Modeling nosocomial infection of COVID-19 transmission dynamics

Abstract

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 𝜃 is studied in the proposed model. Benefiting the next generation matrix method, 𝑅0 was computed. Routh–Hurwitz criterion and stable Metzler matrix theory revealed that COVID-19-free equilibrium point is locally and globally asymptotically stable whenever 𝑅0 < 1. Lyapunov function depicted that the endemic equilibrium point is globally asymptotically stable when 𝑅0 > 1. Further, the dynamics behavior of 𝑅0 was explored when varying 𝜃. In the absence of 𝜃, the value of 𝑅0 was 8.4584 which implies the expansion of the disease. When 𝜃 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.