We present an early version of a Susceptible–Exposed–Infected–Recovered–Deceased (SEIRD) mathematical model based on partial differential equations coupled with a heterogeneous diffusion model. The ...model describes the spatio-temporal spread of the COVID-19 pandemic, and aims to capture dynamics also based on human habits and geographical features. To test the model, we compare the outputs generated by a finite-element solver with measured data over the Italian region of Lombardy, which has been heavily impacted by this crisis between February and April 2020. Our results show a strong qualitative agreement between the simulated forecast of the spatio-temporal COVID-19 spread in Lombardy and epidemiological data collected at the municipality level. Additional simulations exploring alternative scenarios for the relaxation of lockdown restrictions suggest that reopening strategies should account for local population densities and the specific dynamics of the contagion. Thus, we argue that data-driven simulations of our model could ultimately inform health authorities to design effective pandemic-arresting measures and anticipate the geographical allocation of crucial medical resources.
There is a growing realization that traditional “Calculus for Life Sciences” courses do not show their applicability to the Life Sciences and discourage student interest. There have been calls from ...the AAAS, the Howard Hughes Medical Institute, the NSF, and the American Association of Medical Colleges for a new kind of math course for biology students, that would focus on dynamics and modeling, to understand positive and negative feedback relations, in the context of important biological applications, not incidental “examples.” We designed a new course, LS 30, based on the idea of modeling biological relations as dynamical systems, and then visualizing the dynamical system as a vector field, assigning “change vectors” to every point in a state space. The resulting course, now being given to approximately 1400 students/year at UCLA, has greatly improved student perceptions toward math in biology, reduced minority performance gaps, and increased students' subsequent grades in physics and chemistry courses. This new course can be customized easily for a broad range of institutions. All course materials, including lecture plans, labs, homeworks and exams, are available from the authors; supporting videos are posted online.
Mathematical biology education provides key foundational underpinnings for the scholarly work of mathematical biology. Professional societies support such education efforts via funding, public ...speaking opportunities, Web presence, publishing, workshops, prizes, opportunities to discuss curriculum design, and support of mentorship and other means of sustained communication among communities of scholars. Such programs have been critical to the broad expansion of the range and visibility of research and educational activities in mathematical biology. We review these efforts, past and present, across multiple societies—the Society for Mathematical Biology (SMB), the Symposium on Biomathematics and Ecology Education and Research (BEER), the Mathematical Association of America (MAA), and the Society for Industrial and Applied Mathematics (SIAM). We then proceed to suggest ways that professional societies can serve as advocates and community builders for mathematical biologists at all levels, noting that education continues throughout a career and also emphasizing the value of educating new generations of students. Our suggestions include collecting and disseminating data related to biomath education; developing and maintaining mentoring systems and research communities; and providing incentives and visibility for educational efforts within mathematical biology.
The Consolidated Standards of Reporting Trials (CONSORT) statement is a guideline designed to improve the transparency and quality of the reporting of randomised controlled trials (RCTs). In this ...article we present an extension to that statement for randomised pilot and feasibility trials conducted in advance of a future definitive RCT. The checklist applies to any randomised study in which a future definitive RCT, or part of it, is conducted on a smaller scale, regardless of its design (eg, cluster, factorial, crossover) or the terms used by authors to describe the study (eg, pilot, feasibility, trial, study). The extension does not directly apply to internal pilot studies built into the design of a main trial, non-randomised pilot and feasibility studies, or phase II studies, but these studies all have some similarities to randomised pilot and feasibility studies and so many of the principles might also apply.The development of the extension was motivated by the growing number of studies described as feasibility or pilot studies and by research that has identified weaknesses in their reporting and conduct. We followed recommended good practice to develop the extension, including carrying out a Delphi survey, holding a consensus meeting and research team meetings, and piloting the checklist.The aims and objectives of pilot and feasibility randomised studies differ from those of other randomised trials. Consequently, although much of the information to be reported in these trials is similar to those in randomised controlled trials (RCTs) assessing effectiveness and efficacy, there are some key differences in the type of information and in the appropriate interpretation of standard CONSORT reporting items. We have retained some of the original CONSORT statement items, but most have been adapted, some removed, and new items added. The new items cover how participants were identified and consent obtained; if applicable, the prespecified criteria used to judge whether or how to proceed with a future definitive RCT; if relevant, other important unintended consequences; implications for progression from pilot to future definitive RCT, including any proposed amendments; and ethical approval or approval by a research review committee confirmed with a reference number.This article includes the 26 item checklist, a separate checklist for the abstract, a template for a CONSORT flowchart for these studies, and an explanation of the changes made and supporting examples. We believe that routine use of this proposed extension to the CONSORT statement will result in improvements in the reporting of pilot trials.Editor’s note: In order to encourage its wide dissemination this article is freely accessible on the BMJ and Pilot and Feasibility Studies journal websites.
•A model for the expansion of COVID-19 in Italy, Spain and the USA is considered.•Predictions on cumulative deaths due to COVID-19 are provided.•The effect of favourable seasonal conditions is ...assessed in the expansion of COVID-19 in different countries.•The effect of the relaxation of lockdown is assessed in the expansion of COVID- 19 in different countries.
It is well-known that the classical SIR model is unable to make accurate predictions on the course of illnesses such as COVID-19. In this paper, we show that the official data released by the authorities of several countries (Italy, Spain and The USA) regarding the expansion of COVID-19 are compatible with a non-autonomous SIR type model with vital dynamics and non-constant population, calibrated according to exponentially decaying infection and death rates. Using this calibration we construct a model whose outcomes for most relevant epidemiological paramenters, such as the number of active cases, cumulative deaths, daily new deaths and daily new cases (among others) fit available real data about the first and successive waves of COVID-19. In addition to this, we also provide predictions on the evolution of this pandemic in Italy and the USA in several plausible scenarios.
In recent decades, studying the behavior of biological species has become one of the most fascinating areas of applied mathematics. The high importance of conservation of rare species in nature has ...prompted researchers in various fields to pay particular attention to this issue. Therefore, it is essential to develop mathematical models that examine the dynamics of their behavior. On the other hand, the development of new concepts in numerical analysis has enabled us to preserve more information on the evolutionary behavior history of a dynamic system and to use it in predicting the new features of the system. Fractional derivatives have provided such a valuable tool. This paper studies a dynamic system that models the interactions between two densities of immature and mature prey and predator populations. In the model, prey population is divided into two populations, including mature prey and immature prey. Another feature of the model is that predator depends on mature prey only and it followed by Crowley-Martin type functional response. Moreover, the fractional operator used in this model as derivative is of the Atangana-Baleanu AB type. Using this kind of fractional derivative causes the results to depend on the fractional order of the derivative. The addition of the concept of memory to the model is another highlight of using this type of derivative for the biological model. This helps the model to apply all the essential information of the phenomenon from the beginning to the desired time in the calculations. Existence and uniqueness of solutions to the fractional model are also investigated in this manuscript. The numerical method used in the article is also one of the most efficient patterns in solving problems with fractional derivatives. Using this effective method makes the results very consistent with what we actually expect to happen. Many simulations have been carried out to investigate the effect of parameters in the model on its overall behavior. Numerical results show the impressive performance of the fractional operator on the dynamic behavior of the considered predator-prey model. This efficient fractional operator can also be tested in the structure of other existing biological models.
In this paper, we develop a nonconservative kinetic framework to be applied to the study of immune system dysregulation. From the modeling viewpoint, the model regards a system composed of ...stochastically interacting agents, under the action of an eternal force field. According to the application perspectives of this paper, the external force field has a specific analytical shape. In this case, some analytical results are proved, i.e. existence, uniqueness, positivity, and boundedness of solution of the related Cauchy problem, at least locally in time. Then, the model is refined to be implemented for the study of treatment strategies in case of autoimmune response. Specifically, we distinguish the autonomous case from the nonautonomous one, representing the absence or delivery of drugs, respectively. The former allows us to gain some stability results. Whereas, the latter is qualitatively studied. Numerical simulations are provided for both schemes.
•A nonconservative kinetic model with external force field.•Solution existence, uniqueness, positivity, boundedness for nonautonomous system.•Kinetic system applied to autoimmune treatment strategy.
The Consolidated Standards of Reporting Trials (CONSORT) statement is a guideline designed to improve the transparency and quality of the reporting of randomised controlled trials (RCTs). In this ...article we present an extension to that statement for randomised pilot and feasibility trials conducted in advance of a future definitive RCT. The checklist applies to any randomised study in which a future definitive RCT, or part of it, is conducted on a smaller scale, regardless of its design (eg, cluster, factorial, crossover) or the terms used by authors to describe the study (eg, pilot, feasibility, trial, study). The extension does not directly apply to internal pilot studies built into the design of a main trial, non-randomised pilot and feasibility studies, or phase II studies, but these studies all have some similarities to randomised pilot and feasibility studies and so many of the principles might also apply. The development of the extension was motivated by the growing number of studies described as feasibility or pilot studies and by research that has identified weaknesses in their reporting and conduct. We followed recommended good practice to develop the extension, including carrying out a Delphi survey, holding a consensus meeting and research team meetings, and piloting the checklist. The aims and objectives of pilot and feasibility randomised studies differ from those of other randomised trials. Consequently, although much of the information to be reported in these trials is similar to those in randomised controlled trials (RCTs) assessing effectiveness and efficacy, there are some key differences in the type of information and in the appropriate interpretation of standard CONSORT reporting items. We have retained some of the original CONSORT statement items, but most have been adapted, some removed, and new items added. The new items cover how participants were identified and consent obtained; if applicable, the prespecified criteria used to judge whether or how to proceed with a future definitive RCT; if relevant, other important unintended consequences; implications for progression from pilot to future definitive RCT, including any proposed amendments; and ethical approval or approval by a research review committee confirmed with a reference number. This article includes the 26 item checklist, a separate checklist for the abstract, a template for a CONSORT flowchart for these studies, and an explanation of the changes made and supporting examples. We believe that routine use of this proposed extension to the CONSORT statement will result in improvements in the reporting of pilot trials. Editor's note: In order to encourage its wide dissemination this article is freely accessible on
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journal websites.
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