MATHEMATICAL MODEL OF CATTLE DEMOGRAPHICS ON A FARM IN THE EL OCHO LETRAS REGION MATHEMATICAL MODEL OF CATTLE DEMOGRAPHICS ON A FARM IN THE EL OCHO LETRAS REGION

Abstract

In the El Ocho Letras region, cattle ranching causes significant damage to vegetation, natural wetlands, and water resources. Thus, it is necessary to know and understand the transient behavior of the number of cattle of different age groups over time and the effect of exogenous variables on the system’s behavior. To this end, system dynamics is used to describe the behavior of the quantity of livestock on the Laguna Negra property, located in the El Ocho Letras region. The numbers of cattle of different ages during the life cycle were defined as variables. The animals pass through the different ages, each lasting one year. Time delays were used for the fluxes between the different ages. A control strategy was used for limiting the number of animals older than one year. A discrete time mathematical model was formulated and a simulation was performed, showing as a result a periodical oscillatory behavior for the evolution of the variables. Some of the main contributions of this study are related to: analyzing the effect of exogenous variables on the behavior of the level variables; proposing a control of the number of cattle older than one year based on the sale of female calves; and developing a discrete time mathematical model using the chain method with delayed fluxes.