Modeling the Epidemic Outbreak and Dynamics of COVID-19 in Croatia

The paper deals with a modeling of the ongoing epidemic caused by Coronavirus disease 2019 (COVID-19) on the closed territory of the Republic of Croatia. Using the official public information on the number of confirmed infected, recovered and deceased individuals, the modified SEIR compartmental model is developed to describe the underlying dynamics of the epidemic. Fitted modified SEIR model provides the prediction of the disease progression in the near future, considering strict control interventions by means of social distancing and quarantine for infected and at-risk individuals introduced at the beginning of COVID-19 spread on February, 25th by Croatian Ministry of Health. Assuming the accuracy of provided data and satisfactory representativeness of the model used, the basic reproduction number is derived. Obtained results portray potential positive developments and justify the stringent precautionary measures introduced by the Ministry of Health.Comment: 5 pages, 6 figures, to appear in the Proceedings of the SpliTech2020 conferenc

The SIR epidemic model from a PDE point of view

We present a derivation of the classical SIR model through a mean-field approximation from a discrete version of SIR. We then obtain a hyperbolic forward Kolmogorov equation, and show that its projected characteristics recover the standard SIR model. Moreover, we show that the long time limit of the evolution will be a Dirac measure. The exact position will depend on the well-know $R_0$ parameter, and it will be supported on the corresponding stable SIR equilibrium

The Effect of Site Characteristics on the Reproductive Output of Lesser Celandine (Ranunculus ficaria)

Ranunculus ficaria L., an ephemeral perennial invasive plant brought over from Europe, is becoming widespread throughout the Northeastern United States. This herbaceous buttercup is able to create extensive dense mats that limit native species growth. Taking advantage of an early growing season and rapid reproduction rates, this species can create dense monocultures, which threatens native communities and ecosystems. Elimination of native spring ephemerals results in decreased biodiversity. A better understanding of how R. ficaria responds to site characteristics is needed to prioritize management efforts toward high-risk sites.Ranunculus ficaria abundance and reproductive output (seed, bulbil and tuber production rates) were examined in plots spanning a disturbance gradient away from a river. Site characteristics (PAR, aspect, soil pH, soil moisture, texture and nutrient content) were investigated to examine their role in plant performance. I hypothesized that soil characteristics (pH and nutrient availability) drive R. ficaria plant performance; specifically I expected higher biomass and reproductive output to be associated with higher soil pH. I also expected reproductive output and R. ficaria biomass would be highest in moist floodplain at intermediate distances from rivers.Many soil nutrients and characteristics were significantly related to biomass and reproductive output; specifically phosphorus, calcium and LTI (Lime Test Index) all showed significantly positive relationships with plant biomass and bulbil counts, while soil pH was significantly positively related to biomass. Bulbil and tuber counts were significantly higher in soils of high percent silt. These findings suggest that soil characteristics (pH, texture) and nutrients (P, Ca) are strongly linked to plant performance, supporting my hypothesis. Reproductive output and R. ficaria biomass were not significantly greater at intermediate distances from rivers, in contrast to my hypothesis. A plant performance model was generated using object-based image analysis with the aim of creating an accurate classification of sites in terms of suitability for R. ficaria performance. A large scale field survey was used to assess model predictions, which were found be 68 % accurate. Overall, this study was able to expand on the current limited understanding of R. ficaria, which can prove helpful in aiding management to reduce population size and spread

Slightly generalized Generalized Contagion: Unifying simple models of biological and social spreading

We motivate and explore the basic features of generalized contagion, a model mechanism that unifies fundamental models of biological and social contagion. Generalized contagion builds on the elementary observation that spreading and contagion of all kinds involve some form of system memory. We discuss the three main classes of systems that generalized contagion affords, resembling: simple biological contagion; critical mass contagion of social phenomena; and an intermediate, and explosive, vanishing critical mass contagion. We also present a simple explanation of the global spreading condition in the context of a small seed of infected individuals.Comment: 8 pages, 5 figures; chapter to appear in "Spreading Dynamics in Social Systems"; Eds. Sune Lehmann and Yong-Yeol Ahn, Springer Natur

Soil Characteristics Drive Ficaria verna Abundance and Reproductive Output

Lesser celandine (Ficaria verna Huds.), an invasive plant from Europe, is becoming widespread in river valleys throughout the northeastern United States and the Pacific Northwest. Its high rate of asexual bulbil and tuber production creates dense infestations threatening native spring ephemerals. Ficaria verna abundance and reproductive output (seeds, bulbils, and tubers) were examined in invaded transects spanning a disturbance gradient away from a river. Site characteristics (photosynthetically active radiation [PAR], soil pH, moisture, texture, and nutrients) were quantified to examine their roles in plant abundance and reproduction. A larger-scale study examined random transects not specifically chosen based on F. verna infestations. Soil characteristics and slope were hypothesized to drive F. verna abundance and reproduction; we also hypothesized that reproductive output and biomass would be highest at intermediate distances from rivers, where disturbances are infrequent. Ficaria verna abundance and reproductive output varied considerably by site; soil characteristics, rather than landscape placement, appeared to drive plant abundance and reproduction. Lower percent sand was associated with significantly higher F. verna stem density and bulbil and tuber production. CEC was significantly negatively related to F. verna biomass and tuber counts. In the larger-scale survey, slope and PAR were significantly negatively related to F. verna presence and percent cover, respectively. Overall, these findings suggest that soil texture and slope can help explain higher abundance and reproductive outputs. However, reproductive output and biomass were not significantly greater at intermediate distances, contrary to expectations. We did not observe any seed production in any of the plots, although we did see a few plants with seeds outside our study area in the second year, demonstrating a near-complete reliance on asexual reproduction in these populations. This study expands on the current limited understanding of F. verna and can help management by identifying areas likely to support dense infestations

Soil Characteristics Drive Ficaria verna Abundance and Reproductive Output

Lesser celandine (Ficaria verna Huds.), an invasive plant from Europe, is becoming widespread in river valleys throughout the northeastern United States and the Pacific Northwest. Its high rate of asexual bulbil and tuber production creates dense infestations threatening native spring ephemerals. Ficaria verna abundance and reproductive output (seeds, bulbils, and tubers) were examined in invaded transects spanning a disturbance gradient away from a river. Site characteristics (photosynthetically active radiation [PAR], soil pH, moisture, texture, and nutrients) were quantified to examine their roles in plant abundance and reproduction. A larger-scale study examined random transects not specifically chosen based on F. verna infestations. Soil characteristics and slope were hypothesized to drive F. verna abundance and reproduction; we also hypothesized that reproductive output and biomass would be highest at intermediate distances from rivers, where disturbances are infrequent. Ficaria verna abundance and reproductive output varied considerably by site; soil characteristics, rather than landscape placement, appeared to drive plant abundance and reproduction. Lower percent sand was associated with significantly higher F. verna stem density and bulbil and tuber production. CEC was significantly negatively related to F. verna biomass and tuber counts. In the larger-scale survey, slope and PAR were significantly negatively related to F. verna presence and percent cover, respectively. Overall, these findings suggest that soil texture and slope can help explain higher abundance and reproductive outputs. However, reproductive output and biomass were not significantly greater at intermediate distances, contrary to expectations. We did not observe any seed production in any of the plots, although we did see a few plants with seeds outside our study area in the second year, demonstrating a near-complete reliance on asexual reproduction in these populations. This study expands on the current limited understanding of F. verna and can help management by identifying areas likely to support dense infestations

Percolation and Epidemic Thresholds in Clustered Networks

We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant connected component, it cannot restore a finite percolation threshold. In turn, this implies the absence of an epidemic threshold in this class of networks extending, thus, this result to a wide variety of real scale-free networks which shows a high level of transitivity. Our findings are in good agreement with numerical simulations.Comment: 4 Pages and 3 Figures. Final version to appear in PR

Evolution Model for Epidemic Diseases Based on the Kaplan-Meier Curve Determination

[EN] We show a simple model of the dynamics of a viral process based, on the determination of the Kaplan-Meier curvePof the virus. Together with the function of the newly infected individualsI, this model allows us to predict the evolution of the resulting epidemic process in terms of the numberEof the death patients plus individuals who have overcome the disease. Our model has as a starting point the representation ofEas the convolution ofIandP. It allows introducing information about latent patients-patients who have already been cured but are still potentially infectious, and re-infected individuals. We also provide three methods for the estimation ofPusing real data, all of them based on the minimization of the quadratic error: the exact solution using the associated Lagrangian function and Karush-Kuhn-Tucker conditions, a Monte Carlo computational scheme acting on the total set of local minima, and a genetic algorithm for the approximation of the global minima. Although the calculation of the exact solutions of all the linear systems provided by the use of the Lagrangian naturally gives the best optimization result, the huge number of such systems that appear when the time variable increases makes it necessary to use numerical methods. We have chosen the genetic algorithms. Indeed, we show that the results obtained in this way provide good solutions for the model.This research was funded by Ministerio de Ciencia, Innovacion y Universidades: MTM2016-77054-C2-1-P and Generalitat Valenciana: Catedra de Transparencia y Gestion de Datos (U.P.V.). The authors would like to thank the referees for their valuable comments which helped to improve the manuscript. The author gratefully acknowledge the support of Cátedra de Transparencia y Gestión de Datos, Universitat Politècnica de València y Generalitat Valenciana, Spain. The last author gratefully acknowledges the support of the Ministerio de Ciencia, Innovación y Universidades (Spain) and FEDER under grant MTM2016-77054-C2-1-P.Calabuig, JM.; García-Raffi, LM.; García-Valiente, A.; Sánchez Pérez, EA. (2020). Evolution Model for Epidemic Diseases Based on the Kaplan-Meier Curve Determination. Mathematics. 8(8):1-25. https://doi.org/10.3390/math8081260S12588Ai, T., Yang, Z., Hou, H., Zhan, C., Chen, C., Lv, W., … Xia, L. (2020). Correlation of Chest CT and RT-PCR Testing for Coronavirus Disease 2019 (COVID-19) in China: A Report of 1014 Cases. Radiology, 296(2), E32-E40. doi:10.1148/radiol.2020200642Chen, D., Xu, W., Lei, Z., Huang, Z., Liu, J., Gao, Z., & Peng, L. (2020). Recurrence of positive SARS-CoV-2 RNA in COVID-19: A case report. International Journal of Infectious Diseases, 93, 297-299. doi:10.1016/j.ijid.2020.03.003Kaplan, E. L., & Meier, P. (1958). Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association, 53(282), 457-481. doi:10.1080/01621459.1958.10501452Kenah, E. (2010). Contact intervals, survival analysis of epidemic data, and estimation of R0. Biostatistics, 12(3), 548-566. doi:10.1093/biostatistics/kxq068Kenah, E. (2012). Non-parametric survival analysis of infectious disease data. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 75(2), 277-303. doi:10.1111/j.1467-9868.2012.01042.xOgłuszka, M., Orzechowska, M., Jędroszka, D., Witas, P., & Bednarek, A. K. (2019). Evaluate Cutpoints: Adaptable continuous data distribution system for determining survival in Kaplan-Meier estimator. Computer Methods and Programs in Biomedicine, 177, 133-139. doi:10.1016/j.cmpb.2019.05.023Hethcote, H. W. (2000). The Mathematics of Infectious Diseases. SIAM Review, 42(4), 599-653. doi:10.1137/s0036144500371907Silal, S. P., Little, F., Barnes, K. I., & White, L. J. (2016). Sensitivity to model structure: a comparison of compartmental models in epidemiology. Health Systems, 5(3), 178-191. doi:10.1057/hs.2015.2Kamvar, Z. N., Cai, J., Pulliam, J. R. C., Schumacher, J., & Jombart, T. (2019). Epidemic curves made easy using the R package incidence. F1000Research, 8, 139. doi:10.12688/f1000research.18002.1Lectures on Mathematical Modelling of Biological Systemshttp://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.465.8665&rep=rep1&type=pdfKeeling, M. J., & Danon, L. (2009). Mathematical modelling of infectious diseases. British Medical Bulletin, 92(1), 33-42. doi:10.1093/bmb/ldp038Brown, G. D., Oleson, J. J., & Porter, A. T. (2015). An empirically adjusted approach to reproductive number estimation for stochastic compartmental models: A case study of two Ebola outbreaks. Biometrics, 72(2), 335-343. doi:10.1111/biom.12432Huppert, A., & Katriel, G. (2013). Mathematical modelling and prediction in infectious disease epidemiology. Clinical Microbiology and Infection, 19(11), 999-1005. doi:10.1111/1469-0691.12308Paul, M. (2013). Foreseeing the future in infectious diseases: can we? Clinical Microbiology and Infection, 19(11), 991-992. doi:10.1111/1469-0691.12300Roosa, K., Lee, Y., Luo, R., Kirpich, A., Rothenberg, R., Hyman, J. M., … Chowell, G. (2020). Short-term Forecasts of the COVID-19 Epidemic in Guangdong and Zhejiang, China: February 13–23, 2020. Journal of Clinical Medicine, 9(2), 596. doi:10.3390/jcm9020596Package ‘GA’-CRAN-R Projecthttps://luca-scr.github.io/GA/Scrucca, L. (2013). GA: A Package for Genetic Algorithms inR. Journal of Statistical Software, 53(4). doi:10.18637/jss.v053.i0

A Workflow for Software Development within Computational Epidemiology

A critical investigation into computational models developed for studying the spread of communicable disease is presented. The case in point is a spatially explicit micro-meso-macro model for the entire Swedish population built on registry data, thus far used for smallpox and for influenza-like illnesses. The lessons learned from a software development project of more than 100 person months are collected into a check list. The list is intended for use by computational epidemiologists and policy makers, and the workflow incorporating these two roles is described in detail.NOTICE: This is the author’s version of a work that was accepted for publication in Journal of Computationa Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational Science, VOL 2, ISSUE 3, 6 June 2011 DOI 10.1016/j.jocs.2011.05.004.</p

Dynamic Exploration of Networks: from general principles to the traceroute process

Dynamical processes taking place on real networks define on them evolving subnetworks whose topology is not necessarily the same of the underlying one. We investigate the problem of determining the emerging degree distribution, focusing on a class of tree-like processes, such as those used to explore the Internet's topology. A general theory based on mean-field arguments is proposed, both for single-source and multiple-source cases, and applied to the specific example of the traceroute exploration of networks. Our results provide a qualitative improvement in the understanding of dynamical sampling and of the interplay between dynamics and topology in large networks like the Internet.Comment: 13 pages, 6 figure