to infectious stage, recovery, waning immunity, natural death, and disease-induced mortality. The positivity and boundedness of the model were established to ensure epidemiological validity. The basic reproduction number was derived using the next-generation matrix method, while the local and global stability analyses were established using the Jacobian matrix, Routh–Hurwitz criterion, Lyapunov function, and LaSalle’s invariance principle. Numerical simulations using the fourth-order Runge–Kutta method revealed that increased vaccination and recovery rates significantly reduce infection prevalence, whereas high transmission and progression rates intensify disease spread. The study further showed that routine vaccination remains the most effective long-term strategy for diphtheria eradication. The findings established that when , the disease-free equilibrium is both locally and globally asymptotically stable, implying that diphtheria will eventually die out from the population. The study therefore highlights the importance of sustained immunization programs, early treatment, and public health awareness in controlling and preventing diphtheria outbreaks.