Dynamic analysis of Q-fever transmission among cattle in the Tropical Savannah Grassland zone of Ghana.

Abstract

Livestock morbidity and death from Q-fever have been high, endangering local farmers livelihoods and affecting food security in Ghana. It is essential to understand the transmission dynamics of Q-fever to protect both the health of the animals and the main source of income for the community. A non-linear ordinary differential equation incorporating a vaccinated compartment was formulated and analyzed to gain insights into the spread of Q-fever. Routh Hurwitz criterion and Lyapunov function were used respectively to analyze the local and global stability of the disease-free equilibrium (Q0). We analyzed the behavior of the model compartments and discovered that many key factors significantly influence the persistence or eradication of Q-fever. Increased vaccination rates decrease the susceptible livestock while increasing the vaccinated livestock, potentially reducing the risk of outbreaks and limiting the spread of infections. A higher recovery rate leads to a quicker recovery, which aids in epidemic control by boosting population immunity and reducing the infectious time. The infection level rises when R0 > 1, indicating a typical transcritical bifurcation behavior, but this growth stays steady and does not result in unbounded advancement. Author summaryQ-fever presents considerable health hazards to livestock in Ghanas Tropical Savannah Grassland, adversely affecting local farmers income and food security in regions such as North Tongu municipality. To elucidate the transmission dynamics of the disease and safeguard both animal health and the communitys principal economic resource, we proposed a mathematical model employing non-linear differential equations that incorporate a vaccine compartment. This model enables the evaluation of how parameters such as vaccination and recovery rates influence the transmission of Q-fever in livestock. Our findings indicate that increased vaccination rates may diminish the population of susceptible livestock, hence reducing the possibility of outbreaks. In addition, a rapid recovery rate not only diminishes the duration of infectiousness in livestock but also enhances herd immunity, assisting in the containment of possible epidemics. The proposed model indicates that as R0 exceeds 1, the infection level rises, displaying transcritical bifurcation behavior. However, this rise stabilizes and prevents uncontrolled spread. These findings emphasize the value of vaccination and recovery techniques in controlling and possibly eliminating Q-fever in cattle, which would ultimately help Ghanaian farming communities remain sustainable.