AN AGE STRUCTURE MODEL WITH IMPULSE ACTIONS FOR LEPTOSPIROSIS IN LIVESTOCK CATTLE

Abstract

As a zoonotic disease, leptospirosis has now been identified as one of the emerging infectious diseases. In this paper, we analyze the propagation of leptospirosis and find a schedule for control programs to eradicate the disease in a cattle ranch. A mathematical model has been built with ordinary differential equations (ODEs) to understand the epidemiology of leptospirosis and main factors on its transmission. We investigated the disease free equilibrium of the model and its stability using the basic reproduction number, [Formula: see text], and target reproduction number, [Formula: see text]. Then, the model incorporates vaccination and recruitment control programs in the form of impulse actions as measures to prevent the propagation of leptospirosis in the ranch. Parameter estimation and sensitivity analysis are presented as a part of this study.