Modelling the Effects of Treatment Failure on the Minor Outbreak Duration for Carrier-Related Infectious Disease

Background: The complex interplay between treatment interventions and asymptomatic carriers and its effect on the epidemic duration of an infectious disease is not fully understood. Methods: Here, we used Galton-Watson branching process and generating function technique to estimate the density functions of minor outbreak duration. Simulations were used to calculate the central tendency of outbreak duration and address how changing levels of treatment failure affect this estimated duration. Results:Streptococcus pyogenes infection was used as a case study. Given the existence of the threshold, the change in mean duration as the probability of treatment failure increases is shown to be similar to the pattern driven by the basic reproduction number. In a supercritical regime, the mean duration tends to decrease as the probability of treatment failure increases. The distribution changes in tail behavior, from heavy- to light-tailed, if a large fraction of long extinction times develops to a major outbreak. Conclusions: Treatment failure elevates the probability of secondary transmissions by prolonging the overall infectious period, resulting in an extended the outbreak duration. The threshold of treatment failure identifies the maximum tolerable error for medical intervention. An unusually long period implies a critical early warning signal of a potential major outbreak that was successfully contained.