Using posterior predictive distributions to analyse epidemic models: COVID-19 in Mexico City.

Epidemiological models usually contain a set of parameters that must be adjusted based on available observations. Once a model has been calibrated, it can be used as a forecasting tool to make predictions and to evaluate contingency plans. It is customary to employ only point estimators of model parameters for such predictions. However, some models may fit the same data reasonably well for a broad range of parameter values, and this flexibility means that predictions stemming from them will vary widely, depending on the particular values employed within the range that gives a good fit. When data are poor or incomplete, model uncertainty widens further. A way to circumvent this problem is to use Bayesian statistics to incorporate observations and use the full range of parameter estimates contained in the posterior distribution to adjust for uncertainties in model predictions. Specifically, given an epidemiological model and a probability distribution for observations, we use the posterior distribution of model parameters to generate all possible epidemic curves, whose information is encapsulated in posterior predictive distributions. From these, one can extract the worst-case scenario and study the impact of implementing contingency plans according to this assessment. We apply this approach to the evolution of COVID-19 in Mexico City and assess whether contingency plans are being successful and whether the epidemiological curve has flattened.

Incidence of Intestinal Infectious Diseases due to Protozoa and Bacteria in Mexico: Analysis of National Surveillance Records from 2003 to 2012.

BACKGROUND: According to national epidemiological surveillance records, in Mexico six intestinal infectious diseases (IID) are among the top infectious communicable diseases. However, their incidence, relative importance, and spatial patterns have not been studied in detail. AIMS: We examine the epidemiology of IID due to bacteria and protozoa to identify which diseases are most important at two spatial scales, what is their integrated importance locally, and how their incidence correlates with Human Development Index (HDI). METHODS: We retrieved yearly number of new cases of eight IID from the national epidemiological morbidity report from 2003 to 2012 at the national level, by state, and to assess such information at a higher spatial resolution we included the municipalities for Mexico City. However, no comparisons were made to other municipalities due to unavailability of data. We compared incidence, obtained the disease-specific relative importance, and inspected spatial patterns for the integrated incidence. Finally, we tested whether HDI is correlated with incidence. RESULTS: We found that, except for two diseases, the relative importance of the other six IID contrasted not only between the national level and Mexico City, but also among states and municipalities in Mexico City. Besides, at both scales the distribution of the incidence showed disease-specific spatial patterns. Finally, there was a lack of consistent correlation between HDI and individual IID at both scales. CONCLUSION: Our results emphasize the need for local disease-focused selective models for control and prevention of IID. The maps displaying our analyses of epidemiological similarities may be used in orienting such effort.

Epidemiological impact of vaccination on the dynamics of two childhood diseases in rural Senegal.

Measles and pertussis are ubiquitous vaccine-preventable diseases, which remain an important public health problem in developing countries. Hence, developing a deep understanding of their transmission dynamics remains imperative. To achieve this, we compared the impact of vaccination at both individual and population levels in a Senegalese rural community. This study represents the first such comparative study in tropical conditions and constitutes a point of comparison with other studies of disease dynamics in developed countries. Changes in the transmission rates of infections are reflected in their mean ages at infection and basic reproductive ratio calculated before and after vaccination. We explored persistence of both infections in relation to population size in each village and found the inter-epidemic period for the whole area using wavelets analysis. As predicted by epidemiological theory, we observed an increase in the mean age at infection and a decrease in the reproductive ratio of both diseases. We showed for both the pre- vaccination and vaccine eras that persistence depends on population size. After vaccination, persistence decreased and the inter-epidemic period increased. The observed changes suggest that vaccination against measles and pertussis induced a drop in their transmission. Similarities in disease dynamics to those of temperate regions such as England and Wales were also observed.

Implications of partial immunity on the prospects for tuberculosis control by post-exposure interventions.

One-third of the world population (approximately 2 billion individuals) is currently infected with Mycobacterium tuberculosis, the vast majority harboring a latent infection. As the risk of reactivation is around 10% in a lifetime, it follows that 200 million of these will eventually develop active pulmonary disease. Only therapeutic or post-exposure interventions can tame this vast reservoir of infection. Treatment of latent infections can reduce the risk of reactivation, and there is accumulating evidence that combination with post-exposure vaccines can reduce the risk of reinfection. Here we develop mathematical models to explore the potential of these post-exposure interventions to control tuberculosis on a global scale. Intensive programs targeting recent infections appear generally effective, but the benefit is potentially greater in intermediate prevalence scenarios. Extending these strategies to longer-term persistent infections appears more beneficial where prevalence is low. Finally, we consider that susceptibility to reinfection is altered by therapy, and explore its epidemiological consequences. When we assume that therapy reduces susceptibility to subsequent reinfection, catastrophic dynamics are observed. Thus, a bipolar outcome is obtained, where either small or large reductions in prevalence levels result, depending on the rate of detection and treatment of latent infections. By contrast, increased susceptibility after therapy may induce an increase in disease prevalence and does not lead to catastrophic dynamics. These potential outcomes are silent unless a widespread intervention is implemented.