COVID-19 outbreak: a predictive mathematical study incorporating shedding effect

In this paper, a modified SEIR epidemic model incorporating shedding effect is proposed to analyze transmission dynamics of the COVID-19 virus among different individuals' classes. The direct impact of pathogen concentration over susceptible populations through the shedding of COVID-19 virus into the environment is investigated. Moreover, the threshold value of shedding parameters is computed which gives information about their significance in decreasing the impact of the disease. The basic reproduction number (R-0) is calculated using the next-generation matrix method, taking shedding as a new infection. In the absence of disease, the condition for the equilibrium point to be locally and globally asymptotically stable with R-0 < 1 are established. It has been shown that the unique endemic equilibrium point is globally asymptotically stable under the condition R-0 > 1. Bifurcation theory and center manifold theorem imply that the system exhibit backward bifurcation at R-0 = 1. The sensitivity indices of R-0 are computed to investigate the robustness of model parameters. The numerical simulation is demonstrated to illustrate the results.