Modeling the dynamics of pertussis to assess the influence of timely awareness with optimal control analysis

Abstract

Pertussis, also known as whooping cough, is a very infectious respiratory disease that can be easily avoided with vaccination. In this work, a system of nonlinear ordinary differential equations of pertussis has been formulated to examine the impact of early treatment. Through theoretical examination, the model has been extensively analyzed. Numerical experiments are performed to validate the theoretical conclusions. The suggested model has been fitted to real Austrian pertussis data, demonstrating that it is appropriate for the data. The control reproduction number was also used to test the sensitivity analysis of all of the parameters of the proposed model. The results indicate that the effective contact rate is the parameter that is more sensitive to increasing the control reproduction number. In contrast, the awareness rate is the parameter that is most sensitive to decreasing the number of control reproductions, and optimal control analysis has also been performed in this work. Numerical simulation reveals that awareness is the most influential parameter in reducing infection in the population. Moreover, vaccination and treatment are also very important in controlling pertussis in society. © 2025 The Author(s). Published by the Nigerian Society of Physical Sciences under the terms of the Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by-nc-nd/4.0/.