A dynamical study of diarrhea delayed epidemic model: application of mathematical biology in infectious diseases

This manuscript presents the stability analysis of the diarrhea epidemic model with the effect of time delay. The delayed epidemic model for the disease of diarrhea contains four compartments, including susceptible, infective, treated, and recovered classes. The artificial delay parameter is designed with a saturated incidence rate of the model. The mathematical analysis is carried out by studying the equilibria, positivity, boundedness, and reproduction number for the said model. Furthermore, the sensitivity of the parameters is studied to strengthen the mathematical analysis. The diarrhea epidemic model's local and global stabilities are investigated using the acknowledged results of the Routh Hurwitz criterion and Lyapunov function, respectively. Moreover, the numerical results are obtained to support the analysis.