Stability analysis and optimal control strategies of Q fever transmission dynamics in Ghana’s Tropical Grassland

The economic and public health implications of Q fever are significant concerns in developing countries. This disease leads to a notable loss of animal protein and poses health risks to humans. To better understand the complex transmission pathways and develop effective strategies to prevent and control the recent surge in Q fever outbreaks in Ghana’s Tropical Grassland zone, we have proposed a mathematical model. This model is based on fundamental biological properties to ensure it accurately reflects the behavior and constraints of the system. Additionally, we have created a 3-D plot to illustrate how sensitive parameters affect the basic reproduction number, R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}, providing insights into the epidemiological implications. We identify the conditions needed for both local and global stability of the disease-free and endemic states. The model was expanded to provide optimal control utilizing education/sensitization of susceptible humans, treatment of the infected humans, and treatment of infected livestock. Our simulation results highlight that education/sensitization alone, as an optimal strategy, has the long-term potential to mitigate disease transmission effectively. A significant reduction in human infections was observed when education/sensitization was combined with human treatment. Additionally, the combination of education/sensitization and the treatment of infected livestock resulted in one of the most effective reductions in infection levels across humans and livestock. These findings reinforce the importance of integrating education, treatment, and livestock management to effectively control Q fever transmission.