Deterministic SIR models were applied to simulate Susceptible-Infected-Removed and to estimate the threshold condition for varicella outbreaks in children, reported in Medellín, Colombia. The expected numbers of susceptible, infected and removed individuals were compared with observed cases from notification of varicella outbreaks to the local Board of Health and from survey data. The threshold condition was estimated by the basic reproductive ratio and by the relative removal rate, through which measures for preventing and curtailing the outbreaks were identified. The model demonstrated a reasonable fit to the observations, except in two of the six outbreaks which probably reflected under-registration of cases. In order to have prevented these outbreaks, between 4.4% and 52.9% of the susceptible population should have been vaccinated assuming an 85% vaccine effectiveness. Similarly, isolation of affected children should have been increased to between 4.3% and 44.8% per week.

Payares R. Inmunidad colectiva contra la rubéola según una encuesta poblacional en Medellín, Colombia. Rev Panam Salud Publica. 2012;32(2):101-8. Forma de citarEl término inmunidad colectiva, poblacional o de rebaño, se refiere al efecto grupal de los programas de vacunación masiva. Se logra cuando existe una alta proporción (aunque inferior al 100%) de individuos inmunes, lo que reduce la probabilidad de contacto entre un individuo susceptible y uno infectado, evitando la transmisión de la enfermedad (1). El término "inmunidad de rebaño" fue usado por primera vez por Topley y Wilson en 1923, que sugirieron que se separara el estudio de la inmunidad individual del de la inmunidad colectiva (2).Para Theophil Lotz (3), cuando se vacuna no sólo se obtiene un beneficio individual, sino que este se extiende a las personas susceptibles no protegidas de una comunidad. La vacunación puede proteger a los individuos y generar un de 90,0% (IC95% 88,2) y el R e de 0,95 (IC95% 0,8), para una proporción ponderada de protección de 89,4% (IC95% 86,6). La protección fue menor que la P c esperada en ambos sexos, en los estratos socioeconómicos alto y bajo, y en la zona rural. En la zona urbana la protección fue mayor que la P c (89,4%, IC95% 86,7 en comparación con 87,4%, IC95% 85,8

The threshold theorem of an epidemic SIR model was compared when infectious and susceptible individuals have homogeneous mixing and heterogeneous social status and when individuals of random networks have contact heterogeneity. Particularly the effect of vaccination in such models is considered when: individuals or nodes are exposed to impoverished, vaccination and loss of immunity. An equilibrium analysis and local stability of small perturbations about the equilibrium values were implemented using computer algebra. Numerical simulations were executed in order to describe the dynamic of transmission of diseases and changes of the basic reproductive rate. The implications of these results are examined around the threats to the global public health security.

Leptospirosis is a bacterial zoonosis with world distribution and multiform clinical spectrum in men and animals. The etiology of this disease is the pathogenic species of Leptospira, which cause diverse manifestations of the disease, from mild to serious, such as the Weil disease and the lung hemorrhagic syndrome with lethal proportions of 10% -50%. This is an emerging problem of urban health due to the growth of marginal neighborhoods without basic sanitary conditions and an increased number of rodents. The presence of rodents and the probability of having contact with their urine determine the likelihood for humans to get infected. In this paper, we simulate the spatial distribution of risk infection of human leptospirosis according to the proximity to rodent burrows considered as potential source of infection. The Bessel function K 0 with an r distance from the potential point source, and the scale parameter α in meters was used. Simulation inputs were published data of leptospirosis incidence rate (range of 5 to 79 x 10 000), and a distance of 100 to 5000 meters from the source of infection. We obtained an adequate adjustment between the function and the simulated data. The risk of infection increases with the proximity of the potential source. This estimation can become a guide to propose effective measures of control and prevention.