Modeling infectious respiratory diseases considering fear effect and latent period

Abstract

This paper introduces a fractional-order (FO) $SEIR$ epidemic model for respiratory diseases considering a non-human class $P\left(t\right)$ for pathogens to study the effects of fear and awareness programs on disease dynamics. Further, using the basic reproduction number ${ℛ}_0^{\alpha }$, the criteria for the extinction or persistence of the disease is established. Also, the conditions for Hopf bifurcation are derived, considering both FO ($\alpha$) and rate of pathogens $\eta$ as the bifurcation parameters. In addition, a detailed numerical simulation is performed to substantiate our theoretical results. The study of transmission dynamics of Tuberculosis (TB), a particular example of respiratory disease, is carried out in reference to the United States (US). Finally, we have estimated model parameters with the help of actual TB data from the US and then predicted the TB dynamics and disease control. It is pointed out that the fractional order can reduce the complexity of the model and better predict the dynamics of TB in the US than the integer order.