Background: The World Health Organization declared the ongoing Zika virus (ZIKV) epidemic in the Americas a Public Health Emergency of International Concern on February 1, 2016. ZIKV disease in humans is characterized by a “dengue-like” syndrome including febrile illness and rash. However, ZIKV infection in early pregnancy has been associated with severe birth defects, including microcephaly and other developmental issues. Mechanistic models of disease transmission can be used to forecast trajectories and likely disease burden but are currently hampered by substantial uncertainty on the epidemiology of the disease (e.g., the role of asymptomatic transmission, generation interval, incubation period, and key drivers). When insight is limited, phenomenological models provide a starting point for estimation of key transmission parameters, such as the reproduction number, and forecasts of epidemic impact. Methods: We obtained daily counts of suspected Zika cases by date of symptoms onset from the Secretary of Health of Antioquia, Colombia during January-April 2016. We calibrated the generalized Richards model, a phenomenological model that accommodates a variety of early exponential and sub-exponential growth kinetics, against the early epidemic trajectory and generated predictions of epidemic size. The reproduction number was estimated by applying the renewal equation to incident cases simulated from the fitted generalized-growth model and assuming gamma or exponentially-distributed generation intervals derived from the literature. We estimated the reproduction number for an increasing duration of the epidemic growth phase. Results: The reproduction number rapidly declined from 10.3 (95% CI: 8.3, 12.4) in the first disease generation to 2.2 (95% CI: 1.9, 2.8) in the second disease generation, assuming a gamma-distributed generation interval with the mean of 14 days and standard deviation of 2 days. The generalized-Richards model outperformed the logistic growth model and provided forecasts within 22% of the actual epidemic size based on an assessment 30 days into the epidemic, with the epidemic peaking on day 36. Conclusion: Phenomenological models represent promising tools to generate early forecasts of epidemic impact particularly in the context of substantial uncertainty in epidemiological parameters. Our findings underscore the need to treat the reproduction number as a dynamic quantity even during the early growth phase, and emphasize the sensitivity of reproduction number estimates to assumptions on the generation interval distribution.

SUMMARY: 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.

An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler–Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.

Introduction: Serological surveillance (serosurveillance) provides the most direct measure of herd immunity of vaccine-preventable diseases. Little is known about the opportunities and challenges of serosurveillance experiences, particularly pertussis.Objective: To describe the process of serosurveillance for vaccine-preventable diseases with an emphasis on the experience of pertussis in the metropolitan area of Antioquia (Valle de Aburrá) in 2015 and 2016 and analyze the contributions and challenges for its sustainability.Materials and methods: We described the planning and conduction of serosurveillance of pertussis antibodies of mothers and in the umbilical cord at the time of delivery in eight hospitals based on random sampling and their capacity to advance the serosurveillance periodically. We compared the contributions and the challenges of this experience with other probabilistic and non-probabilistic programs.Results: We achieved the participation of hospitals and mothers respecting the delivery care process. We established a serum bank following ethical and technical guidelines. This program based on the random selection of hospitals and mothers has enabled the estimation of antibodies prevalence in mothers and in the umbilical cord, which has been possible given the high coverage of hospital care during childbirth at a lower cost and fewer risks than a population-based survey in conflictive areas. The main challenges for the sustainability of this program are the creation of stable jobs and access to funding and legal and methodological long-term frameworks.Conclusions: Hospital serosurveillance as described is an option to monitor the impact of vaccination on the population. Our experience could be reproduced in other regions under similar conditions if the above-mentioned challenges are solved.