Disease Transmission Model Research Articles

Preserving friendships in school contacts: An algorithm to construct synthetic temporal networks for epidemic modelling.

High-resolution temporal data on contacts between hosts provide crucial information on the mixing patterns underlying infectious disease transmission. Publicly available data sets of contact data are however typically recorded over short time windows with respect to the duration of an epidemic. To inform models of disease transmission, data are thus often repeated several times, yielding synthetic data covering long enough timescales. Looping over short term data to approximate contact patterns on longer timescales can lead to unrealistic transmission chains because of the deterministic repetition of all contacts, without any renewal of the contact partners of each individual between successive periods. Real contacts indeed include a combination of regularly repeated contacts (e.g., due to friendship relations) and of more casual ones. In this paper, we propose an algorithm to longitudinally extend contact data recorded in a school setting, taking into account this dual aspect of contacts and in particular the presence of repeated contacts due to friendships. To illustrate the interest of such an algorithm, we then simulate the spread of SARS-CoV-2 on our synthetic contacts using an agent-based model specific to the school setting. We compare the results with simulations performed on synthetic data extended with simpler algorithms to determine the impact of preserving friendships in the data extension method. Notably, the preservation of friendships does not strongly affect transmission routes between classes in the school but leads to different infection pathways between individual students. Our results moreover indicate that gathering contact data during two days in a population is sufficient to generate realistic synthetic contact sequences between individuals in that population on longer timescales. The proposed tool will allow modellers to leverage existing contact data, and contributes to the design of optimal future field data collection.

Strategic vaccination responses to Chikungunya outbreaks in Rome: Insights from a dynamic transmission model.

Chikungunya virus (CHIKV) outbreaks, driven by the expanding habitat of the Aedes albopictus mosquito and global climate change, pose a significant threat to public health. Our study evaluates the effectiveness of emergency vaccination using a dynamic disease transmission model for a potential large-scale outbreak in Rome, Italy. The model incorporates a susceptible-exposed-infected-recovered (SEIR) framework for human and mosquito populations, taking into account temperature-dependent mosquito lifecycle dynamics, human-mosquito interactions, and various vaccination scenarios. Results indicate that emergency vaccination could significantly mitigate the impact of a CHIKV outbreak. Without vaccination, an outbreak is estimated to infect up to 6.21% of Rome's population, equating to approximately 170,762 individuals. Implementing rapid vaccination after detecting the virus in ten individuals and achieving 40% coverage could reduce infection rates by 82%, preventing 139,805 cases. Scenario and sensitivity analyses confirm that even with lower vaccination coverage rates, significant benefits are observed: at 10% coverage, the number of infections drops to 115,231, and at 20% coverage, it further reduces to 76,031. These scenarios indicate prevention of approximately 33% and 55% of infections, respectively. The findings highlight the critical role of timely vaccination interventions in outbreak settings, demonstrating that even modest coverage levels can markedly decrease the spread of CHIKV. This study underscores the importance of preparedness, early detection and adaptive response capabilities to manage emerging infectious diseases in urban centres, advocating for strategic vaccine stockpiling and rapid deployment mechanisms to enhance public health outcomes.

Modeling the interplay between disease spread, behaviors, and disease perception with a data-driven approach

Individuals’ perceptions of disease influence their adherence to preventive measures, shaping the dynamics of disease spread. Despite extensive research on the interaction between disease spread, human behaviors, and interventions, few models have incorporated real-world behavioral data on disease perception, limiting their applicability. In this study, we propose an approach to integrate survey data on contact patterns and disease perception into a data-driven compartmental model, by hypothesizing that perceived severity is a determinant of behavioral change. We explore scenarios involving a competition between a COVID-19 wave and a vaccination campaign, where individuals’ behaviors vary based on their perceived severity of the disease. Results indicate that behavioral heterogeneities influenced by perceived severity affect epidemic dynamics, in a way depending on the interplay between two contrasting effects. On the one hand, longer adherence to protective measures by groups with high perceived severity provides greater protection to vulnerable individuals, while premature relaxation of behaviors by low perceived severity groups facilitates virus spread. Differences in behavior across different population groups may impact strongly the epidemiological curves, with a transition from a scenario with two successive epidemic peaks to one with only one (higher) peak and overall more numerous severe outcomes and deaths. The specific modeling choices for how perceived severity modulates behavior parameters do not strongly impact the model’s outcomes. Moreover, the study of several simplified models indicate that the observed phenomenology depends on the combination of data describing age-stratified contact patterns and of the feedback loop between disease perception and behavior, while it is robust with respect to the lack of precise information on the distribution of perceived severity in the population. Sensitivity analyses confirm the robustness of our findings, emphasizing the consistent impact of behavioral heterogeneities across various scenarios. Our study underscores the importance of integrating risk perception into infectious disease transmission models and gives hints on the type of data that further extensive data collection should target to enhance model accuracy and relevance.

Hospital population density and risk of respiratory infection: is close contact density dependent?

Respiratory infections acquired in hospital depend on close contact, which may be affected by hospital population density. Models of infectious disease transmission typically assume that contact rates are independent of density (frequency dependence) or proportional to it (linear density dependence), without justification. We evaluate these assumptions by measuring contact rates in hospitals under different population densities.We analysed data from a study in 15 wards in which staff, patients and visitors carried wearable sensors which detected close contacts. We proposed a general model, non-linear density dependence, and fit this to data on several types of interactions. Finally, we projected the fitted models to predict the effect of increasing population density on epidemic risk.We identified considerable heterogeneity in density dependence between wards, even those with the same medical specialty. Interactions between all persons present usually depended little on the population density. However, increasing patient density was associated with higher rates of patient contact for staff and for other patients. Simulations suggested that a 10% increase in patient population density would carry a markedly increased risk in many wards.This study highlights the variance in density dependent dynamics and the complexity of predicting contact rates.

Investigation of an optimal control strategy for a cholera disease transmission model with programs

Cholera is a disease of poverty affecting people with inadequate access to safe water and basic sanitation. Conflict, unplanned urbanization and climate change all increase the risk of cholera. In this article, an optimal control deterministic mathematical model of cholera disease with cost-effectiveness analysis is developed and analyzed considering both direct and indirect contact transmission pathways. The model qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction number of the model is obtained. We also performed sensitivity analysis of the basic parameters of the model. Then an optimal control problem is designed with a control functional having five controls: vaccination, treatment, environment sanitation and personal hygiene, and water quality improvement program. We examined the existence and uniqueness of the optimal controls of the system. Through the implementation of Pontryagin's maximum principle, the characterization of the optimal controls optimality system is established. The numerical simulation results the integrated control strategies demonstrated that strategy 2, 7, and 12 are effective programs to combat cholera disease from the community. Based on the local circumstances, available funds, and resources, it is recommended to the government stakeholders and policymakers to execute any one of the three integrated intervention programs.

Ventilation effectiveness and incomplete mixing in air distribution design for airborne transmission

How ventilation should be arranged to be effective at reasonable air change rates is one key question as ventilation criteria and standard airborne disease transmission models are based on the well-mixed assumption, but air distribution patterns lead to non-uniform spatial concentrations. In this study a new method for ventilation effectiveness application in ventilation design for airborne transmission was developed and tested with tracer gas measurements in 22 rooms. Contrary to existing ventilation effectiveness values measured with distributed source, the developed method uses a couple of point source locations corresponding to an infector to quantify infection risk for each occupant. Novelty of the method is new ventilation effectiveness indicator that makes it possible to describe the effect of spatial variation of concentration and risk with single parameter. Quanta were used as input data to calculate the ventilation rate supplied by air distribution system corresponding to a specified risk level, but the differences between studied cases do not significantly depend on the quanta values. Application of the method to measured rooms showed that simple ventilation effectiveness calculation from average concentration at the breathing height, not requiring quanta data, provided lower ventilation effectiveness and higher ventilation rate in all cases. In many cases the difference in required ventilation rates was only a few percent, but in some large spaces it exceeded 10% with maximum of 39% in large open plan office with high concentration differences. Measured ventilation effectiveness values ranging from 0.5 to 1.4 indicate a substantial improvement potential in many cases.

Choice of landscape discretisation method affects the inferred rate of spread in wildlife disease spread models

Disease modelling at the livestock-wildlife interface is an important topic for which discrete-space models are used for the wildlife component. One prominent example is African Swine Fever, where wild boar play an influential role as reservoirs of disease spillover into domestic pig farms. In this paper, we present a simulation study that demonstrates the impact of seemingly arbitrary choices of landscape discretisation method on the inferred rate of spread within the model. We use an ordinary differential equation model to implement a simplified model of disease transmission between discrete groups of wild boar with spillover into domestic pig farms contained within a homogeneous landscape. We examine a range of scenarios whereby the landscape is discretised into wild boar patches of varying size and shape, and compare the rate of spread between domestic pig farms placed at fixed points on the landscape. Our results demonstrate a non-monotonic relationship between patch size and rate of spread, which is particularly unstable and unpredictable for square and triangular shaped patches. Discretisation of the landscape into hexagons appears to produce a more stable relationship between patch size and rate of spread for the three types of transmission kernel we investigated. Although the rate of disease spread does converge to a stable value, this occurs at patch sizes that are much smaller than would be used in practice for wild boar. We conclude that outputs of disease models containing a wildlife component should not be considered to be robust to arbitrary choices for patch size and placement, but rather as a source of uncertainty to be examined using sensitivity analysis. Furthermore, we strongly recommend the use of hexagons rather than squares or right triangles for landscape discretisation.

Pairwise Accelerated Failure Time Regression Models for Infectious Disease Transmission in Close-Contact Groups With External Sources of Infection.

Many important questions in infectious disease epidemiology involve associations between covariates (e.g., age or vaccination status) and infectiousness or susceptibility. Because disease transmission produces dependent outcomes, these questions are difficult or impossible to address using standard regression models from biostatistics. Pairwise survival analysis handles dependent outcomes by calculating likelihoods in terms of contact interval distributions in ordered pairs of individuals. The contact interval in the ordered pair is the time from the onset of infectiousness in to infectious contact from to , where an infectious contact is sufficient to infect if they are susceptible. Here, we introduce a pairwise accelerated failure time regression model for infectious disease transmission that allows the rate parameter of the contact interval distribution to depend on individual-level infectiousness covariates for , individual-level susceptibility covariates for , and pair-level covariates (e.g., type of relationship). This model can simultaneously handle internal infections (caused by transmission between individuals under observation) and external infections (caused by environmental or community sources of infection). We show that this model produces consistent and asymptotically normal parameter estimates. In a simulation study, we evaluate bias and confidence interval coverage probabilities, explore the role of epidemiologic study design, and investigate the effects of model misspecification. We use this regression model to analyze household data from Los Angeles County during the 2009 influenza A (H1N1) pandemic, where we find that the ability to account for external sources of infection increases the statistical power to estimate the effect of antiviral prophylaxis.

A new model of the impact of information dissemination with emotional responses on disease transmission in multilayer networks

During disease transmission, the dissemination of information about the disease prompts safety concerns among individuals. Individuals’ various emotional responses to information may affect infection prevention measures and, consequently, disease transmission. In this paper, we propose a new coupled information and disease transmission model with emotional factors in multiplex networks. Our specific focus is on the impact of diverse emotional responses on the dynamics process. We employ the Microscopic Markov Chain Approach (MMCA) to analyze the model, and obtaining state transfer equations, and deriving the disease transmission threshold. Extensive numerical simulations show that dissemination of information by relevant authorities motivates individuals to adopt scientific self-protective behaviors, thus helping to control disease transmission. Furthermore, individuals who have different emotional responses after obtaining information have varying effects on disease transmission, and reducing the anxiety response or increasing the calm response of individuals can more effectively decrease the scale of disease transmission and increase the disease transmission threshold. In summary, improving the quality of information released by the emergency management department, reducing the individual’s anxiety response, and encouraging the adoption of positive and effective protective measures are of paramount importance for epidemic prevention and control.

Spatial distribution of poultry farms using point pattern modelling: A method to address livestock environmental impacts and disease transmission risks.

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.

Human behavior-based COVID-19 transmission in two dining spaces

Since December 2019, the COVID-19 pandemic has rapidly disseminated globally, posing significant threats to the world. The dining spaces are high-risk indoor environments for the transmission of SARS-CoV-2, posing challenges for intervention and control. This study, based on surveillance videos from two COVID-19 outbreak cases in restaurants, obtained real data on human behaviors of close contact and surface touch. A respiratory infectious disease transmission model was developed, incorporating four transmission routes: short-range airborne, long-range airborne, fomite and large droplet. The results indicate that diners and staff spent 21.9 %−28.7 % and 17.5 %−27.8 % of their time on speaking, respectively, while spending 85.9 %−90.7 % and 83.4 %−87.6 % of their time on surface touching. The primary transmission routes were short-range (contributing 5.8 %−70.9 %) and long-range airborne (contributing 28.4 %−93.0 %), with fomite and large droplet routes contributing less than 12.0 %. Staff-only mask wearing reduced infection risk by 12.8 %−31.8 %. It is recommended that mandatory mask wearing for staff is necessary, while diners should wear masks as much as possible, and that the equivalent ventilation rate of clean fresh air is suggested to 30.0 m3/ (h·person). This study provides a scientific support to make non-pharmaceutical interventions in dinning spaces.

Understanding the transmission of bacterial agents of sapronotic diseases using an ecosystem-based approach: A first spatially realistic metacommunity model.

Pathogens such as bacteria, fungi and viruses are important components of soil and aquatic communities, where they can benefit from decaying and living organic matter, and may opportunistically infect human and animal hosts. One-third of human infectious diseases is constituted by sapronotic disease agents that are natural inhabitants of soil or aquatic ecosystems. They are capable of existing and reproducing in the environment outside of the host for extended periods of time. However, as ecological research on sapronosis is infrequent and epidemiological models are even rarer, very little information is currently available. Their importance is overlooked in medical and veterinary research, as well as the relationships between free environmental forms and those that are pathogenic. Here, using dynamical models in realistic aquatic metacommunity systems, we analyze sapronosis transmission, using the human pathogen Mycobacterium ulcerans that is responsible for Buruli ulcer. We show that the persistence of bacilli in aquatic ecosystems is driven by a seasonal upstream supply, and that the attachment and development of cells to aquatic living forms is essential for such pathogen persistence and population dynamics. Our work constitutes the first set of metacommunity models of sapronotic disease transmission, and is highly flexible for adaptation to other types of sapronosis. The importance of sapronotic agents on animal and human disease burden needs better understanding and new models of sapronosis disease ecology to guide the management and prevention of this important group of pathogens.

A two-variant model of SARS-COV-2 transmission: estimating the characteristics of a newly emerging strain

BackgroundThe Covid-19 pandemic has been characterized by the emergence of novel SARS-CoV-2 variants, each with distinct properties influencing transmission dynamics, immune escape, and virulence, which, in turn, influence their impact on local populations. Swift analysis of the properties of newly emerged variants is essential in the initial days and weeks to enhance readiness and facilitate the scaling of clinical and public health system responses.MethodsThis paper introduces a two-variant metapopulation compartmental model of disease transmission to simulate the dynamics of disease transmission during a period of transition to a newly dominant strain. Leveraging novel S-gene dropout analysis data and genomic sequencing data, combined with confirmed Covid-19 case data, we estimate the epidemiological characteristics of the Omicron variant, which replaced the Delta variant in late 2021 in Philadelphia, PA. We utilized a grid-search method to identify plausible combinations of model parameters, followed by an ensemble adjustment Kalman filter for parameter inference.ResultsThe model successfully estimated key epidemiological parameters; we estimated the ascertainment rate of 0.22 (95% credible interval 0.15–0.29) and transmission rate of 5.0 (95% CI 2.4–6.6) for the Omicron variant.ConclusionsThe study demonstrates the potential for this model-inference framework to provide real-time insights during the emergence of novel variants, aiding in timely public health responses.

The impact of household size on measles transmission: A long-term perspective

Households play an important role in the transmission of infectious diseases due to the close contact therein. Previous modeling studies on disease transmission with household-level mixing have explored the relationship between household size distribution and epidemic characteristics such as final epidemic sizes and the basic reproduction number but have not considered the epidemic impact of declining household sizes caused by demographic shifts. Here, we use a disease transmission model that incorporates demographic changes in household sizes to study the long-term transmission dynamics of measles in communities with varying household size distributions. We explore the impact of incorporating both household- and age-structured mixing on the dynamic properties of the transmission model and compare these dynamics across different household size distributions. Our analysis, based on the household- and age-structured model, shows that communities with larger household sizes require higher vaccination thresholds and bear a greater burden of infections. However, simulations show the apparent impact of changing household sizes is the combined result of changing birth rates and household mixing, and that changing birth rates likely play a larger role than changes in household mixing in shaping measles transmission dynamics (n.b, life-long immunity makes replenishment of population susceptibility from births a crucial transmission driver for measles). In addition, simulations of endemic transmission of measles within a hypothetical population formulated using aggregated world demographic data suggest the decline in household size (driven by changing fertility rates of the population), in addition to increasing vaccination coverage, could have had a significant impact on the incidence of measles over time.

Contagious Vibrations: Sympathetic Resonance as a Model for Disease Transmission in the Writings of Ficino, Fracastoro, and Cardano.

Contagious diseases were among the most vexing problems in ancient theories of health, which could not easily account for how a corruption of one person's humors could cause a similar corruption in another's. One useful explanatory concept for Renaissance doctors tackling this theoretical gap was the phenomenon of resonance or "sympathetic vibration" - where one stationary string begins to vibrate spontaneously when a similarly tuned string is plucked nearby - as both resonance and contagion involved some mysterious, insensible action at a distance between an agent and a patient. Tracing the writings of Marsilio Ficino, Girolamo Fracastoro, and Girolamo Cardano, this essay explores the relationships between the writers' accounts of sympathetic vibrations and their contagion theories. It argues that different conceptions of the acoustic phenomenon - either as a manifestation of a Neo-Platonic World-Soul that underpinned the universe or else as a physical effect - revealed the writers' cosmological views that, in turn, informed their accounts of the human body and disease.

Estimating the value of new antibiotic treatment strategies in Zhejiang province, China: cost-effectiveness analysis based on a validated dynamic model

ObjectivesThis analysis aims to better reflect the value of new antibiotic treatment strategies, thereby informing clinical antibiotic use, antimicrobial reimbursement and/or hospital formulary decision-making in China.DesignWe adapted a published and...

Methodology for assessing the impact of emergencies on the spread of infectious diseases

The spread of infectious diseases is significantly influenced by emergencies, particularly military conflicts, which disrupt healthcare systems and increase the risks of epidemics. The full-scale Russian invasion of Ukraine has exacerbated these challenges, causing environmental damage, mass displacement, and the breakdown of healthcare services, all of which contribute to the spread of infectious diseases. This study aims to develop a comprehensive methodology for assessing the impact of emergencies on the spread of infectious diseases, focusing on the full-scale invasion of Ukraine. The object of this study is to address epidemic threats posed by emergencies, particularly the increased spread of infectious diseases due to war-related disruptions. The subject of this study is methods and models of infectious disease transmission under conditions of emergencies, emphasizing the Russian full-scale invasion of Ukraine. The tasks of this study are to provide an analysis of the current state of research and develop a methodology for assessing the impact of emergencies on the spread of infectious diseases. The proposed methodology includes several key components. Comprehensive data from public health organizations includes infectious disease statistics, demographic shifts, healthcare disruptions, and environmental factors exacerbated by emergencies. Data preprocessing removes inconsistencies, standardization of formats, and normalization for population size differences. Machine learning models, including convolutional neural networks and recurrent neural networks, have been developed to simulate the spread of diseases based on demographic, environmental, and healthcare-related variables. Deep learning models analyze spatial and temporal patterns, whereas compartmental models such as SIR estimate changes in reproductive numbers (R₀ and Re). Additionally, models of excess mortality incorporate mixed effects to account for regional and time-based variations. The methodology incorporates real-time monitoring of epidemic threats using real-time data from multiple sources, enabling dynamic assessments of disease spread and facilitating predictive modeling. The models were trained on historical data and validated using cross-validation techniques to ensure robustness and reliability, with a specific focus on the pre- and post-invasion phases in Ukraine.Results: The study provides a comprehensive framework for collecting and processing data on infectious diseases and epidemic threats in emergencies. The proposed model introduces advanced machine learning and epidemiological models trained on pre- and post-invasion data to analyze disease transmission patterns and forecast future epidemic dynamics. Conclusion: The proposed methodology addresses current gaps in infectious disease during emergencies by integrating real-time data and machine learning techniques. This research improves decision-making in public health management and biosafety during crises, particularly in war-affected regions like Ukraine.

Utilizing large language models in infectious disease transmission modelling for public health preparedness

IntroductionOpenAI's ChatGPT, a Large Language Model (LLM), is a powerful tool across domains, designed for text and code generation, fostering collaboration, especially in public health. Investigating the role of this advanced LLM chatbot in assisting public health practitioners in shaping disease transmission models to inform infection control strategies, marks a new era in infectious disease epidemiology research. This study used a case study to illustrate how ChatGPT collaborates with a public health practitioner in co-designing a mathematical transmission model. MethodsUsing natural conversation, the practitioner initiated a dialogue involving an iterative process of code generation, refinement, and debugging with ChatGPT to develop a model to fit 10 days of prevalence data to estimate two key epidemiological parameters: i) basic reproductive number (Ro) and ii) final epidemic size. Verification and validation processes are conducted to ensure the accuracy and functionality of the final model. ResultsChatGPT developed a validated transmission model which replicated the epidemic curve and gave estimates of Ro of 4.19 (95 % CI: 4.13- 4.26) and a final epidemic size of 98.3 % of the population within 60 days. It highlighted the advantages of using maximum likelihood estimation with Poisson distribution over least squares method. ConclusionIntegration of LLM in medical research accelerates model development, reducing technical barriers for health practitioners, democratizing access to advanced modeling and potentially enhancing pandemic preparedness globally, particularly in resource-constrained populations.

Internal and external drivers interact to create highly dynamic mosquito blood-feeding behaviour.

Blood-feeding, which is necessary for most female mosquitoes to reproduce, provides an opportunity for pathogen transmission. Blood-feeding is influenced by external factors such as light, temperature, humidity and intra- and inter-specific interactions. Physiologically, blood-feeding cycles are linked to nutritional conditions and governed by conserved hormonal signalling pathways that prepare mosquito sensory systems to locate and evaluate hosts. Human activities also alter mosquito blood-feeding behaviour through selection pressures such as insecticide usage, habitat and ecosystem alterations, and climate change. Notably, blood-feeding behaviour changes within a mosquito's lifespan, an underexplored phenomenon from an epidemiological standpoint. A review of the literature indicates that our understanding of mosquito biology and blood-feeding behaviour is predominantly based on studies of a handful of primarily tropical species. This focus likely skews our comprehension of the diversity of critical drivers of blood-feeding behaviour, especially under constraints imposed by harsh conditions. We found evidence of remarkable adaptability in blood-feeding and significant knowledge gaps regarding the determinants of host use. Specifically, epidemiological analyses assume host use is modified by external factors, while neglecting internal physiology. Integrating all significant factors is essential for developing effective models of mosquito-borne disease transmission in a rapidly changing world.

Fitting Epidemic Models to Data: A Tutorial in Memory of Fred Brauer.

Fred Brauer was an eminent mathematician who studied dynamical systems, especially differential equations. He made many contributions to mathematical epidemiology, a field that is strongly connected to data, but he always chose to avoid data analysis. Nevertheless, he recognized that fitting models to data is usually necessary when attempting to apply infectious disease transmission models to real public health problems. He was curious to know how one goes about fitting dynamical models to data, and why it can be hard. Initially in response to Fred's questions, we developed a user-friendly R package, fitode, that facilitates fitting ordinary differential equations to observed time series. Here, we use this package to provide a brief tutorial introduction to fitting compartmental epidemic models to a single observed time series. We assume that, like Fred, the reader is familiar with dynamical systems from a mathematical perspective, but has limited experience with statistical methodology or optimization techniques.