Mathematical Modeling: Global Stability Analysis of Super Spreading Transmission of Respiratory Syncytial Virus (RSV) Disease

In this paper, a model for the transmission of respiratory syncytial virus (RSV) in a constant human population in which there exist super spreading infected individuals (who infect many people during a single encounter) is considered. It has been observed in the epidemiological data for the diseases caused by this virus that there are cases where some individuals are super-spreaders of the virus. We formulate a simply SEIrIsR (susceptible-exposed-regular infected-super-spreading infected-recovered) mathematical model to describe the dynamics of the transmission of this disease. The proposed model is analyzed using the standard stability method by using Routh-Hurwitz criteria. We obtain the basic reproductive number (R-0) using the next generation method. We establish that when R-0 < 1, the disease-free state is locally asymptotically stable and the disease endemic state is unstable. The reverse is true when R-0 > 1, the disease endemic state becomes the locally asymptotically stable state and the disease-free state becomes unstable. It is also established that the two equilibrium states are globally asymptotically stable. The numerical simulations show how the dynamics of the disease change as values of the parameters in the SEIrIsR are varied.