On the Mathematical Analysis of a Campylobacteriosis Model for Human and Animal Population

Campylobacteriosis, a major cause of foodborne illnesses has continued to claim millions of lives globally. Thus, concerted needs to be put in place in order to curtail further loss of lives due to the disease. In this study, an analysis is conducted on the reproduction number, sensitivity analysis is also carried out on the parameters of the model connected to the reproduction number and the possibility of backward bifurcation of the campylobacteriosis mathematical model is explored. Results from the sensitivity analysis show that the most sensitive parameters are the infection rates, progression rate and the treatment rate for humans. It is further observed that as the human recruitment rate and treatment rate for symptomatic human population increases, the reproduction number also increases. This implies that it will not be possible to eliminate campylobacteriosis in the community with at least 70% treatment rate administered to the symptomatic human population. The analysis of the campylobacteriosis model reveals that the model exhibits the phenomenon of backward bifurcation under certain conditions, where a stable disease-free equilibrium (DFE) coexists with a stable endemic equilibrium (EE) when the associated reproduction number is less than unity. It is further shown for a special case that, a unique endemic equilibrium exists whenever the associated reproduction number is greater than unity.