SUMMARYThe weekly number of dengue cases in Peru, South America, stratified by province for the period 1994-2006 were analysed in conjunction with associated demographic, geographic and climatological data. Estimates of the reproduction number, moderately correlated with population size (Spearman rho=0.28, P=0.03), had a median of 1.76 (IQR 0.83-4.46). The distributions of dengue attack rates and epidemic durations follow power-law (Pareto) distributions (coefficient of determination >85%, P<0.004). Spatial heterogeneity of attack rates was highest in coastal areas followed by mountain and jungle areas. Our findings suggest a hierarchy of transmission events during the large 2000-2001 epidemic from large to small population areas when serotypes DEN-3 and DEN-4 were first identified (Spearman rho=-0.43, P=0.03). The need for spatial and temporal dengue epidemic data with a high degree of resolution not only increases our understanding of the dynamics of dengue but will also generate new hypotheses and provide a platform for testing innovative control policies.

Resumen: En el presente trabajo, se realiza un modelo computacional mediante los Autómatas Celulares (Cell-DEVS) que describa la dinámica de transmisión de la Varicela en un grupo cerrado de personas donde se pueda propagar la enfermedad. Desde la perspectiva de la epidemiología matemática se tiene el modelo matemático SEIR de W. O. Kermack y A. G. McKendrick que representa la dinámica de la epidemia, en nuestro caso la Varicela, donde se realizará las simulaciones computacionales tanto por los Métodos Numéricos como los Autómatas Celulares para analizar el desarrollo de la enfermedad. Palabras clave: epidemiología matemática; ecuaciones diferenciales; autómatas celulares; formalismo DEVS; simulaciones computacionales. Computational Modeling of Varicella Transmission Dynamics through CellularAutomata ( .0/) que permite el uso no comercial, distribución y reproducción en cualquier medio, siempre que la obra original sea debidamente citada. Para información, por favor póngase en contacto con

Modelamiento computacional de la dinámica de transmisión sexual del VIH/SIDA mediante autómatas celulares (Cell-DEVS) Computational modeling of the dynamics of sexual transmission of HIV/AIDS through cellular automats (Cell-DEVS

In this work, we study the dynamical behavior of a modified SIR epidemiological model by introducing negative feedback and a nonpharmaceutical intervention. The first model to be defined is the usceptible–Isolated–Infected–Recovered–Dead (SAIRD) epidemics model and then the S-A-I-R-D-Information Index (SAIRDM) model that corresponds to coupling the SAIRD model with the negative feedback. Controlling the information about nonpharmaceutical interventions is considered by the addition of a new variable that measures how the behavioral changes about isolation influence pandemics. An analytic expression of a replacement ratio that depends on the absence of the negative feedback is determined. The results obtained show that the global stability of the disease-free equilibrium is determined by the value of a certain threshold parameter called the basic reproductive number $\mathcal{R}_{0}$ R 0 and the local stability of the free disease equilibrium depends on the replacement ratios. A Hopf bifurcation is analytically verified for the delay parameter. The qualitative analysis shows that the feedback information index promotes more changes to the propagation of the disease than other parameters. Finally, the sensitivity analysis and simulations show the efficiency of the infection rate of the information index on an epidemics model with nonpharmaceutical interventions.