The role of asymptomatic cattle for leptospirosis dynamics in a herd with imperfect vaccination

Leptospirosis is an emerging zoonotic disease with high health and economic damage. In this study, we developed a deterministic mathematical model that describes the dynamics of leptospirosis transmission within a cattle herd, incorporating asymptomatic infected and vaccinated compartments. The study examined the transmission role of asymptomatic cattle that contaminate herds without farmers' knowledge. We proved the well-posedness of the proposed model and found the basic reproduction number using the next-generation matrix. Analytically, we demonstrated that the disease-free equilibrium point is locally and globally asymptotically stable when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi> <mml:mn>0</mml:mn></mml:msub> </mml:math> is less than unity and is otherwise unstable. Graphically, we further established the local asymptotic stability of disease-free and endemic equilibria. Sensitivity analysis showed that the contact rate with asymptomatic infected cattle, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>β</mml:mi> <mml:mi>A</mml:mi></mml:msub> </mml:math> , is the most sensitive parameter in the stated model, followed by the recovery rate of asymptomatic infected cattle, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>σ</mml:mi></mml:math> , and the vaccination rate of susceptible cattle, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>τ</mml:mi></mml:math> . Numerical simulations revealed that a reduction in contact rate with asymptomatic infected cattle significantly reduced pathogen Leptospira transmission in the herd. In addition, fostering the recovery rate of asymptomatic infected cattle can significantly reduce new infections in the herd. Furthermore, augmenting the vaccination rate among susceptible cattle resulted in a notable decrease in disease prevalence within the herd. Findings of this study underscore the remarkable importance of targeted interventions, such as reducing contact rates with asymptomatic infected cattle, increasing recovery rates using proper treatments, and enhancing vaccination efforts to manage leptospirosis transmission in cattle herds.