The role of post-exposure acquired immunity in the dynamics and control of diphtheria

Diphtheria remains a vaccine-preventable disease of public-health importance, and recurrent outbreaks continue to be reported in settings where vaccination coverage and access to health care are limited. This study develops a deterministic compartmental model of diphtheria transmission that incorporates post-exposure acquired immunity. The treatment of post-exposure immunity is the distinguishing feature of the model. Exposed individuals who clear the pathogen subclinically without active infection acquire immunity, which confers lasting protection, at a constant rate. This differs from earlier diphtheria models, in which individuals with strong immunity remain at risk of reinfection. Our treatment of post-exposure immunity represents the acquisition of protective immunity following subclinical exposure. The elasticity of the reproduction number with respect to post-exposure immunity is smaller than that of the other controls, but the mechanism markedly reduces the exposed population, and its effect on the exposed class is larger than its elasticity would suggest, because it acts directly on that class rather than through the threshold quantity. The results indicate that isolation and primary vaccination are the dominant controls and act through complementary routes, and that post-exposure immunity, although of secondary importance for the reproduction number, has a substantial effect on the exposed population and on the progression from exposure to active disease. These findings support the development of post-exposure vaccination as well as an integrated strategy combining sustained vaccination and booster programmes with prompt detection and isolation of infectious cases.