The proliferation of misinformation on social media threatens public trust, public health, and democratic processes. We propose three models that analyze fake news propagation and evaluate intervention strategies. Grounded in epidemiological dynamics, the models include: (1) a baseline Awareness Spread Model (ASM), (2) an Extended Model with fact-checking (EM), and (3) a Generative AI-Influenced Spread model (GIFS). Each incorporates user behavior, platform-specific dynamics, and cognitive biases such as confirmation bias and emotional contagion. We simulate six distinct scenarios: (1) Accurate Content Environment, (2) Peer Network Dynamics, (3) Emotional Engagement, (4) Belief Alignment, (5) Source Trust, and (6) Platform Intervention. All models converge to a single, stable equilibrium. Sensitivity analysis across key parameters confirms model robustness and generalizability. In the ASM, forwarding rates were lowest in scenarios 1, 4, and 6 (1.47%, 3.41%, 2.95%) and significantly higher in 2, 3, and 5 (19.67%, 56.52%, 29.47%). The EM showed that fact-checking reduced spread to as low as 0.73%, with scenario-based variation from 1.16 to 17.47%. The GIFS model revealed that generative AI amplified spread by 5.7%–37.8%, depending on context. ASM highlights the importance of awareness; EM demonstrates the effectiveness of fact-checking mechanisms; GIFS underscores the amplifying impact of generative AI tools. Early intervention, coupled with targeted platform moderation (scenarios 1, 4, 6), consistently yields the lowest misinformation spread, while emotionally resonant content (scenario 3) consistently drives the highest propagation.

These frequencies were used to simulate patients to find the likeliest paths of symptom onset for discernible symptoms of COVID-19. The dataset from China contains 55,924 patients, and the dataset from USA contains 373,883 patients. (XLSX)

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.

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.

In this paper, a non-linear mathematical model for the spread of two political parties has been proposed and analyzed by using epidemiological approach.

Technical note on testing random walk hypotheses, derivation of dynamics under "spread regulation" of new-site ratios, models used for simulated spread scenarios, and mathematical approximation showing approximate "spread regulation" expected slope of -1.

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.

Sexual contact patterns determine the spread of sexually transmitted infections and are a central input parameter for mathematical models in this field. We evaluated the importance of country-specific sexual contact pattern parametrization for high-income countries with similar cultural backgrounds by comparing data from two independent studies (HaBIDS and SBG) in Germany, a country without systematic sexual contact pattern data, with data from the National Survey of Sexual Attitudes and Lifestyles (Natsal) in the UK, and the National Survey of Family Growth (NSFG) in the US, the two longest running sexual contact studies in high-income countries. We investigated differences in the distribution of the reported number of opposite-sex partners, same-sex partners and both-sex partners using weighted negative binomial regression adjusted for age and sex (as well as stratified by age). In our analyses, UK and US participants reported a substantially higher number of lifetime opposite-sex sexual partners compared to both German studies. The difference in lifetime partners was caused by a higher proportion of individuals with many partners in the young age group (

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

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.

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

A population at low census might go extinct, or instead transition into exponential growth to become firmly established. Whether this pivotal event occurs for a within-host pathogen can be the difference between health and illness. Here we define the principles governing whether HIV-1 spread among cells fails or becomes established, by coupling stochastic modeling with laboratory experiments. Following ex vivo activation of latently-infected CD4 T cells without de novo infection, stochastic cell division and death contributes to high variability in the magnitude of initial virus release. Transition to exponential HIV-1 spread often fails due to release of an insufficient amount of replication-competent virus. Establishment of exponential growth occurs when virus produced from multiple infected cells exceeds a critical population size. We quantitatively define the crucial transition to exponential viral spread. Thwarting this process would prevent HIV transmission or rebound from the lat...

In this article, we use a compartmental mathematical model of the dynamics of measles spread within a population with variable size to provide this framework.

These frequencies were used to simulate patients to find the likeliest paths of symptom onset for discernible symptoms of COVID-19. The dataset from Hong Kong contains 59 patients, and the dataset from Brazil contains at least 50,000 patients. (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

We offer a video showing real time spread of a cylinder of slime and challenge students to build a mathematical model for this phenomenon.

A nonlinear mathematical model of differential equations with piecewise constant arguments is proposed. This model is analyzed by using the theory of both differential and difference equations to show the spread of HIV in a homogeneous population.

These frequencies were used to simulate patients to find the likeliest paths of symptom onset for discernible symptoms of COVID-19. The dataset from Japan before the outbreak of the D614G variant contains 244 patients, and the dataset from Japan after the outbreak of the D614G variant reports symptoms of 2,636 patients, except for cough, where only 2,634 of the patients were recorded. (XLSX)

The COVID-19 pandemic, stemming from the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), initially emerged in December 2019 in Wuhan city, Hubei province, China, and swiftly spread worldwide. India, too, faced a significant impact from this viral disease. In response to the escalating number of infections and fatalities, and with the aim of ensuring the healthcare system's capacity to treat severe cases, the Government of India, like many other nations, implemented, or is in the process of implementing, measures to curb the spread of the virus.

This dataset is obsolete, superseded by this one and will not be updated anymore..

Fitted on data points as on 3 April 2020

Context

This dataset is created as a part of covid-19 global forecasting challenge. It contains parameters for the SIR model for different locations worldwide.

The model is defined as ODE system as follows: https://wikimedia.org/api/rest_v1/media/math/render/svg/29728a7d4bebe8197dca7d873d81b9dce954522e" alt="SIR ODE equations">

The models are fitted on John Hopkins University data (time series) using several runs of Nelder-Mead simplex optimization method (best run is taken) starting at different initial locations and RMSE as a loss.

What parameters are fitted (estimated) per country/province: * the day when the infection emerged in the country * the initial infected count on the first day of the infection * beta - an average number of contacts (sufficient to spread the disease) per day each infected individual has * gamma - fixed fraction of the infected group that will recover during any given day * R0 - how many susceptible people are infected (on average) by single infected individual. Equals beta/gamma * initial susceptible population (e.g. init suscept pop in the figures) - how many people are susceptible with regards to the quarantine measures at the modelled location

How to read the figures. * points are real observed data provided by Johns Hopkins University * curves are model prediction

• blue is susceptible population - people that are not yet infected but can get the infection
• red is infected population
• green is removed population (recovered or dead). people that are not susceptible any more as they came through the infection.

Content

The dataset contains 3 data portions:

1. Fitted SIR model parameters for different locations worldwide.
2. Figures that visually show how the fitted parameters match the data points.
3. CSV files with prediction for one year in the future for each individual location.

Warning

Always do visual check of the model fit (per_location_figures directory) for quality control before start to use the corresponding parameter values in your analysis.

Acknowledgements

Thanks a lot Kaggle for organizing data sharing and challenges that make the world better.

Also many thanks to John Hopkins University for their hard work of gathering COVID-19 statistics worldwide.

Inspiration

You can try to find correlation between model parameters (e.g. gamma - patient recovery rate) and other properties of the modelled locations worldwide (e.g. weather, population density, level of medical care, etc.)