Impact of a New SARS-CoV-2 Variant on the Population: A Mathematical Modeling Approach

[EN] Several SARS-CoV-2 variants have emerged around the world, and the appearance of other variants depends on many factors. These new variants might have different characteristics that can affect the transmissibility and death rate. The administration of vaccines against the coronavirus disease 2019 (COVID-19) started in early December of 2020 and in some countries the vaccines will not soon be widely available. For this article, we studied the impact of a new more transmissible SARS-CoV-2 strain on prevalence, hospitalizations, and deaths related to the SARS-CoV-2 virus. We studied different scenarios regarding the transmissibility in order to provide a scientific support for public health policies and bring awareness of potential future situations related to the COVID-19 pandemic. We constructed a compartmental mathematical model based on differential equations to study these different scenarios. In this way, we are able to understand how a new, more infectious strain of the virus can impact the dynamics of the COVID-19 pandemic. We studied several metrics related to the possible outcomes of the COVID-19 pandemic in order to assess the impact of a higher transmissibility of a new SARS-CoV-2 strain on these metrics. We found that, even if the new variant has the same death rate, its high transmissibility can increase the number of infected people, those hospitalized, and deaths. The simulation results show that health institutions need to focus on increasing non-pharmaceutical interventions and the pace of vaccine inoculation since a new variant with higher transmissibility, such as, for example, VOC-202012/01 of lineage B.1.1.7, may cause more devastating outcomes in the population.Funding support from the National Institute of General Medical Sciences (P20GM103451) via NM-INBRE is gratefully acknowledged by the first author.González Parra, G.; Martínez-Rodríguez, D.; Villanueva Micó, RJ. (2021). Impact of a New SARS-CoV-2 Variant on the Population: A Mathematical Modeling Approach. Mathematical and Computational Applications (Online). 26(2):1-21. https://doi.org/10.3390/mca26020025S12126

Analysis of Key Factors of a SARS-CoV-2 Vaccination Program: A Mathematical Modeling Approach

[EN] The administration of vaccines against the coronavirus disease 2019 (COVID-19) started in early December of 2020. Currently, there are only a few approved vaccines, each with different efficacies and mechanisms of action. Moreover, vaccination programs in different regions may vary due to differences in implementation, for instance, simply the availability of the vaccine. In this article, we study the impact of the pace of vaccination and the intrinsic efficacy of the vaccine on prevalence, hospitalizations, and deaths related to the SARS-CoV-2 virus. Then we study different potential scenarios regarding the burden of the COVID-19 pandemic in the near future. We construct a compartmental mathematical model and use computational methodologies to study these different scenarios. Thus, we are able to identify some key factors to reach the aims of the vaccination programs. We use some metrics related to the outcomes of the COVID-19 pandemic in order to assess the impact of the efficacy of the vaccine and the pace of the vaccine inoculation. We found that both factors have a high impact on the outcomes. However, the rate of vaccine administration has a higher impact in reducing the burden of the COVID-19 pandemic. This result shows that health institutions need to focus on increasing the vaccine inoculation pace and create awareness in the population about the importance of COVID-19 vaccines.Funding support from the National Institute of General Medical Sciences (P20GM103451) via NM-INBRE is gratefully acknowledged by the second authorMartínez-Rodríguez, D.; González Parra, G.; Villanueva Micó, RJ. (2021). Analysis of Key Factors of a SARS-CoV-2 Vaccination Program: A Mathematical Modeling Approach. Epidemiologia. 2(2):140-161. https://doi.org/10.3390/epidemiologia2020012S1401612

Extending the deterministic Riemann-Liouville and Caputo operators to the random framework: A mean square approach with applications to solve random fractional differential equations

[EN] This paper extends both the deterministic fractional Riemann¿Liouville integral and the Caputo fractional derivative to the random framework using the mean square random calculus. Characterizations and sufficient conditions to guarantee the existence of both fractional random operators are given. Assuming mild conditions on the random input parameters (initial condition, forcing term and diffusion coefficient), the solution of the general random fractional linear differential equation, whose fractional order of the derivative is ¿ ¿ [0, 1], is constructed. The approach is based on a mean square chain rule, recently established, together with the random Fröbenius method. Closed formulae to construct reliable approximations for the mean and the covariance of the solution stochastic process are also given. Several examples illustrating the theoretical results are included.This work has been partially supported by the Ministerio de Economia y Competitividad grant MTM2013-41765-P. The co-author Prof. L. Villafuerte acknowledges the support by Mexican Conacyt.Burgos, C.; Cortés, J.; Villafuerte, L.; Villanueva Micó, RJ. (2017). Extending the deterministic Riemann-Liouville and Caputo operators to the random framework: A mean square approach with applications to solve random fractional differential equations. Chaos, Solitons and Fractals. 102:305-318. https://doi.org/10.1016/j.chaos.2017.02.008S30531810

Calibration of an agent-based simulation model to the data of women infected by Human Papillomavirus with uncertainty

[EN] Recently, the transmission dynamics of the Human Papillomavirus (HPV) has been studied. In previous works, we have designed and implemented a computational model (agent-based simulation model) where the contagion of the HPV is described on a network of lifetime sexual partners. The run of a single simulation of this computational model, composed of a network with 500 000 nodes, takes about one hour and a half. In addition to set an adequate model, finding out the model parameters that best fit the proposed model to the available data of prevalence is a crucial goal. Taking into account that the necessary number of simulations to perform the calibration of the model may be very high, the aforementioned goal may become unaffordable. In this paper, we present a procedure to fit the proposed HPV model to the available data and the design of an asynchronous version of the Particle Swarm Optimization (PSO) algorithm adapted to the distributed computing environment. In the process, the number of particles used in PSO should be set carefully looking for a compromise between quality of the solutions and computation time. Another feature of the procedure presented here is that we want to capture the intrinsic uncertainty in the data (data come from a survey) when calibrating the model. To do so, we also propose the design of an algorithm to select the model parameter sets obtained during the calibration that best capture the data uncertainty.This work has been supported by the Spanish Ministerio de Economia y Competitividad grants MTM2017-89664-P, TIN2014-54806-R and RTI2018-095180-B-I00, Grants Y2018/NMT-4668 (Micro-Stres-MAP-CM) and GenObIA-CM (S2017/BMD-3773) financed by the Community of Madrid, Spain and co-financed with EU Structural Funds, Spain, and by GLENO project financed by Fundacion Eugenio Rodriguez Pascual, Spain.Villanueva Micó, RJ.; Hidalgo, J.; Cervigon, C.; Villanueva-Oller, J.; Cortés, J. (2019). Calibration of an agent-based simulation model to the data of women infected by Human Papillomavirus with uncertainty. Applied Soft Computing. 80:546-556. https://doi.org/10.1016/j.asoc.2019.04.015S5465568

Modeling Chickenpox Dynamics with a Discrete Time Bayesian Stochastic Compartmental Model

[EN] We present a Bayesian stochastic susceptible-exposed-infectious-recovered model in discrete time to understand chickenpox transmission in the Valencian Community, Spain. During the last decades, different strategies have been introduced in the routine immunization program in order to reduce the impact of this disease, which remains a public health's great concern. Under this scenario, a model capable of explaining closely the dynamics of chickenpox under the different vaccination strategies is of utter importance to assess their effectiveness. The proposed model takes into account both heterogeneous mixing of individuals in the population and the inherent stochasticity in the transmission of the disease. As shown in a comparative study, these assumptions are fundamental to describe properly the evolution of the disease. The Bayesian analysis of the model allows us to calculate the posterior distribution of the model parameters and the posterior predictive distribution of chickenpox incidence, which facilitates the computation of point forecasts and prediction intervals.This work has been supported by a research grant from the Spanish Ministry of Economy and Competitiveness (MTM2017-83850-P).Corberán-Vallet, A.; Santonja, F.; Jornet-Sanz, M.; Villanueva Micó, RJ. (2018). Modeling Chickenpox Dynamics with a Discrete Time Bayesian Stochastic Compartmental Model. Complexity. 1-9. https://doi.org/10.1155/2018/3060368S19Acedo, L., Moraño, J.-A., Santonja, F.-J., & Villanueva, R.-J. (2016). A deterministic model for highly contagious diseases: The case of varicella. Physica A: Statistical Mechanics and its Applications, 450, 278-286. doi:10.1016/j.physa.2015.12.153Díez-Gandía, A., Villanueva, R.-J., Moraño, J.-A., Acedo, L., Mollar, J., & Díez-Domingo, J. (2016). Studying the Herd Immunity Effect of the Varicella Vaccine in the Community of Valencia, Spain. Lecture Notes in Computer Science, 38-46. doi:10.1007/978-3-319-31744-1_4Stochastic epidemic models with a backward bifurcation. (2006). Mathematical Biosciences and Engineering, 3(3), 445-458. doi:10.3934/mbe.2006.3.445Roberts, M., Andreasen, V., Lloyd, A., & Pellis, L. (2015). Nine challenges for deterministic epidemic models. Epidemics, 10, 49-53. doi:10.1016/j.epidem.2014.09.006Corberán-Vallet, A., & Santonja, F. J. (2014). A Bayesian SIRS model for the analysis of respiratory syncytial virus in the region of Valencia, Spain. Biometrical Journal, 56(5), 808-818. doi:10.1002/bimj.201300194Bjørnstad, O. N., Finkenstädt, B. F., & Grenfell, B. T. (2002). DYNAMICS OF MEASLES EPIDEMICS: ESTIMATING SCALING OF TRANSMISSION RATES USING A TIME SERIES SIR MODEL. Ecological Monographs, 72(2), 169-184. doi:10.1890/0012-9615(2002)072[0169:domees]2.0.co;2Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Analysis, 1(3), 515-534. doi:10.1214/06-ba117aLunn, D., Spiegelhalter, D., Thomas, A., & Best, N. (2009). Rejoinder to commentaries on ‘The BUGS project: Evolution, critique and future directions’. Statistics in Medicine, 28(25), 3081-3082. doi:10.1002/sim.369

A nonlinear dynamic age-structured model of e-commerce in Spain: Stability analysis of the equilibrium by delay and stochastic perturbations

[EN] First, we propose a deterministic age-structured epidemiological model to study the diffusion of e-commerce in Spain. Afterwards, we determine the parameters (death, birth and growth rates) of the underlying demographic model as well as the parameters (transmission of the use of e-commerce rates) of the proposed epidemiological model that best fit real data retrieved from the Spanish National Statistical Institute. Motivated by the two following facts: first the dynamics of acquiring the use of a new technology as e-commerce is mainly driven by the feedback after interacting with our peers (family, friends, mates, mass media, etc.), hence having a certain delay, and second the inherent uncertainty of sampled real data and the social complexity of the phenomena under analysis, we introduce aftereffect and stochastic perturbations in the initial deterministic model. This leads to a delayed stochastic model for e-commerce. We then investigate sufficient conditions in order to guarantee the stability in probability of the equilibrium point of the dynamic e-commerce delayed stochastic model. Our theoretical findings are numerically illustrated using real data. (C) 2018 Elsevier B.V. All rights reserved.This work has been partially supported by the Ministerio de Economia y Competitividad grant MTM2017-89664-P.Burgos-Simon, C.; Cortés, J.; Shaikhet, L.; Villanueva Micó, RJ. (2018). A nonlinear dynamic age-structured model of e-commerce in Spain: Stability analysis of the equilibrium by delay and stochastic perturbations. Communications in Nonlinear Science and Numerical Simulation. 64:149-158. https://doi.org/10.1016/j.cnsns.2018.04.022S1491586

A computational technique to predict the level of glucose of a diabetic patient with uncertainty in the short term

[EN] On advanced stages of the disease, diabetic patients have to inject insulin doses to maintain blood glucose levels inside of a healthy range. The decision of how much insulin is injected implies somehow to predict the level of glucose they will have after a certain time. Due to the sudden changes in the glucose levels, their estimation is a very difficult task. If we were able to give reliable estimations in advance, it would facilitate the process of taking therapeutic decisions to control the disease and improve the health of the patient. In this work, we present a technique to estimate the glucose level of a diabetic patient, capturing the measurement errors produced by continuous glucose monitoring systems (CGMSs), smart devices that measure glucose levels. To do that, we will use a model of glucose dynamics and we calibrate it with the aim to capture the glucose level data of the patient in a time interval of 30 minutes and the uncertainty given by the glucose measurement. Then, we use the calibrated parameters to predict the levels of glucose over the next 15 minutes. Repeating this procedure every 15 minutes, we are able to give short¿term accurate predictions.This work has been partially supported by the Spanish Ministerio de Economía y Competitividad under grant MTM2017-89664-P and RTI2018-095180-B-I00 and by Fundación Eugenio Rodriguez Pascual 2019 -GLENO ProjectBurgos Simon, C.; Cervigón, C.; Hidalgo, J.; Villanueva Micó, RJ. (2019). A computational technique to predict the level of glucose of a diabetic patient with uncertainty in the short term. Computational and Mathematical Methods. 2(2):1-11. https://doi.org/10.1002/cmm4.1064S11122(2004). Third-Party Reimbursement for Diabetes Care, Self-Management Education, and Supplies. Diabetes Care, 28(Supplement 1), S62-S63. doi:10.2337/diacare.28.suppl_1.s62Bloomgarden, Z. T. (2004). Consequences of Diabetes: Cardiovascular disease. Diabetes Care, 27(7), 1825-1831. doi:10.2337/diacare.27.7.1825BrownA.Time‐in‐range: what's an achievable goal with diabetes?2017.https://diatribe.org/time-range-whats-achievable-goal-diabetesFonseca, V. A., Grunberger, G., Anhalt, H., Bailey, T. S., Blevins, T., … Garg, S. K. (2016). CONTINUOUS GLUCOSE MONITORING: A CONSENSUS CONFERENCE OF THE AMERICAN ASSOCIATION OF CLINICAL ENDOCRINOLOGISTS AND AMERICAN COLLEGE OF ENDOCRINOLOGY. Endocrine Practice, 22(8), 1008-1021. doi:10.4158/ep161392.csChristiansen, M. P., Klaff, L. J., Brazg, R., Chang, A. R., Levy, C. J., Lam, D., … Bailey, T. S. (2018). A Prospective Multicenter Evaluation of the Accuracy of a Novel Implanted Continuous Glucose Sensor: PRECISE II. Diabetes Technology & Therapeutics, 20(3), 197-206. doi:10.1089/dia.2017.0142Bock, A., François, G., & Gillet, D. (2015). A therapy parameter-based model for predicting blood glucose concentrations in patients with type 1 diabetes. Computer Methods and Programs in Biomedicine, 118(2), 107-123. doi:10.1016/j.cmpb.2014.12.002Acedo, L., Botella, M., Cortés, J. C., Hidalgo, J. I., Maqueda, E., & Villanueva, R. J. (2018). Swarm hybrid optimization for a piecewise model fitting applied to a glucose model. Journal of Systems and Information Technology, 20(4), 404-416. doi:10.1108/jsit-10-2017-0103Alegre-Sanahuja, J., Cortés, J.-C., Villanueva, R.-J., & Santonja, F.-J. (2017). Predicting mobile apps spread: An epidemiological random network modeling approach. SIMULATION, 94(2), 123-130. doi:10.1177/003754971771260

A Bayesian stochastic SIRS model with a vaccination strategy for the analysis of respiratory syncytial virus

[EN] Our objective in this paper is to model the dynamics of respiratory syncytial virus in the region of Valencia (Spain) and analyse the effect of vaccination strategies from a health-economic point of view. Compartmental mathematical models based on differential equations are commonly used in epidemiology to both understand the underlying mechanisms that influence disease transmission and analyse the impact of vaccination programs. However, a recently proposed Bayesian stochastic susceptible-infected-recovered-susceptible model in discrete-time provided an improved and more natural description of disease dynamics. In this work, we propose an extension of that stochastic model that allows us to simulate and assess the effect of a vaccination strategy that consists on vaccinating a proportion of newborns.This work has been supported by Grant Number MTM2014-56233-P from the Spanish Ministry of Economy and Competitiveness.Jornet-Sanz, M.; Corberán-Vallet, A.; Santonja, F.; Villanueva Micó, RJ. (2017). A Bayesian stochastic SIRS model with a vaccination strategy for the analysis of respiratory syncytial virus. SORT. Statistics and Operations Research Transactions. 41(1):159-175. https://doi.org/10.2436/20.8080.02.56S15917541

Probabilistic prediction of outbreaks of meningococcus W-135 infections over the next few years in Spain

[EN] The genogroups of meningococcal and other bacteria are in competition in the ecosystem they form with the human hosts. Changes in vaccination strategies, prophylactic measures or usual habits, may also change the distribution of the genogroups in the ecosystem but, usually, this competition is ignored in most epidemiological models, despite it can be highly influential in the evolution of infection diseases and outbreaks. Our goal is to propose a susceptible carrier susceptible (SCS) epidemiological model to determine the percentage of carriers in the population, and introduce a fractional Lotka Volterra competition model to describe the evolution of the meningococcal genogroups in Spain among the carriers. Using data from the distribution of the genogroups in Spain in 2011 and 2012, we find the model parameters and their uncertainties according to a probabilistic fitting approach. On this basis, we predict the evolution of the carriers of the different genogroups over the next few years and, in particular, the percentage of carriers of meningococcus W-135 with a 95% confidence interval. Then, we estimate the probability of having a possible outbreak of meningococcus W-135 in Spain over the next few years. According to our model and, under the present conditions, the risk of a serious outbreak of W-135 in Spain in the next 3 years is below 0.3%.This work has been partially supported by the Ministerio de Economia y Competitividad grant MTM2013-41765-P and the FIS grant PI13/01459. We also acknowledge Dr. Julio Vazquez from the Carlos III Institute of Health for providing the epidemiological data used in this work.Acedo Rodríguez, L.; Burgos-Simon, C.; Cortés, J.; Villanueva Micó, RJ. (2017). Probabilistic prediction of outbreaks of meningococcus W-135 infections over the next few years in Spain. Physica A Statistical Mechanics and its Applications. 486:106-117. https://doi.org/10.1016/j.physa.2017.05.043S10611748

A deterministic model for highly contagious diseases: The case of varicella

[EN] The classic nonlinear Kermack-McKendrick model based upon a system of differential equations has been widely applied to model the rise and fall of global pandemic and also seasonal epidemic by introducing a forced harmonic infectivity which would change throughout the year. These methods work well in their respective domains of applicability, and for certain diseases, but they fail when both seasonality and high infectivity are combined. In this paper we consider a Susceptible-Infected-Recovered, or SIR, model with two latent states to model the propagation and evolutionary history of varicella in humans. We show that infectivity can be calculated from real data and we find a nonstandard seasonal variation that cannot be fitted with a single harmonic. Moreover, we show that infectivity for the present strains of the virus has raised following a sigmoid function in a period of several centuries. This could allow the design of vaccination strategies and the study of the epidemiology of varicella and herpes zoster. (C) 2016 Elsevier B.V. All rights reserved.Acedo Rodríguez, L.; Moraño Fernández, JA.; Santonja, F.; Villanueva Micó, RJ. (2016). A deterministic model for highly contagious diseases: The case of varicella. Physica A: Statistical Mechanics and its Applications. 450:278-286. doi:10.1016/j.physa.2015.12.153S27828645