Publicación: ANALYSIS OF A SEIR-KS MATHEMATICAL MODEL FOR COMPUTER VIRUS PROPAGATION IN A PERIODIC ENVIRONMENT
Fecha
2020
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MATHEMATICS
Resumen
IN THIS WORK WE DEVELOP A STUDY OF POSITIVE PERIODIC SOLUTIONS FOR A MATHEMATICAL MODEL OF THE DYNAMICS OF COMPUTER VIRUS PROPAGATION. WE PROPOSE A GENERALIZED COMPARTMENT MODEL OF SEIR-KS TYPE, SINCE WE CONSIDER THAT THE POPULATION IS PARTITIONED IN FIVE CLASSES: SUSCEPTIBLE (S); EXPOSED (E); INFECTED (I); RECOVERED (R); AND KILL SIGNALS (K), AND ASSUME THAT THE RATES OF VIRUS PROPAGATION ARE TIME DEPENDENT FUNCTIONS. THEN, WE INTRODUCE A SUFFICIENT CONDITION FOR THE EXISTENCE OF POSITIVE PERIODIC SOLUTIONS OF THE GENERALIZED SEIR-KS MODEL. THE PROOF OF THE MAIN RESULTS ARE BASED ON A PRIORI ESTIMATES OF THE SEIR-KS SYSTEM SOLUTIONS AND THE APPLICATION OF COINCIDENCE DEGREE THEORY. MOREOVER, WE PRESENT AN EXAMPLE OF A GENERALIZED SYSTEM SATISFYING THE SUFFICIENT CONDITION.
