A non-linear mathematical model for typhoid fever transmission dynamics with medically hygienic compartment

Typhoid fever is a contagious waterborne disease that is widespread throughout the world. This study develops a non-linear mathematical model for the dynamics of typhoid fever transmission, including a medically vigilant group (that is, those who strictly adhere to typhoid fever precautionary and control measures) to study the role of human self-hygienics in disease prevention and control. Based on the qualitative analysis of the model, a forward bifurcation exist whenever typhoid fever-free equilibrium and typhoid fever-present equilibrium coexist as the control reproduction number, \({\mathcal {R}}_0\) ${\mathcal{R}}_0$ , crosses one, which suggests that intensifying the control efforts to bring \(\mathcal R_0\) ${\mathcal{R}}_0$ below unity may be sufficient for the disease elimination in the community. In line with the available facts and data, the control reproduction number is estimated for the disease outbreak in Nigeria. The model’s sensitivity analysis revealed how the model parameters affect disease transmission in the community. The results of the analysis suggest that lowering the disease transmission probability, enhancing the recovery rate of symptomatic individuals, reducing the bacteria shedding and decay rates can reduce the community transmission and spread of typhoid fever, while the disease elimination may be possible with an increased fraction of medically vigilant and hygienic individuals in the community.