SENSITIVITY ANALYSIS OF TRANSMISSION PARAMETERS IN A DIPHTHERIA-VACCINE-TREATMENT MODEL

Abstract

Diphtheria continues to pose a major public health concern, particularly across various regions of sub-Saharan Africa. Recent diphtheria outbreaks highlight the critical need for sustained high vaccination coverage within communities. Without vaccination and appropriate treatment, the disease remains highly dangerous, with a fatality rate of approximately 30% among unprotected individuals, posing an even greater threat to young children. This study introduces a diphtheria-vaccine-treatment compartmental model designed to capture the disease dynamics through eight distinct epidemiological states: Susceptible (unvaccinated) population (), fully vaccinated (, Partially vaccinated (,  Exposed (E), Asymptomatic infected (), Symptomatic infected (), Treated (T), and Recovered (R). The basic reproduction number () was calculated to be 0.1323. With  < 1, the model predicts asymptotic stability, indicating that diphtheria transmission will gradually decline, ultimately leading to disease eradication over time. Sensitivity analysis revealed that the most positively sensitive parameter influencing  is the asymptomatic infection transmission rate, , where    = 0.7716799884. Conversely, the only negatively sensitive parameter is the proportion of the infectious population, , where  = -0.08281740530, suggesting that an increase in this parameter would lead to a reduction in  . Based on these findings, targeted interventions should focus on reducing asymptomatic transmission, as asymptomatic carriers play a critical role in sustaining disease spread. Strengthening surveillance systems to improve early detection, enhancing vaccination coverage to increase immunity, and ensuring timely treatment of both symptomatic and asymptomatic cases are essential measures for controlling diphtheria transmission.