Numerical simulation of the SIR and Lotka-Volterra models used in biology

Abstract

In this work, we will simulate different mathematical models used in biology, the first one is used to describe the dynamics of biological systems in which a predator and its prey interact with each other, called the lotka-volterra model, the second one is used to describe the evolution of an infectious disease in any population, and the last is used in the Monod model which describe bacterial growth in a given environment. First, we will present the three mathematical models that govern the evolution of the prey relative to the predator and vice versa, the spread of an infectious agent within a population, or even bacterial growth in a given environment. These models form a system of non-linear and coupled equations, which requires special numerical processing because of the biological terms used in these one. The numerical simulation is based on the explicit Runge-Kutter method of order 4 (ODE 45) which is best suited to solve this type of equation system.