Gustavo Delgado Reyes

Numerical Approaching of SIR Epidemic Model for Propagation of Computer Worms

In this paper we analyzed the model susceptible-infected-recovered (SIR); this model is based on differential equations, in this sense it cannot be implemented directly on a computer, in this context as motivation of the study presented, we propose an approximate model based on finite difference equations to achieve a simulation of the epidemic, using for this set theory and cardinality obtaining an iterative numerical method which consists on basics arithmetic operations, in addition, to be an approximate model, it will present an error due to truncation or rounding. At the end of this paper it is presented a case of study developed in SIMULINK of MATLAB software, and the results of the model based on difference equations.

Aproximación numérica del modelo epidemiológico SI para la propagación de gusanos informáticos, simulación y análisis de su error

ABSTRACT In the biological environment, there has been created epidemiological models that attempt to explain the spread dynamics of an epidemic in a population to predict the behavior of possible epidemics that can affect humanity. Based on that, this paper focused on the study of epidem-ics worms because they can spread by themselves from one infected host to the entire network of susceptible hosts. In this paper we analyzed the susceptible-infected ( SI ) model which assumes that in a community with n individuals, the num-ber of individuals in the susceptible state S ( t ) are in direct contact with the number of individuals that are in infected state I ( t ). These last individuals can spread the infection or switch to an infectious state with the factor β as a speed of infection. This model is based on differential equations so it can-not be implemented directly on a computer. Due to the complexity of this model, it is proposed an approximate model based on finite different equa-tions to achieve a simulation of the epidemic us-ing a set theory and cardinality obtaining an itera -tive numerical method which consists on basics arithmetic operations. Additionally, having in mind this is an approximate model, it will be pre-sented an error due to truncation or rounding. At the end of this paper it will be presented a case of study developed in Simulink of Matlab software, and the results of the model based on difference equations is compared with the finite-difference approximate model including the analysis of ap-proximation errors.