Mathematical modeling of COVID-19 transmission dynamics between healthcare workers and community

Highlights

• Mathematical model COVID-19 in Tanzania with the purpose of protecting health personnel and general public.

• Protection of Healthcare workers can be achieved through an effective use of protective gears or equipment (PPE).

• COVID-19 spread in the community can be minimized through control measures such as physical distancing, face masks and hygiene sanitizers.

• Protection of healthcare workers can be illustrated mathematically through an effective use of protective measures and also through minimization of infection in the community.

Abstract

Corona-virus disease 2019 (COVID-19) is an infectious disease that has affected different groups of humankind such as farmers, soldiers, drivers, educators, students, healthcare workers and many others. The transmission rate of the disease varies from one group to another depending on the contact rate. Healthcare workers are at a high risk of contracting the disease due to the high contact rate with patients. So far, there exists no mathematical model which combines both public control measures (as a parameter) and healthcare workers (as an independent compartment). Combining these two in a given mathematical model is very important because healthcare workers are protected through effective use of personal protective equipment, and control measures help to minimize the spread of COVID-19 in the community. This paper presents a mathematical model named SWE $I_s{I}_a$HR; susceptible individuals (S), healthcare workers (W), exposed (E), symptomatic infectious ($I_s$), asymptomatic infectious ($I_a$), hospitalized (H), recovered (R). The value of basic reproduction number $R_0$ for all parameters in this study is 2.8540. In the absence of personal protective equipment $\xi$ and control measure in the public $\theta$, the value of $R_0\approx 4.6047$ which implies the presence of the disease. When $\theta$ and $\xi$ were introduced in the model, basic reproduction number is reduced to 0.4606, indicating the absence of disease in the community. Numerical solutions are simulated by using Runge–Kutta fourth-order method. Sensitivity analysis is performed to presents the most significant parameter. Furthermore, identifiability of model parameters is done using the least square method. The results indicated that protection of healthcare workers can be achieved through effective use of personal protective equipment by healthcare workers and minimization of transmission of COVID-19 in the general public by the implementation of control measures. Generally, this paper emphasizes the importance of using protective measures.