José Antonio Moraño

Non-standard numerical method for a mathematical model of RSV epidemiological transmission

Respiratory Syncytial Virus (RSV) has long been recognized as the single most important virus causing acute severe respiratory-tract infections with symptoms ranging from rhinitis to bronchitis in children who may require hospitalization. Outbreaks of RSV occur every year and all children become infected within the first two years of life, and that overloads hospital casualty services. The transmission dynamics of RSV are strongly seasonal. Epidemics occur each winter in temperate climates and often coincide with the seasonal rainfall in tropical climates. In this paper we develop a non-standard numerical scheme for a SIRS seasonal epidemiological model for RSV transmission. This non-standard numerical scheme preserves the positivity of the continuous model and is applied to approximate the solution using different sizes of step. Finally this method is compared with some well-known explicit methods and simulations with data from Gambia and Finland are carried out.

Stochastic modeling of the transmission of respiratory syncytial virus (RSV) in the region of Valencia, Spain

In this paper, we study the dynamics of the transmission of respiratory syncytial virus (RSV) in the population using stochastic models. The stochastic models are developed introducing stochastic perturbations on the demographic parameter as well as on the transmission rate of the RSV. Numerical simulations of the deterministic and stochastic models are performed in order to understand the effect of fluctuating birth rate and transmission rate of the RSV on the population dynamics. The numerical solutions of stochastic models are calculated using Euler-Maruyama and Milstein schemes, and confidence intervals for stochastic solutions are given using Monte-Carlo method. Analysis of the numerical results reveals that perturbations on the transmission rate are more decisive in the dynamics of RSV than perturbations on demographic parameters. In addition, the stochastic models show the advantage of reproducing more effectively the noisy RSV hospitalization data. It is concluded that these stochastic models are a viable option to provide a realistic modeling of the RSV dynamics on the population.

Cost analysis of a vaccination strategy for respiratory syncytial virus (RSV) in a network model

In this paper an age-structured mathematical model for respiratory syncytial virus (RSV) is proposed where children younger than one year old, who are the most affected by this illness, are specially considered. Real data of hospitalized children in the Spanish region of Valencia are used in order to determine some seasonal parameters of the model. Once the parameters are determined, we propose a complete stochastic network model to study the seasonal evolution of the respiratory syncytial virus (RSV) epidemics. In this model every susceptible individual can acquire the disease after a random encounter with any infected individual in the social network. The edges of a complete graph connecting every pair of individuals in the network simulate these encounters and a season dependent probability, @b(t), determines whether the healthy susceptible individual becomes infected or not. We show that the prediction of this model is compatible with the above mentioned age-structured model based upon differential equations, but sharper peaks are obtained in the case of the network. Then, on the network model, we propose the vaccination of children at 2 months, 4 months and 1 year old, and we study the cost of this vaccination strategy, which is emerging as the most plausible one to be applied when the vaccine hits the market. It is worth to note that this vaccination strategy is simulated in the network model because to implement it in the continuous model is very difficult and increases its complexity.

Using random networks to study the dynamics of respiratory syncytial virus (RSV) in the Spanish region of Valencia

Seasonal fluctuations in the incidence of several respiratory infections are a feature of epidemiological surveys all around the world. This phenomenon is characteristic of influenza and respiratory syncytial virus pandemics. However, the explanation of the seasonal outbreaks of these diseases remains poorly understood. Many statistical studies have been carried out in order to provide a correlation of the outbreaks with climatic or social factors without achieving a definitive conclusion. Here we show that, in a random social network, self-sustained seasonal epidemics emerge as a process modulated by the infection probability and the immunity period after recovering from the infection. This is a purely endogenous phenomenon that does not require any exogenous forcing. Assuming that this is the dominant mechanism for seasonal epidemics, many implications for public health policies for infectious respiratory diseases could be drawn.

Optimizing strategies for meningococcal C disease vaccination in Valencia (Spain)

BackgroundMeningococcal C (MenC) conjugate vaccines have controlled invasive diseases associated with this serogroup in countries where they are included in National Immunization Programs and also in an extensive catch-up program involving subjects up to 20 years of age. Catch-up was important, not only because it prevented disease in adolescents and young adults at risk, but also because it decreased transmission of the bacteria, since it was in this age group where the organism was circulating. Our objective is to develop a new vaccination schedule to achieve maximum seroprotection in these groups.MethodsA recent study has provided detailed age-structured information on the seroprotection levels against MenC in Valencia (Spain), where vaccination is routinely scheduled at 2 months and 6 months, with a booster dose at 18 months of age. A complementary catch-up campaign was also carried out in n for children from 12 months to 19 years of age. Statistical analyses of these data have provided an accurate picture on the evolution of seroprotection in the last few years.ResultsAn agent-based model has been developed to study the future evolution of the seroprotection histogram. We have shown that the optimum strategy for achieving high protection levels in all infants, toddlers and adolescents is a change to a 2 months, 12 months and 12 years of age vaccination pattern. If the new schedule were implemented in January 2014, high-risk subjects between 15-19 years of age would have very low seroprotection for the next 6 years, thereby threatening the program.ConclusionsHigh protection levels and a low incidence of meningococcal C disease can be achieved in the future by means of a cost-free change in vaccination program. However, we recommend a new catch-up program simultaneous to the change in regular vaccination program.

Studying the Herd Immunity Effect of the Varicella Vaccine in the Community of Valencia, Spain

In 2013, the Spanish Agency of Medicines blocked the varicella vaccine distribution based on a partial coverage of the vaccine that hypothetically could induce an increase of cases in adults: as non vaccinated children reach adulthood without having had contact with the virus in case the herd immunity stopped the virus circulation, or a hypothetical loss of vaccine protection in the long run. Also, this measure wanted to avoid increasing the number of cases of herpes zoster in adults. In this paper we develop a mathematical model to study the transmission dynamics of varicella in order to assess the impact of the partial coverage of the vaccination program. This is of paramount importance because, from the Public Health point of view, the herd immunity may be an undesirable effect of the partial vaccination due to that varicella and/or herpes zoster in adults use to be severe.

Evaluación y Calificación en Grupo de Laboratorio de Matemática Computacional

Current methodologies involve personal and group intervention by students leading to consider new approaches in the evaluation methods maintaining the relationship with the learning objectives that must cover the subjects of the degree courses. We intend to show an innovation made in the form of oral presentations evaluating the group work in the course of Computational Mathematics Laboratory of the first year in the Degree of Electronic Engineering and Automation. This evaluation will consider both the teachers qualification as those made by each of the group members. It is desirable this cooperative attitude and responsibility of all team members and convey the message that each of them is responsible for work done both against their partners as to the teacher. The evaluation method used is presented in detail and also the results obtained. Subsequently, the opinion of the students about this change in the evaluation of group work will be exhibited.

Mathematics competences assessment at lab sessions of aerospace engineering freshmen

At the Design Engineering Higher Technical School (Valencia, Spain) we started introducing Lab sessions as a part of the Mathematics curriculum almost 20 years ago. Nowadays they are an integral part of the general assessment of the subject and hardly may we disassociate them given the actual constrains in time that we are facing with the arrival of the new student centered university structure. On the other hand we have widely implemented the use of an educational platform with several tools in Lab classes and their exams and, additionally, this year we have developed a new approach to the realization of Lab sessions turning all of them from a traditional system to another one based on a flipped classroom methodology. This new approach aims to facilitate an increasing interest from engineering students by motivating them to work the subject of Mathematics in their first university course. Within this approach each session is divided into three parts: preparation, solving doubts and assessment of the competences assigned to that session. In this paper we will present the methodology developed, difficulties, results and a questionnaire we aim to ask our Aerospace Engineering students in order to get their perception of the course.

Whole mathematics competences assessment at aerospace engineering sophomore

Mathematics background of Engineering students changes drastically between freshmen and sophomore students. This brings out the way in which lab sessions are incorporated must be taken into account as well in the continuous assessment of the subject being a key issue how to incorporate the assessment of lab sessions. At the Higher Technical School of Design Engineering of the Universität Politècnica of Valencia (UPV) we started using CAS almost 20 years ago and have evolved from the initial lab sessions and their corresponding evaluation. Our learning tells us that the final approach depends on the content of the subject and how relevant are the methods used as well as the capabilities of the CAS used. In addition, the standard use of assignments to reinforce the learning process of each student has also shown to be a keystone to increase the Engineering students competences before each assessment test. Results will be presented concerning a second year Mathematics course in Aerospace Engineering where 100% students attendance was achieved at the end of the third semester, all of them taking all exams, and where we experienced a success rate above 91% which is far of being standard at Spanish Engineering studies.