Modeling nosocomial infection of COVID-19 transmission dynamics

COVID-19 epidemic has posed an unprecedented threat to global public health. The disease has alarmed the healthcare system with the harm of nosocomial infection. Nosocomial spread of COVID-19 has been discovered and reported globally in different healthcare facilities. Asymptomatic patients and super-spreaders are sough to be among of the source of these infections. Thus, this study contributes to the subject by formulating a SEIHR mathematical model to gain the insight into nosocomial infection for COVID-19 transmission dynamics. The role of personal protective equipment theta is studied in the proposed model. Benefiting the next generation matrix method, R-0 was computed. Routh-Hurwitz criterion and stable Metzler matrix theory revealed that COVID-19-free equilibrium point is locally and globally asymptotically stable whenever R-0 < 1. Lyapunov function depicted that the endemic equilibrium point is globally asymptotically stable when R-0 > 1. Further, the dynamics behavior of R-0 was explored when varying theta. In the absence of theta, the value of R-0 was 8.4584 which implies the expansion of the disease. When theta is introduced in the model, R0 was 0.4229, indicating the decrease of the disease in the community. Numerical solutions were simulated by using Runge-Kutta fourth-order method. Global sensitivity analysis is performed to present the most significant parameter. The numerical results illustrated mathematically that personal protective equipment can minimizes nosocomial infections of COVID-19.