Análisis no-lineal de la dinámica de enfermedades infecciosas en Chile / Non linear analysis of the infectious disease dynamics in Chile

ABSTRACT

Background: The incidence of infectious diseases generally has large fluctuations, probably due to interactions between seasonal fluctuations and those secondary to case-susceptible host interactions. Aim: To analyze the complexity and attractant topological resemblance of seven infectious diseases in Chile. Material and methods: The annual incidence of measles, whooping cough, scarlet fever, meningococcal meningitis, diphtheria, typhoid fever and poliomyelitis was obtained from the annual reports of diseases. Correlation dimensions and the largest Lyapunov series exponents were estimated. The resemblance among their attractants was assessed by Hausdorff distance. The measures were performed both before and after seasonal filtering. Results: All series showed a dynamics near low dimensional chaos. The correlation dimensions ranged between 2.12 and 2.76. The correlation dimensions did not change after seasonal differentiation. Apart from one, all disease dynamics had large Lyapunov exponents, near 0.6 Bits/year. These decreased if series were differentiated. Before differentiation, the topological resemblance was mainly caused by the seasonal component of the dynamics but thereafter, the resemblance increased. In spite of different transmission mechanisms and etiologies, all analyzed infectious diseases conformed a truly single group, during cluster analyses. Conclusions: These results suggest that beneath the dynamics of infectious diseases, obscured by seasonal environmental factors, lays a very consistent nonlinear agent-susceptible host dynamics