These files are videos generated by a stochastic simulation that was created by Nikki Steenbakkers under the supervision of Marko Boon and Bert Zwart (all affiliated with Eindhoven University of Technology) for her bachelor final project "Simulating the Spread of COVID-19 in the Netherlands". The report can be found in the TU/e repository of bachelor project reports:https://research.tue.nl/en/studentTheses/simulating-the-spread-of-covid-19-in-the-netherlandsThe report contains more information about the project and the simulation. It explicitly refers to these files.

Students perform experiments to model spread of information within a population. Students collect data, determine essential components and parameters and build a mathematical model culminating with a separable linear first order differential equation.

Detailed model specification and supportive figures including all data used as input in the analyses of this paper. (PDF)

In examples 1 to 3, we have demonstrated how to use Excel to calculate variables Sn, En, In, Rn, yn in l-i SEIR (Susceptible-Exposed-Infectious-Recovered) model, to determine the time-dependent kn, and to find the number of actual total infections in the absence of vaccination and breakthrough infections. In the l-i SEIR model, l is the time length of latent period, i is the time length of infectious period, and yn is the number of daily-confirmed cases of infections. In this section (Example 4), we will extend l-i SEIR model to l-i SEIR-vaccination model for examining the effect of vaccination on COVID-19 transmission. Two files (one Word file and one Excel files) are attached. In the Word file, the author described how to build the l-i SEIR-vaccination model and how to calculate the number of daily confirmed cases of COVID-19 infections, yn, in Excel. The calculated yn and the reported yn have been compared to each other and displayed graphically in the Excel file

spatial_mathematical_modelThe file contains 1) a system of ordinary differential equations used in the model and 2). a model runner that calls the function

Previous research has shown that norms around the role of women in society could help explain the gender gap in mathematics, and that these norms could be transmitted within the family. Using data from the Florida Department of Education combined with birth certificates we uncover important heterogeneity in the transmission of gender biases within the family. We find that gender role norms can explain the lower performance of girls in mathematics only in relatively affluent White families, whereas they do not apparently matter for the performance of Black girls.

Code to recreate simulation results, and data/code to recreate data analysis results

In this paper, we present a mathematical model to assess the impact of reducing the quarantine period and lifting the indoor mask mandate on the spread of Coronavirus Disease 2019 (COVID-19) in Korea. The model incorporates important epidemiological parameters, such as transmission rates and mortality rates, to simulate the transmission of the virus under different scenarios. Our findings reveal that the impact of mask wearing fades in the long term, which highlights the crucial role of quarantine in controlling the spread of the disease. In addition, balancing the confirmed cases and costs, the lifting of mandatory indoor mask wearing is cost-effective; however, maintaining the quarantine period remains essential. A relationship between the disease transmission rate and vaccine efficiency was also apparent, with higher transmission rates leading to a greater impact of the vaccine efficiency. Moreover, our findings indicate that a higher disease transmission rate exacerbates the consequences of early quarantine release.

In this article, I present an experiment that can be conducted in a calculus class to investigate the difference quotient and the derivative, using mathematical modeling with student-collected data.

Compositional data, which is data consisting of fractions or probabilities, is common in many fields including ecology, economics, physical science and political science. If these data would otherwise be normally distributed, their spread can be conveniently represented by a multivariate normal distribution truncated to the non-negative space under a unit simplex. Here this distribution is called the simplex-truncated multivariate normal distribution. For calculations on truncated distributions, it is often useful to obtain rapid estimates of their integral, mean and covariance; these quantities characterising the truncated distribution will generally possess different values to the corresponding non-truncated distribution.

In the paper "Adams, Matthew (2022) Integral, mean and covariance of the simplex-truncated multivariate normal distribution. PLoS One, 17(7), Article number: e0272014. ", three different approaches that can estimate the integral, mean and covariance of any simplex-truncated multivariate normal distribution are described and compared. These three approaches are (1) naive rejection sampling, (2) a method described by Gessner et al. that unifies subset simulation and the Holmes-Diaconis-Ross algorithm with an analytical version of elliptical slice sampling, and (3) a semi-analytical method that expresses the integral, mean and covariance in terms of integrals of hyperrectangularly-truncated multivariate normal distributions, the latter of which are readily computed in modern mathematical and statistical packages. Strong agreement is demonstrated between all three approaches, but the most computationally efficient approach depends strongly both on implementation details and the dimension of the simplex-truncated multivariate normal distribution.

This dataset consists of all code and results for the associated article.

The development of a mathematical model for predicting rate of fire spread and intensity applicable to a wide range of wildland fuels is presented from the conceptual stage through evaluation and demonstration of results to hypothetical fuel models.

Update — December 7, 2014. – Evidence-based medicine (EBM) is not working for many reasons, for example: 1. Incorrect in their foundations (paradox): hierarchical levels of evidence are supported by opinions (i.e., lowest strength of evidence according to EBM) instead of real data collected from different types of study designs (i.e., evidence). http://dx.doi.org/10.6084/m9.figshare.1122534 2. The effect of criminal practices by pharmaceutical companies is only possible because of the complicity of others: healthcare systems, professional associations, governmental and academic institutions. Pharmaceutical companies also corrupt at the personal level, politicians and political parties are on their payroll, medical professionals seduced by different types of gifts in exchange of prescriptions (i.e., bribery) which very likely results in patients not receiving the proper treatment for their disease, many times there is no such thing: healthy persons not needing pharmacological treatments of any kind are constantly misdiagnosed and treated with unnecessary drugs. Some medical professionals are converted in K.O.L. which is only a puppet appearing on stage to spread lies to their peers, a person supposedly trained to improve the well-being of others, now deceits on behalf of pharmaceutical companies. Probably the saddest thing is that many honest doctors are being misled by these lies created by the rules of pharmaceutical marketing instead of scientific, medical, and ethical principles. Interpretation of EBM in this context was not anticipated by their creators. “The main reason we take so many drugs is that drug companies don’t sell drugs, they sell lies about drugs.” ―Peter C. Gøtzsche “doctors and their organisations should recognise that it is unethical to receive money that has been earned in part through crimes that have harmed those people whose interests doctors are expected to take care of. Many crimes would be impossible to carry out if doctors weren’t willing to participate in them.” —Peter C Gøtzsche, The BMJ, 2012, Big pharma often commits corporate crime, and this must be stopped. Pending (Colombia): Health Promoter Entities (In Spanish: EPS ―Empresas Promotoras de Salud). 3. Misinterpretations New technologies or concepts are difficult to understand in the beginning, it doesn’t matter their simplicity, we need to get used to new tools aimed to improve our professional practice. Probably the best explanation is here in these videos (credits to Antonio Villafaina for sharing these videos with me). English https://www.youtube.com/watch?v=pQHX-SjgQvQ&w=420&h=315 Spanish https://www.youtube.com/watch?v=DApozQBrlhU&w=420&h=315 ----------------------- Hypothesis: hierarchical levels of evidence based medicine are wrong Dear Editor, I have data to support the hypothesis described in the title of this letter. Before rejecting the null hypothesis I would like to ask the following open question:
Could you support with data that hierarchical levels of evidence based medicine are correct? (1,2) Additional explanation to this question: – Only respond to this question attaching publicly available raw data.
– Be aware that more than a question this is a challenge: I have data (i.e., evidence) which is contrary to classic (i.e., McMaster) or current (i.e., Oxford) hierarchical levels of evidence based medicine. An important part of this data (but not all) is publicly available. References 1. Ramirez, Jorge H (2014): The EBM challenge. figshare. http://dx.doi.org/10.6084/m9.figshare.1135873 2. The EBM Challenge Day 1: No Answers. Competing interests: I endorse the principles of open data in human biomedical research Read this letter on The BMJ – August 13, 2014.
http://www.bmj.com/content/348/bmj.g3725/rr/762595
Re: Greenhalgh T, et al. Evidence based medicine: a movement in crisis? BMJ 2014; 348: g3725. _ Fileset contents Raw data: Excel archive: Raw data, interactive figures, and PubMed search terms. Google Spreadsheet is also available (URL below the article description). Figure 1. Unadjusted (Fig 1A) and adjusted (Fig 1B) PubMed publication trends (01/01/1992 to 30/06/2014). Figure 2. Adjusted PubMed publication trends (07/01/2008 to 29/06/2014) Figure 3. Google search trends: Jan 2004 to Jun 2014 / 1-week periods. Figure 4. PubMed publication trends (1962-2013) systematic reviews and meta-analysis, clinical trials, and observational studies. Figure 5. Ramirez, Jorge H (2014): Infographics: Unpublished US phase 3 clinical trials (2002-2014) completed before Jan 2011 = 50.8%. figshare.
http://dx.doi.org/10.6084/m9.figshare.1121675 Raw data: "13377 studies found for: Completed | Interventional Studies | Phase 3 | received from 01/01/2002 to 01/01/2014 | Worldwide". This database complies with the terms and conditions of ClinicalTrials.gov: http://clinicaltrials.gov/ct2/about-site/terms-conditions Supplementary Figures (S1-S6).
PubMed publication delay in the indexation processes does not explain the descending trends in the scientific output of evidence-based medicine. Acknowledgments I would like to acknowledge the following persons for providing valuable concepts in data visualization and infographics: - Maria Fernanda Ramírez. Professor of graphic design. Universidad del Valle. Cali, Colombia. - Lorena Franco. Graphic design student. Universidad del Valle. Cali, Colombia. Related articles by this author (Jorge H. Ramírez) 1. Ramirez JH. Lack of transparency in clinical trials: a call for action. Colomb Med (Cali) 2013;44(4):243-6. URL: http://www.ncbi.nlm.nih.gov/pubmed/24892242 2. Ramirez JH. Re: Evidence based medicine is broken (17 June 2014). http://www.bmj.com/node/759181 3. Ramirez JH. Re: Global rules for global health: why we need an independent, impartial WHO (19 June 2014). http://www.bmj.com/node/759151 4. Ramirez JH. PubMed publication trends (1992 to 2014): evidence based medicine and clinical practice guidelines (04 July 2014). http://www.bmj.com/content/348/bmj.g3725/rr/759895 Recommended articles 1. Greenhalgh Trisha, Howick Jeremy,Maskrey Neal. Evidence based medicine: a movement in crisis? BMJ 2014;348:g3725 2. Spence Des. Evidence based medicine is broken BMJ 2014; 348:g22 3. Schünemann Holger J, Oxman Andrew D,Brozek Jan, Glasziou Paul, JaeschkeRoman, Vist Gunn E et al. Grading quality of evidence and strength of recommendations for diagnostic tests and strategies BMJ 2008; 336:1106 4. Lau Joseph, Ioannidis John P A, TerrinNorma, Schmid Christopher H, OlkinIngram. The case of the misleading funnel plot BMJ 2006; 333:597 5. Moynihan R, Henry D, Moons KGM (2014) Using Evidence to Combat Overdiagnosis and Overtreatment: Evaluating Treatments, Tests, and Disease Definitions in the Time of Too Much. PLoS Med 11(7): e1001655. doi:10.1371/journal.pmed.1001655 6. Katz D. A-holistic view of evidence based medicine
http://thehealthcareblog.com/blog/2014/05/02/a-holistic-view-of-evidence-based-medicine/ ---

Advanced imaging techniques generate large datasets that are capable of describing the structure and kinematics of tissue spreading in embryonic development, wound healing, and the progression of many diseases. Information in these datasets can be integrated with mathematical models to infer important biomechanical properties of the system. Standard computational tools for estimating relevant parameters rely on methods such as gradient descent and typically identify a single set of optimal parameters for a single experiment. These methods offer little information on the robustness of the fit and are ill-suited for statistical tests of different experimental groups. To overcome this limitation and use large datasets in a rigorous experimental design, we sought an automated methodology that could integrate kinematic data with a mathematical model. Estimated model parameters are represented probability density distributions, which can be constructed by implementing the approximate Bayesian computation rejection algorithm. Here, we demonstrate this method with a 2D Eulerian continuum mechanical model of spreading embryonic tissue. The model is tightly integrated with quantitative image analysis of different sized embryonic tissue explants spreading on extracellular matrix (ECM). Tissue spreading is regulated by a small set of parameters including forces on the free edge, tissue stiffness, strength of cell-ECM adhesions, and active cell shape changes. From thousands of simulations of each experiment, we find statistically significant trends in key parameters that vary with initial size of the explant, e.g., cell-ECM adhesion forces are weaker and free edge forces are stronger for larger explants. Furthermore, we demonstrate that estimated parameters for one explant can be used to predict the behavior of other explants of similar size. The predictive methods described here can be used to guide further experiments to better understand how collective cell migration is regulated during development and dysregulated during the metastasis of cancer.

The columns of the frequencies correspond to dataset. From left to right, they represent a dataset containing patients with COVID-19 and comorbidities in China [33], patients with COVID-19 and comorbidities in the USA [31], patients with COVID-19 and cancer in China [36], patients with COVID-19 and cancer in the USA [37], patients with COVID-19 and COPD in the USA [35], and patients with COVID-19 and HIV in the USA [34]. These frequencies were used to simulate patients to find the likeliest paths of symptom onset for discernible symptoms of COVID-19. The dataset representing patients with comorbidities from China and the USA contains 399 and 463, respectively. The dataset representing patients with cancer from China and the USA contains 205 and 423, respectively. The dataset representing patients with COPD and HIV contains 164 and 93, respectively. (XLSX)

These are the results from 10000 simulations of the CMV stochastic ODE model. Replication code and analysis available on github at: https://github.com/bryanmayer/CMV-Transient-Infections

Countries around the world are in a state of lockdown to help limit the spread of SARS-CoV-2. However, as the number of new daily confirmed cases begins to decrease, governments must decide how to release their populations from quarantine as efficiently as possible without overwhelming their health services. We applied an optimal control framework to an adapted Susceptible-Exposure-Infection-Recovery (SEIR) model framework to investigate the efficacy of two potential lockdown release strategies, focusing on the UK population as a test case. To limit recurrent spread, we find that ending quarantine for the entire population simultaneously is a high-risk strategy, and that a gradual re-integration approach would be more reliable. Furthermore, to increase the number of people that can be first released, lockdown should not be ended until the number of new daily confirmed cases reaches a sufficiently low threshold. We model a gradual release strategy by allowing different fractions of those in lockdown to re-enter the working non-quarantined population. Mathematical optimization methods, combined with our adapted SEIR model, determine how to maximize those working while preventing the health service from being overwhelmed. The optimal strategy is broadly found to be to release approximately half the population 2–4 weeks from the end of an initial infection peak, then wait another 3–4 months to allow for a second peak before releasing everyone else. We also modeled an “on-off” strategy, of releasing everyone, but re-establishing lockdown if infections become too high. We conclude that the worst-case scenario of a gradual release is more manageable than the worst-case scenario of an on-off strategy, and caution against lockdown-release strategies based on a threshold-dependent on-off mechanism. The two quantities most critical in determining the optimal solution are transmission rate and the recovery rate, where the latter is defined as the fraction of infected people in any given day that then become classed as recovered. We suggest that the accurate identification of these values is of particular importance to the ongoing monitoring of the pandemic.

R scripts and data used to generate figures and supplementary materials for manuscript.

Attached file provides supplementary data for linked article.

Modelling disease dynamics is most useful when data are limited. We present a spatial transmission model for the spread of canine rabies in the currently rabies-free wild dog population of Australia. The introduction of a sub-clinically infected dog from Indonesia is a distinct possibility, as is the spillover infection of wild dogs. Ranges for parameters were estimated from the literature and expert opinion, or set to span an order of magnitude. Rabies was judged to have spread spatially if a new infectious case appeared 120 km from the index case. We found 21% of initial value settings resulted in canine rabies spreading 120km, and on doing so at a median speed of 67 km/year. Parameters governing dog movements and behaviour, around which there is a paucity of knowledge, explained most of the variance in model outcomes. Dog density, especially when interactions with other parameters were included, explained some of the variance in whether rabies spread 120km, but dog demography (mean lifespan and mean replacement period) had minimal impact. These results provide a clear research direction if Australia is to improve its preparedness for rabies.

These frequencies were used to simulate patients to find the likeliest paths of symptom onset for discernible symptoms of COVID-19. The dataset from Shanghai, Osaka, Atlanta, and New York contains 249, 244, 531, and 393 patients, respectively. (XLSX)

This research introduced an extensive mathematical model to capture the dynamics of diphtheria transmission. The study examined the interaction of five control measures viz: routine diphtheria vaccination, often administered with tetanus and pertussis vaccines; interventions for symptomatic to isolated treatment transitions; collaborative efforts addressing asymptomatic to home quarantine transitions; surveillance measures for home quarantine to isolated treatment transitions; and vigilance to detect cases in individuals exposed to symptomatic cases. We established the epidemiological viability of the model by proving, among others, its positivity, equilibrium under endemic conditions, equilibrium in the absence of disease, global and local stability and boundedness. Also the sensitivity analysis of the model highlighted the importance of the important variables in influencing disease occurrence and spread. In addition, the control measures significantly impact virus transmission dynamics, and results from simulations demonstrated that combination of these control strategies effectively flattened the curve of diphtheria transmission. These findings provided healthcare professionals and policymakers with valuable insights into crucial measures for eradicating diphtheria from the population.