Analysis, Simulation and Control of a New Measles Epidemic Model

In this paper the problem of modeling and controlling the measles epidemic spread is faced. A new model is proposed and analysed; besides the categories usually considered in measles modeling, the susceptible, the exposed, the infected, the removed and, less frequently, the quarantine individuals, two new categories are herein introduced: the immunosuppressed subjects, that can not be vaccinated, and the patients with an additional complication, not risky by itself but dangerous if caught togeter with the measles. These two novelties are taken into account in designing and scheduling suitably control actions such as vaccination, whenever possible, prevention, quarantine and treatment, when limited resources are available. An analysis of the model is developed and the optimal control strategies are compared with other not optimized actions. By using the Pontryagin principle, it is shown the prevailing role of the vaccination in guaranteeing the protection to immunosuppressed individuals, as well as the importance of a prompt response of the society when an epidemic spread occurs, such as the quarantine intervention

The dynamics of measles in sub-Saharan Africa.

Although vaccination has almost eliminated measles in parts of the world, the disease remains a major killer in some high birth rate countries of the Sahel. On the basis of measles dynamics for industrialized countries, high birth rate regions should experience regular annual epidemics. Here, however, we show that measles epidemics in Niger are highly episodic, particularly in the capital Niamey. Models demonstrate that this variability arises from powerful seasonality in transmission-generating high amplitude epidemics-within the chaotic domain of deterministic dynamics. In practice, this leads to frequent stochastic fadeouts, interspersed with irregular, large epidemics. A metapopulation model illustrates how increased vaccine coverage, but still below the local elimination threshold, could lead to increasingly variable major outbreaks in highly seasonally forced contexts. Such erratic dynamics emphasize the importance both of control strategies that address build-up of susceptible individuals and efforts to mitigate the impact of large outbreaks when they occur

Predicting unobserved exposures from seasonal epidemic data

We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model with a contact rate that fluctuates seasonally. Through the use of a nonlinear, stochastic projection, we are able to analytically determine the lower dimensional manifold on which the deterministic and stochastic dynamics correctly interact. Our method produces a low dimensional stochastic model that captures the same timing of disease outbreak and the same amplitude and phase of recurrent behavior seen in the high dimensional model. Given seasonal epidemic data consisting of the number of infectious individuals, our method enables a data-based model prediction of the number of unobserved exposed individuals over very long times.Comment: 24 pages, 6 figures; Final version in Bulletin of Mathematical Biolog

Emerging Challenges and Opportunities in Infectious Disease Epidemiology.

Much of the intellectual tradition of modern epidemiology stems from efforts to understand and combat chronic diseases persisting through the 20th century epidemiologic transition of countries such as the United States and United Kingdom. After decades of relative obscurity, infectious disease epidemiology has undergone an intellectual rebirth in recent years amid increasing recognition of the threat posed by both new and familiar pathogens. Here, we review the emerging coalescence of infectious disease epidemiology around a core set of study designs and statistical methods bearing little resemblance to the chronic disease epidemiology toolkit. We offer our outlook on challenges and opportunities facing the field, including the integration of novel molecular and digital information sources into disease surveillance, the assimilation of such data into models of pathogen spread, and the increasing contribution of models to public health practice. We next consider emerging paradigms in causal inference for infectious diseases, ranging from approaches to evaluating vaccines and antimicrobial therapies to the task of ascribing clinical syndromes to etiologic microorganisms, an age-old problem transformed by our increasing ability to characterize human-associated microbiota. These areas represent an increasingly important component of epidemiology training programs for future generations of researchers and practitioners

The use of a formal sensitivity analysis on epidemic models with immune protection from maternally acquired antibodies

This paper considers the outcome of a formal sensitivity analysis on a series of epidemic model structures developed to study the population level effects of maternal antibodies. The analysis is used to compare the potential influence of maternally acquired immunity on various age and time domain observations of infection and serology, with and without seasonality. The results of the analysis indicate that time series observations are largely insensitive to variations in the average duration of this protection, and that age related empirical data are likely to be most appropriate for estimating these characteristics

Modeling the long term dynamics of pre-vaccination pertussis

The dynamics of strongly immunizing childhood infections is still not well understood. Although reports of successful modeling of several incidence data records can be found in the literature, the key determinants of the observed temporal patterns have not been clearly identified. In particular, different models of immunity waning and degree of protection applied to disease and vaccine induced immunity have been debated in the literature on pertussis. Here we study the effect of disease acquired immunity on the long term patterns of pertussis prevalence. We compare five minimal models, all of which are stochastic, seasonally forced, well-mixed models of infection based on susceptible-infective-recovered dynamics in a closed population. These models reflect different assumptions about the immune response of naive hosts, namely total permanent immunity, immunity waning, immunity waning together with immunity boosting, reinfection of recovered, and repeat infection after partial immunity waning. The power spectra of the output prevalence time series characterize the long term dynamics of the models. For epidemiological parameters consistent with published data for pertussis, the power spectra show quantitative and even qualitative differences that can be used to test their assumptions by comparison with ensembles of several decades long pre-vaccination data records. We illustrate this strategy on two publicly available historical data sets.Comment: paper (31 pages, 11 figures, 1 table) and supplementary material (19 pages, 5 figures, 2 tables