Modeling nosocomial infection of COVID-19 transmission dynamics

Lemjini Masandawa; Silas Steven Mirau; Isambi Sailon Mbalawata; James Nicodemus Paul; Katharina Kreppel; Oscar M Msamba

doi:10.1016/j.rinp.2022.105503

Modeling nosocomial infection of COVID-19 transmission dynamics

Results Phys. 2022 Jun:37:105503. doi: 10.1016/j.rinp.2022.105503. Epub 2022 Apr 21.

Authors

Lemjini Masandawa¹, Silas Steven Mirau¹, Isambi Sailon Mbalawata², James Nicodemus Paul¹, Katharina Kreppel¹, Oscar M Msamba³

Affiliations

¹ School of Computational and Communication Science and Engineering, The Nelson Mandela African Institution of Science and Technology, P.O. Box 447, Arusha, Tanzania.
² African Institute for Mathematical Sciences, NEI Globla Secretariat, Rue KG590 ST, Kigali, Rwanda.
³ Arusha Technical College, P.O. Box 296, Arusha, Tanzania.

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 $S E I H R$ 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, $R_{0}$ 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 $θ$ . In the absence of $θ$ , the value of $R_{0}$ was 8.4584 which implies the expansion of the disease. When $θ$ is introduced in the model, $R_{0}$ 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.

Keywords: Basic reproduction number; Hospital-acquired infection; PRCC; Personal protective equipment; Proposed C0VID-19 model.