Dynamics analysis of typhoid fever with public health education programs and final epidemic size relation

Abstract

In this paper, an epidemic model is develop and use to investigate the transmission dynamics of the typhoid fever epidemic (TF, a bacterial infection caused by Salmonella serotype Typhi bacteria). The model assesses the impact of public health education programs (PHEP) on reducing the pathogenesis of TF which can cause large outbreaks especially in resource-poor settings. The model is fitted well to the data for TF cases for Taiwan, China. Results from our mathematical analysis reveal that the disease-free equilibrium (DFE) of the model is globally asymptotically stable (GAS) when the basic reproduction number (R0) is below or equal to unity, and unstable when it is above unity. Further analysis also shows that the endemic equilibrium (EE) of the model is GAS whenever the R0 is above unity with some certain conditions , indicating the potential for the TF to spread and cause outbreaks in the community. We obtain a final size relation with consideration of human-to-human transmission route that could be used to report the actual size of the outbreaks over the cause of the epidemic period. Furthermore, sensitivity analysis results reveal the most sensitive parameters that are vital to combat the TF epidemic in Taiwan. Also, a wavelets analysis is performed to explore significant periodicities of the TF outbreaks in Taiwan, China.