A Risk Assessment Model for Airborne Infection in a Ventilated Room using the Adaptive Runge-Kutta Method with Cubic Spline Interpolation

Abstract

Bacteria or viruses that are spread by tiny respiratory droplets are known as airborne infections. These infectious vehicles can move along air currents, stay in the air, or stick to surfaces before being inhaled by another person. Airborne transmission may happen across long ranges and time periods. Increased infection rates or clusters of airborne infections are linked to a lack of ventilation or low ventilation rates. While normal people remain in the same room as infectors, this research will utilize a mathematical model for estimating the concentration of exhaled air in a space with an outlet ventilation system, as well as the risk of infection. As a result, the exhaled air concentration and infection risk are affected by the actual concentration level, the number of users, and the rate of ventilation. The adaptive Runge-Kutta technique and the standard fourth-order Runge-Kutta technique are used to estimate the model solution. Because the number of individuals who stay in the space varies over time, the Lagrange interpolating polynomial and cubic splines interpolation are employed to represent the number of individuals in the space. A good agreement solution is obtained using the adaptive Runge-Kutta method with cubic spline interpolation. The proposed strategy represents the balance in the air quality management process between the number of individuals allowed to stay in the space and the performance of the air ventilation system. For the optimal outcomes, the proposed technique was capable of converting field data from a the number of individuals using cubic splines and adaptive RK methods. The model can also be utilized as a part of an internet of things (IoT) system to develop new approaches to controlling infection-free zones. We demonstrate that the proposed strategy works in real-world scenarios.