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

The model fit and outcomes (post-vaccination prevalence) under different model assumptions about duration of natural immunity (1/w), weight of the secondary force of infection (γ base-case = 0.4), increased new partner acquisition rate for young adults (+20% partners), and different natural immunity waning model (SIS) only for males. The measure of model fit is a weighted sum of squared residuals (WSR). The calibrated model parameters: clearance rate of persistent infection (ηpers), transmission probability per partnership (β), waning rate of natural immunity (w). The mean and standard deviation (SD) are given for each parameter. The high-risk HPV (hrHPV) infection includes both transient and persistent infections (pers.inf.).

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

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.

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

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.

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

List of Spatial Predictors with their sources and units used in the LGCP and RF models.

The following data and scripts are part of the manuscript titled 'Curbing zoonotic disease spread in multi-host-species systems will require integrating novel data streams and analytical approaches: evidence from a scoping review of bovine tuberculosis' which will be soon sent for peer-review as well as preprint. Please read the README.txt file for information on the files uploaded.

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.

Theories of word learning differentially weigh the role of repeated experience with a novel item, leading to internalization of statistical regularities over time, and the learners use of prior knowledge to infer in-the-moment. Bayesian theories suggest both are critical, but which is weighed more heavily depends on how ambiguous the situation is. To examine this interplay and how it relates to memory, we adapted a Bayesian model of learning (Tenanbaum, Kemp, Griffiths, & Goodman, 2011; Xu & Tenanbaum, 2007) to an inferential word learning task of novel animals, as outline in the following article: “Bayesians learn best: an inferred Bayesian model accounts for individual differences in prior knowledge use during word learning.” Briefly, the model used (i) contextual information provided in the task, quantified by collecting norms for how informative each trial was (likelihood) and (ii) participant’s trial selection accuracy (posterior distribution) to (iii) infer their prior distribution, a proxy for their belief before exposure to the contextual information. Trial accuracy data for the word learning task was collected on one day, and free recall and recognition memory of learned animal names was completed the next day. Norms for how informative each trial was to guide correct selection were collected in a single session with a separate group of participants. Primary data include trial informativeness norms and trial accuracy in the task, both of which were used as input for the Bayesian model. The model infers prior distribution shape parameters from task accuracy and trial norms, completed using the Excel add-in Solver. This is also included in the primary dataset. Output of the model were used to mathematically derive measures of central tendency and spread for participants’ inferred prior distributions, included in the Secondary dataset. These values, along with average block accuracy, were regressed for each participant to examine change across the task. Output from these regressions (slope, intercept and error terms) were used in the statistical analyses with memory measures, which can be found in the Secondary data.

In 2022, there was a global resurgence of mpox, with different clinico-epidemiological features compared with previous
outbreaks. During this resurgence, sexual contact was hypothesized as the primary transmission route, with the community
of men having sex with men (MSM) being disproportionately affected. Because of the stigma associated with sexually
transmitted infections, especially those impacting MSM, the real burden of mpox could be masked.
We quantified the basic reproduction number (R0) and the under-estimated fraction of mpox cases in 16 countries, from the
onset of the outbreak until early September 2022, using Bayesian inference and a compartmentalized, risk-structured (high-
and low-risk populations), two-route (sexual and non-sexual transmission) mathematical model. Machine learning (ML) was
leveraged to identify under-estimation determinants.
Estimated R0 ranged between 1·37 (Canada) and 3·68 (Germany). The under-estimation rates for the high- and low-risk
populations varied between 25-93% and 65-85%, respectively. The estimated total number of mpox cases, relative to the
reported cases, is highest in Colombia (3·60) and lowest in Canada (1·08). In the ML analysis, two clusters of countries could
be identified, differing in terms of attitudes towards the 2SLGBTQIAP+ community and importance of religion.
Given the substantial mpox under-estimation, surveillance should be enhanced and campaigns against the stigmatization of
MSM should be organized. Countries have different social characteristics, potentially explaining the various degrees of under-
reporting in mpox cases, which should be considered by studies assessing the effectiveness of community-based
interventions.

Please refer to the published manuscript for methods associated with data collection and analysis.

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)

Lexical dynamics, just as epidemiological dynamics, represent spreading phenomena. In both domains, constituents (words, pathogens) are transmitted within populations of individuals. In linguistics, such dynamics have been modeled by drawing on mathematical models originating from epidemiology. The basic reproductive ratio is a quantity that figures centrally in epidemiological research but not so much in linguistics. It is defined as the average number of individuals that acquire a constituent (infectious pathogen) from a single individual carrying it. In this contribution, we examine a set of lexical innovations, i.e., words that have spread recently, in four different languages (English, German, Spanish, and Italian). We use and compare different ways of estimating the basic reproductive ratio in the lexical domain. Our results show that the basic reproductive ratio can be somewhat reliably estimated by exploiting estimates of lexical age of acquisition and prevalence but that the derivation based on diachronic corpus data comes with certain challenges. Based on our empirical results, we argue that the basic reproductive ratio can inform about the stability of newly emerging words and about how often such words are successfully propagated in linguistic contact events. Our analysis shows that an average lexical innovation that has spread in the previous two centuries has been passed on by each individual only to a handful of contacts.

In 2024, five percent of GCSE entries in England were awarded the highest grade of 9, with a further 7.1 percent of entries being awarded an 8, the second-highest grade. A 5 grade was the most common individual grade level achieved by GCSE students, at 16.6 percent of all entries.

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.

Appendix A Derivation of contact tracing terms with early and late infectious individuals, Appendix B Modeling social and hygiene measures and changes in the tracing coverage, Appendix C Parameterization, Appendix D Stability analysis. (ZIP)

In this paper, we suggest a mathematical model of COVID-19 with multiple variants of the virus under optimal control. Mathematical modeling has been used to gain deeper insights into the transmission of COVID-19, and various prevention and control strategies have been implemented to mitigate its spread. Our model is a SEIR-based model for multi-strains of COVID-19 with 7 compartments. We also consider the circulatory structure to account for the termination of immunity for COVID-19. The model is established in terms of the positivity and boundedness of the solution and the existence of equilibrium points, and the local stability of the solution. As a result of fitting data of COVID-19 in Ghana to the model, the basic reproduction number of the original virus and Delta variant was estimated to be 1.9396, and the basic reproduction number of the Omicron variant was estimated to be 3.4905, which is 1.8 times larger than that. We observe that even small differences in the incubation and recovery periods of two strains with the same initial transmission rate resulted in large differences in the number of infected individuals. In the case of COVID-19, infections caused by the Omicron variant occur 1.5 to 10 times more than those caused by the original virus. In terms of the optimal control strategy, we formulate three control strategies focusing on social distancing, vaccination, and testing-treatment. We have developed an optimal control model for the three strategies outlined above for the multi-strain model using the Pontryagin’s Maximum Principle. Through numerical simulations, we analyze three optimal control strategies for each strain and also consider combinations of the two control strategies. As a result of the simulation, all control strategies are effective in reducing disease spread, in particular, vaccination strategies are more effective than the other two control strategies. In addition the combination of the two strategies also reduces the number of infected individuals by 1/10 compared to implementing one strategy, even when mild levels are implemented. Finally, we show that if the testing-treatment strategy is not properly implemented, the number of asymptomatic and unidentified infections may surge. These results could help guide the level of government intervention and prevention strategy formulation.

Median estimates for all methods (i-iii) of estimating the basic reproductive ratio in all languages.