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)

No description was included in this Dataset collected from the OSF

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.

Malaria, an infectious disease transmitted by mosquitoes and caused by the Plasmodium parasite, poses a significant global public health challenge, especially in areas lacking modern medical infrastructure. Traditional medicine often serves as either a primary or complementary treatment avenue. This study introduces a novel deterministic model that considers the impact of treatment seeking-behaviors on malaria transmission dynamics. Expanding upon the existing model, we incorporate distinct groups: individuals seeking treatment at health facilities and those self-treating with traditional remedies, which lack clinical validation. The study employs mathematical techniques for a comprehensive analysis of the model, including positivity, boundedness, existence and uniqueness, equilibrium, reproduction number, sensitivity, optimal control, and numerical simulations performed using MATLAB and the fourth-order Runge-Kutta method. Furthermore, we explore three time-dependent optimal control variables: antimalarial drug treatment, personal protective measures like ITNs, and promoting awareness to discourage inappropriate traditional medicine usage, all aimed at reducing disease transmission. Sensitivity analysis helps identify key parameters affecting malaria dynamics. Notably, increased utilization of health facilities for treatment significantly reduces the basic reproduction number, highlighting the importance of effective healthcare interventions. Numerical simulations underscore the vital role of treating infected individuals at health facilities in malaria eradication efforts. Optimal control analysis suggests that a combination of the three control strategies is most effective in combating malaria. This provides insights for public health policies to address the risk factors of using clinically not validated traditional medicine in malaria-endemic areas.

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

The distribution of farm locations and sizes is paramount to characterize patterns of disease spread. With some regions undergoing rapid intensification of livestock production, resulting in increased clustering of farms in peri-urban areas, measuring changes in the spatial distribution of farms is crucial to design effective interventions. However, those data are not available in many countries, their generation being resource-intensive. Here, we develop a farm distribution model (FDM), which allows the prediction of locations and sizes of poultry farms in countries with scarce data. The model combines (i) a Log-Gaussian Cox process model to simulate the farm distribution as a spatial Poisson point process, and (ii) a random forest model to simulate farm sizes (i.e. the number of animals per farm). Spatial predictors were used to calibrate the FDM on intensive broiler and layer farm distributions in Bangladesh, Gujarat (Indian state) and Thailand. The FDM yielded realistic farm distributions in terms of spatial clustering, farm locations and sizes, while providing insights on the factors influencing these distributions. Finally, we illustrate the relevance of modelling realistic farm distributions in the context of epidemic spread by simulating pathogen transmission on an array of spatial distributions of farms. We found that farm distributions generated from the FDM yielded spreading patterns consistent with simulations using observed data, while random point patterns underestimated the probability of large outbreaks. Indeed, spatial clustering increases vulnerability to epidemics, highlighting the need to account for it in epidemiological modelling studies. As the FDM maintains a realistic distribution of farm location and sizes, its use to inform mathematical models of disease transmission is particularly relevant for regions where these data are not available.

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

Malaria is a mosquito-borne disease spread by an infected vector (infected female Anopheles mosquito) or through transfusion of plasmodium-infected blood to susceptible individuals. The disease burden has resulted in high global mortality, particularly among children under the age of five. Many intervention responses have been implemented to control malaria disease transmission, including blood screening, Long-Lasting Insecticide Bed Nets (LLIN), treatment with an anti-malaria drug, spraying chemicals/pesticides on mosquito breeding sites, and indoor residual spray, among others. As a result, the SIR (Susceptible—Infected—Recovered) model was developed to study the impact of various malaria control and mitigation strategies. The associated basic reproduction number and stability theory is used to investigate the stability analysis of the model equilibrium points. By constructing an appropriate Lyapunov function, the global stability of the malaria-free equilibrium is investigated. By determining the direction of bifurcation, the implicit function theorem is used to investigate the stability of the model endemic equilibrium. The model is fitted to malaria data from Benue State, Nigeria, using R and MATLAB. Estimates of parameters were made. Following that, an optimal control model is developed and analyzed using Pontryaging's Maximum Principle. The malaria-free equilibrium point is locally and globally stable if the basic reproduction number (R0) and the blood transfusion reproduction number (Rα) are both less or equal to unity. The study of the sensitive parameters of the model revealed that the transmission rate of malaria from mosquito-to-human (βmh), transmission rate from humans-to-mosquito (βhm), blood transfusion reproduction number (Rα) and recruitment rate of mosquitoes (bm) are all sensitive parameters capable of increasing the basic reproduction number (R0) thereby increasing the risk in spreading malaria disease. The result of the optimal control shows that five possible controls are effective in reducing the transmission of malaria. The study recommended the combination of five controls, followed by the combination of four and three controls is effective in mitigating malaria transmission. The result of the optimal simulation also revealed that for communities or areas where resources are scarce, the combination of Long Lasting Insecticide Treated Bednets (u2), Treatment (u3), and Indoor insecticide spray (u5) is recommended. Numerical simulations are performed to validate the model's analytical results.

This material includes the data from Ghana we used and the code written in MATLAB to obtain data fitting results and optimal control results. (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.

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.

TTIQ parameter ranges considered in the sensitivity analysis.

Plant attributes and results of company-initiated testing.

List of mitigation measures utilized by some or all plants.

The prediction of the number of infected and dead due to COVID-19 has challenged scientists and government bodies, prompting them to formulate public policies to control the virus’ spread and public health emergency worldwide. In this sense, we propose a hybrid method that combines the SIRD mathematical model, whose parameters are estimated via Bayesian inference with a seasonal ARIMA model. Our approach considers that notifications of both, infections and deaths are realizations of a time series process, so that components such as non-stationarity, trend, autocorrelation and/or stochastic seasonal patterns, among others, must be taken into account in the fitting of any mathematical model. The method is applied to data from two Colombian cities, and as hypothesized, the prediction outperforms the obtained with the fit of only the SIRD model. In addition, a simulation study is presented to assess the quality of the estimators of SIRD model in the inverse problem solution.

This study presents a reliable mathematical model to explain the spread of typhoid fever, covering stages of susceptibility, infection, carrying, and recovery, specifically in the Sheno town community. A detailed analysis is done to ensure the solutions are positive, stay within certain limits, and are stable for both situations where the disease is absent and where it is consistently present. The Routh-Hurwitz stability criterion has been used and applied for the purpose of stability analysis. Using the next-generation matrix, we determined the intrinsic potential for disease transmission. It showing that typhoid fever is spreading actively in Sheno town, with cases above a critical level. Our findings reveal the instability of the disease-free equilibrium point alongside the stability of the endemic equilibrium point. We identified two pivotal factors for transmission of the disease: the infectious rate, representing the speed of disease transmission, and the recruitment rate, indicating the rate at which new individuals enter the susceptible population. These parameters are indispensable for devising effective control measures. It is imperative to keep these parameters below specific thresholds to maintain a basic reproduction number favorable for disease control. Additionally, the study carefully examines how different factors affect the spread of typhoid fever, giving a detailed understanding of its dynamics. At the end, this study provides valuable insights and specific strategies for managing the disease in the Sheno town community.

Model parameters, prior and posterior distributions, and convergence diagnostic.

Xenografts -as simplified animal models of cancer- differ substantially in vasculature and stromal architecture when compared to clinical tumours. This makes mathematical model-based predictions of clinical outcome challenging. Our objective is to further understand differences in tumour progression and physiology between animal models and the clinic.To achieve that, we propose a mathematical model based upon tumour pathophysiology, where oxygen -as a surrogate for endocrine delivery- is our main focus. The Oxygen-Driven Model (ODM), using oxygen diffusion equations, describes tumour growth, hypoxia and necrosis. The ODM describes two key physiological parameters. Apparent oxygen uptake rate () represents the amount of oxygen cells seem to need to proliferate. The more oxygen they appear to need, the more the oxygen transport. gathers variability from the vasculature, stroma and tumour morphology. Proliferating rate (kp) deals with cell line specific factors to promote growth. The KH,KN describe the switch of hypoxia and necrosis. Retrospectively, using archived data, we looked at longitudinal tumour volume datasets for 38 xenografted cell lines and 5 patient-derived xenograft-like models.Exploration of the parameter space allows us to distinguish 2 groups of parameters. Group 1 of cell lines shows a spread in values of and lower kp, indicating that tumours are poorly perfused and slow growing. Group 2 share the value of the oxygen uptake rate () and vary greatly in kp, which we interpret as having similar oxygen transport, but more tumour intrinsic variability in growth.However, the ODM has some limitations when tested in explant-like animal models, whose complex tumour-stromal morphology may not be captured in the current version of the model. Incorporation of stroma in the ODM will help explain these discrepancies. We have provided an example. The ODM is a very simple -and versatile- model suitable for the design of preclinical experiments, which can be modified and enhanced whilst maintaining confidence in its predictions.