| Summary: | 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 SEIHRmathematical 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, R0was 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 R0was explored when varying θ. In the absence of θ, the value of R0was 8.4584 which implies the expansion of the disease. When θ is introduced in the model, R0was 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.
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