Neuronal morphology enhances robustness to perturbations of channel densities.

Biological neurons show significant cell-to-cell variability but have the striking ability to maintain their key firing properties in the face of unpredictable perturbations and stochastic noise. Using a population of multi-compartment models consisting of soma, neurites, and axon for the lateral pyloric neuron in the crab stomatogastric ganglion, we explore how rebound bursting is preserved when the 14 channel conductances in each model are all randomly varied. The coupling between the axon and other compartments is critical for the ability of the axon to spike during bursts and consequently determines the set of successful solutions. When the coupling deviates from a biologically realistic range, the neuronal tolerance of conductance variations is lessened. Thus, the gross morphological features of these neurons enhance their robustness to perturbations of channel densities and expand the space of individual variability that can maintain a desired output pattern.

Semiparametric inference of effective reproduction number dynamics from wastewater pathogen surveillance data.

Concentrations of pathogen genomes measured in wastewater have recently become available as a new data source to use when modeling the spread of infectious diseases. One promising use for this data source is inference of the effective reproduction number, the average number of individuals a newly infected person will infect. We propose a model where new infections arrive according to a time-varying immigration rate which can be interpreted as an average number of secondary infections produced by one infectious individual per unit time. This model allows us to estimate the effective reproduction number from concentrations of pathogen genomes, while avoiding difficulty to verify assumptions about the dynamics of the susceptible population. As a byproduct of our primary goal, we also produce a new model for estimating the effective reproduction number from case data using the same framework. We test this modeling framework in an agent-based simulation study with a realistic data generating mechanism which accounts for the time-varying dynamics of pathogen shedding. Finally, we apply our new model to estimating the effective reproduction number of SARS-CoV-2, the causative agent of COVID-19, in Los Angeles, CA, using pathogen RNA concentrations collected from a large wastewater treatment facility.

A modeling framework for the analysis of the SARS-CoV2 transmission dynamics.

Despite the progress in medical data collection the actual burden of SARS-CoV-2 remains unknown due to under-ascertainment of cases. This was apparent in the acute phase of the pandemic and the use of reported deaths has been pointed out as a more reliable source of information, likely less prone to under-reporting. Since daily deaths occur from past infections weighted by their probability of death, one may infer the total number of infections accounting for their age distribution, using the data on reported deaths. We adopt this framework and assume that the dynamics generating the total number of infections can be described by a continuous time transmission model expressed through a system of nonlinear ordinary differential equations where the transmission rate is modeled as a diffusion process allowing to reveal both the effect of control strategies and the changes in individuals behavior. We develop this flexible Bayesian tool in Stan and study 3 pairs of European countries, estimating the time-varying reproduction number ( R t $$ {R}_t $$ ) as well as the true cumulative number of infected individuals. As we estimate the true number of infections we offer a more accurate estimate of R t $$ {R}_t $$ . We also provide an estimate of the daily reporting ratio and discuss the effects of changes in mobility and testing on the inferred quantities.

A compartmental model for smoking dynamics in Italy: a pipeline for inference, validation, and forecasting under hypothetical scenarios.

We propose a compartmental model for investigating smoking dynamics in an Italian region (Tuscany). Calibrating the model on local data from 1993 to 2019, we estimate the probabilities of starting and quitting smoking and the probability of smoking relapse. Then, we forecast the evolution of smoking prevalence until 2043 and assess the impact on mortality in terms of attributable deaths. We introduce elements of novelty with respect to previous studies in this field, including a formal definition of the equations governing the model dynamics and a flexible modelling of smoking probabilities based on cubic regression splines. We estimate model parameters by defining a two-step procedure and quantify the sampling variability via a parametric bootstrap. We propose the implementation of cross-validation on a rolling basis and variance-based Global Sensitivity Analysis to check the robustness of the results and support our findings. Our results suggest a decrease in smoking prevalence among males and stability among females, over the next two decades. We estimate that, in 2023, 18% of deaths among males and 8% among females are due to smoking. We test the use of the model in assessing the impact on smoking prevalence and mortality of different tobacco control policies, including the tobacco-free generation ban recently introduced in New Zealand.

A generalized risk assessment index for forecasting insect population under the effect of temperature.

Life history traits have been studied under various environmental factors, but the ability to combine them into a simple function to assess pest response to climate is still lacking complete understanding. This study proposed a risk index derived by combining development, mortality, and fertility rates from a stage-structured dynamic mathematical model. The first part presents the theoretical framework behind the risk index. The second part of the study is concerned with the application of the index in two case studies of major economic pest: the brown planthopper (Nilaparvata lugens) and the spotted wing drosophila (Drosophila suzukii), pests of rice crops and soft fruits, respectively. The mathematical calculations provided a single function composed of the main thermal biodemographic rates. This function has a threshold value that determines the possibility of population increase as a function of temperature. The tests carried out on the two pest species showed the capability of the index to describe the range of favourable conditions. With this approach, we were able to identify areas where pests are tolerant to climatic conditions and to project them on a geospatial risk map. The theoretical background developed here provided a tool for understanding the biogeography of Nilaparvata lugens and Drosophila suzukii. It is flexible enough to deal with mathematically simple (N. lugens) and complex (D. Suzukii) case studies of crop insect pests. It produces biologically sound indices that behave like thermal performance curves. These theoretical results also provide a reasonable basis for addressing the challenge of pest management in the context of seasonal weather variations and climate change. This may help to improve monitoring and design management strategies to limit the spread of pests in invaded areas, as some non-invaded areas may be suitable for the species to develop.

Fitting a stochastic model of intensive care occupancy to noisy hospitalization time series during the COVID-19 pandemic.

Intensive care occupancy is an important indicator of health care stress that has been used to guide policy decisions during the COVID-19 pandemic. Toward reliable decision-making as a pandemic progresses, estimating the rates at which patients are admitted to and discharged from hospitals and intensive care units (ICUs) is crucial. Since individual-level hospital data are rarely available to modelers in each geographic locality of interest, it is important to develop tools for inferring these rates from publicly available daily numbers of hospital and ICU beds occupied. We develop such an estimation approach based on an immigration-death process that models fluctuations of ICU occupancy. Our flexible framework allows for immigration and death rates to depend on covariates, such as hospital bed occupancy and daily SARS-CoV-2 test positivity rate, which may drive changes in hospital ICU operations. We demonstrate via simulation studies that the proposed method performs well on noisy time series data and apply our statistical framework to hospitalization data from the University of California, Irvine (UCI) Health and Orange County, California. By introducing a likelihood-based framework where immigration and death rates can vary with covariates, we find, through rigorous model selection, that hospitalization and positivity rates are crucial covariates for modeling ICU stay dynamics and validate our per-patient ICU stay estimates using anonymized patient-level UCI hospital data.

An age-of-infection model with both symptomatic and asymptomatic infections.

We formulate a general age-of-infection epidemic model with two pathways: the symptomatic infections and the asymptomatic infections. We then calculate the basic reproduction number [Formula: see text] and establish the final size relation. It is shown that the ratio of accumulated counts of symptomatic patients and asymptomatic patients is determined by the symptomatic ratio f which is defined as the probability of eventually becoming symptomatic after being infected. We also formulate and study a general age-of-infection model with disease deaths and with two infection pathways. The final size relation is investigated, and the upper and lower bounds for final epidemic size are given. Several numerical simulations are performed to verify the analytical results.

The microcircuits of striatum in silico.

The basal ganglia play an important role in decision making and selection of action primarily based on input from cortex, thalamus, and the dopamine system. Their main input structure, striatum, is central to this process. It consists of two types of projection neurons, together representing 95% of the neurons, and 5% of interneurons, among which are the cholinergic, fast-spiking, and low threshold-spiking subtypes. The membrane properties, soma-dendritic shape, and intrastriatal and extrastriatal synaptic interactions of these neurons are quite well described in the mouse, and therefore they can be simulated in sufficient detail to capture their intrinsic properties, as well as the connectivity. We focus on simulation at the striatal cellular/microcircuit level, in which the molecular/subcellular and systems levels meet. We present a nearly full-scale model of the mouse striatum using available data on synaptic connectivity, cellular morphology, and electrophysiological properties to create a microcircuit mimicking the real network. A striatal volume is populated with reconstructed neuronal morphologies with appropriate cell densities, and then we connect neurons together based on appositions between neurites as possible synapses and constrain them further with available connectivity data. Moreover, we simulate a subset of the striatum involving 10,000 neurons, with input from cortex, thalamus, and the dopamine system, as a proof of principle. Simulation at this biological scale should serve as an invaluable tool to understand the mode of operation of this complex structure. This platform will be updated with new data and expanded to simulate the entire striatum.

The challenges of modeling and forecasting the spread of COVID-19.

The coronavirus disease 2019 (COVID-19) pandemic has placed epidemic modeling at the forefront of worldwide public policy making. Nonetheless, modeling and forecasting the spread of COVID-19 remains a challenge. Here, we detail three regional-scale models for forecasting and assessing the course of the pandemic. This work demonstrates the utility of parsimonious models for early-time data and provides an accessible framework for generating policy-relevant insights into its course. We show how these models can be connected to each other and to time series data for a particular region. Capable of measuring and forecasting the impacts of social distancing, these models highlight the dangers of relaxing nonpharmaceutical public health interventions in the absence of a vaccine or antiviral therapies.

Effect of sojourn time distributions on the early dynamics of COVID-19 outbreak.

Compartmental models are commonly used in practice to investigate the dynamical response of infectious diseases such as the COVID-19 outbreak. Such models generally assume exponentially distributed latency and infectiousness periods. However, the exponential distribution assumption fails when the sojourn times are expected to distribute around their means. This study aims to derive a novel S (Susceptible)-E (Exposed)-P (Presymptomatic)-A (Asymptomatic)-D (Symptomatic)-C (Reported) model with arbitrarily distributed latency, presymptomatic infectiousness, asymptomatic infectiousness, and symptomatic infectiousness periods. The SEPADC model is represented by nonlinear Volterra integral equations that generalize ordinary differential equation-based models. Our primary aim is the derivation of a general relation between intrinsic growth rate r and basic reproduction number R0 with the help of the well-known Lotka-Euler equation. The resulting r-R0 equation includes separate roles of various stages of the infection and their sojourn time distributions. We show that R0 estimates are considerably affected by the choice of the sojourn time distributions for relatively higher values of r. The well-known exponential distribution assumption has led to the underestimation of R0 values for most of the countries. Exponential and delta-distributed sojourn times have been shown to yield lower and upper bounds of the R0 values depending on the r values. In quantitative experiments, R0 values of 152 countries around the world were estimated through our novel formulae utilizing the parameter values and sojourn time distributions of the COVID-19 pandemic. The global convergence, R0=4.58, has been estimated through our novel formulation. Additionally, we have shown that increasing the shape parameter of the Erlang distributed sojourn times increases the skewness of the epidemic curves in entire dynamics.

Lilly Absorption Modeling Platform: A Tool for Early Absorption Assessment.

Oral drug absorption modeling has developed at a rapid pace in the 40 years or so since the first ideas for mathematical approaches to oral absorption were introduced. The success of compartmental approaches accelerated the uptake of absorption modeling, and over the last 20 years, work on absorption modeling has shifted almost exclusively to the compartmental framework. This report describes a new noncompartmental absorption modeling framework, the Lilly Absorption Modeling Platform (LAMP). LAMP connects a well-mixed stomach to a continuous tube model of the small intestine with plug flow. Within the continuous tube framework, the model includes intestinal mixing and a novel highly tunable precipitation model that can describe a combination of rapid nucleation and slow growth. The framework is designed to balance speed, consistency, and ease of use with a minimum of model complexity to capture the essential features of gastrointestinal (GI) physiology and critical elements of the oral absorption process. The model was validated based on predictions of the fraction absorbed and the maximum absorbable dose for a set of Eli Lilly and Company clinical compounds.

Extending the susceptible-exposed-infected-removed (SEIR) model to handle the false negative rate and symptom-based administration of COVID-19 diagnostic tests: SEIR-fansy.

False negative rates of severe acute respiratory coronavirus 2 diagnostic tests, together with selection bias due to prioritized testing can result in inaccurate modeling of COVID-19 transmission dynamics based on reported "case" counts. We propose an extension of the widely used Susceptible-Exposed-Infected-Removed (SEIR) model that accounts for misclassification error and selection bias, and derive an analytic expression for the basic reproduction number R0 as a function of false negative rates of the diagnostic tests and selection probabilities for getting tested. Analyzing data from the first two waves of the pandemic in India, we show that correcting for misclassification and selection leads to more accurate prediction in a test sample. We provide estimates of undetected infections and deaths between April 1, 2020 and August 31, 2021. At the end of the first wave in India, the estimated under-reporting factor for cases was at 11.1 (95% CI: 10.7,11.5) and for deaths at 3.58 (95% CI: 3.5,3.66) as of February 1, 2021, while they change to 19.2 (95% CI: 17.9, 19.9) and 4.55 (95% CI: 4.32, 4.68) as of July 1, 2021. Equivalently, 9.0% (95% CI: 8.7%, 9.3%) and 5.2% (95% CI: 5.0%, 5.6%) of total estimated infections were reported on these two dates, while 27.9% (95% CI: 27.3%, 28.6%) and 22% (95% CI: 21.4%, 23.1%) of estimated total deaths were reported. Extensive simulation studies demonstrate the effect of misclassification and selection on estimation of R0 and prediction of future infections. A R-package SEIRfansy is developed for broader dissemination.

The predicted impact of resource provisioning on the epidemiological responses of different parasites.

Anthropogenic activities and natural events such as periodic tree masting can alter resource provisioning in the environment, directly affecting animals, and potentially impacting the spread of infectious diseases in wildlife. The impact of these additional resources on infectious diseases can manifest through different pathways, affecting host susceptibility, contact rate and host demography. To date however, empirical research has tended to examine these different pathways in isolation, for example by quantifying the effects of provisioning on host behaviour in the wild or changes in immune responses in controlled laboratory studies. Furthermore, while theory has investigated the interactions between these pathways, this work has focussed on a narrow subset of pathogen types, typically directly transmitted microparasites. Given the diverse ways that provisioning can affect host susceptibility, contact patterns or host demography, we may expect the epidemiological consequences of provisioning to vary among different parasite types, dependent on key aspects of parasite life history, such as the duration of infection and transmission mode. Focusing on an exemplar empirical system, the wood mouse Apodemus sylvaticus, and its diverse parasite community, we developed a suite of epidemiological models to compare how resource provisioning alters responses for a range of these parasites that vary in their biology (microparasite and macroparasite), transmission mode (direct, environmental and vector transmitted) and duration of infection (acute, latent and chronic) within the same host population. We show there are common epidemiological responses to host resource provisioning across all parasite types examined. In particular, the epidemiological impact of provisioning could be driven in opposite directions, depending on which host pathways (contact rate, susceptibility or host demography) are most altered by the addition of resources to the environment. Broadly, these responses were qualitatively consistent across all parasite types, emphasising the importance of identifying general trade-offs between provisioning-altered parameters. Despite the qualitative consistency in responses to provisioning across parasite types, we predicted notable quantitative differences between parasites, with directly transmitted parasites (those conforming to SIR and SIS frameworks) predicted to show the strongest responses to provisioning among those examined, whereas the vector-borne parasites showed negligible responses to provisioning. As such, these analyses suggest that different parasites may show different scales of response to the same provisioning scenario, even within the same host population. This highlights the importance of knowing key aspects of host-parasite biology, to understand and predict epidemiological responses to provisioning for any specific host-parasite system.

Spreading of fake news, competence and learning: kinetic modelling and numerical approximation.

The rise of social networks as the primary means of communication in almost every country in the world has simultaneously triggered an increase in the amount of fake news circulating online. The urgent need for models that can describe the growing infodemic of fake news has been highlighted by the current pandemic. The resulting slowdown in vaccination campaigns due to misinformation and generally the inability of individuals to discern the reliability of information is posing enormous risks to the governments of many countries. In this research using the tools of kinetic theory, we describe the interaction between fake news spreading and competence of individuals through multi-population models in which fake news spreads analogously to an infectious disease with different impact depending on the level of competence of individuals. The level of competence, in particular, is subject to evolutionary dynamics due to both social interactions between agents and external learning dynamics. The results show how the model is able to correctly describe the dynamics of diffusion of fake news and the important role of competence in their containment. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

Discrete Models in Epidemiology: New Contagion Probability Functions Based on Real Data Behavior.

Mathematical modeling is a tool used for understanding diseases dynamics. The discrete-time model is an especial case in modeling that satisfactorily describes the epidemiological dynamics because of the discrete nature of the real data. However, discrete models reduce their descriptive and fitting potential because of assuming a homogeneous population. Thus, in this paper, we proposed contagion probability functions according to two infection paradigms that consider factors associated with transmission dynamics. For example, we introduced probabilities of establishing an infectious interaction, the number of contacts with infectious and the level of connectivity or social distance within populations. Through the probabilities design, we overcame the homogeneity assumption. Also, we evaluated the proposed probabilities through their introduction into discrete-time models for two diseases and different study zones with real data, COVID-19 for Germany and South Korea, and dengue for Colombia. Also, we described the oscillatory dynamics for the last one using the contagion probabilities alongside parameters with a biological sense. Finally, we highlight the implementation of the proposed probabilities would improve the simulation of the public policy effect of control strategies over an infectious disease outbreak.

Inference in Gaussian state-space models with mixed effects for multiple epidemic dynamics.

The estimation from available data of parameters governing epidemics is a major challenge. In addition to usual issues (data often incomplete and noisy), epidemics of the same nature may be observed in several places or over different periods. The resulting possible inter-epidemic variability is rarely explicitly considered. Here, we propose to tackle multiple epidemics through a unique model incorporating a stochastic representation for each epidemic and to jointly estimate its parameters from noisy and partial observations. By building on a previous work for prevalence data, a Gaussian state-space model is extended to a model with mixed effects on the parameters describing simultaneously several epidemics and their observation process. An appropriate inference method is developed, by coupling the SAEM algorithm with Kalman-type filtering. Moreover, we consider here incidence data, which requires to develop a new version of the filtering algorithm. Its performances are investigated on SIR simulated epidemics for prevalence and incidence data. Our method outperforms an inference method separately processing each dataset. An application to SEIR influenza outbreaks in France over several years using incidence data is also carried out. Parameter estimations highlight a non-negligible variability between influenza seasons, both in transmission and case reporting. The main contribution of our study is to rigorously and explicitly account for the inter-epidemic variability between multiple outbreaks, both from the viewpoint of modeling and inference with a parsimonious statistical model.

Simulation applications to support teaching and research in epidemiological dynamics.

BACKGROUND: An understanding of epidemiological dynamics, once confined to mathematical epidemiologists and applied mathematicians, can be disseminated to a non-mathematical community of health care professionals and applied biologists through simple-to-use simulation applications. We used Numerus Model Builder RAMP Ⓡ (Runtime Alterable Model Platform) technology, to construct deterministic and stochastic versions of compartmental SIR (Susceptible, Infectious, Recovered with immunity) models as simple-to-use, freely available, epidemic simulation application programs. RESULTS: We take the reader through simulations used to demonstrate the following concepts: 1) disease prevalence curves of unmitigated outbreaks have a single peak and result in epidemics that 'burn' through the population to become extinguished when the proportion of the susceptible population drops below a critical level; 2) if immunity in recovered individuals wanes sufficiently fast then the disease persists indefinitely as an endemic state, with possible dampening oscillations following the initial outbreak phase; 3) the steepness and initial peak of the prevalence curve are influenced by the basic reproductive value R0, which must exceed 1 for an epidemic to occur; 4) the probability that a single infectious individual in a closed population (i.e. no migration) gives rise to an epidemic increases with the value of R0>1; 5) behavior that adaptively decreases the contact rate among individuals with increasing prevalence has major effects on the prevalence curve including dramatic flattening of the prevalence curve along with the generation of multiple prevalence peaks; 6) the impacts of treatment are complicated to model because they effect multiple processes including transmission, recovery and mortality; 7) the impacts of vaccination policies, constrained by a fixed number of vaccination regimens and by the rate and timing of delivery, are crucially important to maximizing the ability of vaccination programs to reduce mortality. CONCLUSION: Our presentation makes transparent the key assumptions underlying SIR epidemic models. Our RAMP simulators are meant to augment rather than replace classroom material when teaching epidemiological dynamics. They are sufficiently versatile to be used by students to address a range of research questions for term papers and even dissertations.

Closed-form expressions and nonparametric estimation of COVID-19 infection rate.

Quantitative assessment of the infection rate of a virus is key to monitor the evolution of an epidemic. However, such variable is not accessible to direct measurement and its estimation requires the solution of a difficult inverse problem. In particular, being the result not only of biological but also of social factors, the transmission dynamics can vary significantly in time. This makes questionable the use of parametric models which could be unable to capture their full complexity. In this paper we exploit compartmental models which include important COVID-19 peculiarities (like the presence of asymptomatic individuals) and allow the infection rate to assume any continuous-time profile. We show that these models are universal, i.e. capable to reproduce exactly any epidemic evolution, and extract from them closed-form expressions of the infection rate time-course. Building upon such expressions, we then design a regularized estimator able to reconstruct COVID-19 transmission dynamics in continuous-time. Using real data collected in Italy, our technique proves to be an useful tool to monitor COVID-19 transmission dynamics and to predict and assess the effect of lockdown restrictions.

Modeling nonlocal behavior in epidemics via a reaction-diffusion system incorporating population movement along a network.

The outbreak of COVID-19, beginning in 2019 and continuing through the time of writing, has led to renewed interest in the mathematical modeling of infectious disease. Recent works have focused on partial differential equation (PDE) models, particularly reaction-diffusion models, able to describe the progression of an epidemic in both space and time. These studies have shown generally promising results in describing and predicting COVID-19 progression. However, people often travel long distances in short periods of time, leading to nonlocal transmission of the disease. Such contagion dynamics are not well-represented by diffusion alone. In contrast, ordinary differential equation (ODE) models may easily account for this behavior by considering disparate regions as nodes in a network, with the edges defining nonlocal transmission. In this work, we attempt to combine these modeling paradigms via the introduction of a network structure within a reaction-diffusion PDE system. This is achieved through the definition of a population-transfer operator, which couples disjoint and potentially distant geographic regions, facilitating nonlocal population movement between them. We provide analytical results demonstrating that this operator does not disrupt the physical consistency or mathematical well-posedness of the system, and verify these results through numerical experiments. We then use this technique to simulate the COVID-19 epidemic in the Brazilian region of Rio de Janeiro, showcasing its ability to capture important nonlocal behaviors, while maintaining the advantages of a reaction-diffusion model for describing local dynamics.

A network SIRX model for the spreading of COVID-19.

Infectious diseases, such as the current COVID-19, have a huge economic and societal impact. The ability to model its transmission characteristics is critical to minimize its impact. In fact, predicting how fast an infection is spreading could be a major factor in deciding on the severity, extent and strictness of the applied mitigation measures, such as the recent lockdowns. Even though modelling epidemics is a well studied subject, usually models do not include quarantine or other social measures, such as those imposed in the recent pandemic. The current work builds upon a recent paper by Maier and Brockmann (2020), where a compartmental SIRX model was implemented. That model included social or individual behavioural changes during quarantine, by introducing state X , in which symptomatic quarantined individuals are not transmitting the infection anymore, and described well the transmission in the initial stages of the infection. The results of the model were applied to real data from several provinces in China, quite successfully. In our approach we use a Monte-Carlo simulation model on networks. Individuals are network nodes and the links are their contacts. We use a spreading mechanism from the initially infected nodes to their nearest neighbours, as has been done previously. Initially, we find the values of the rate constants (parameters) the same way as in Maier and Brockmann (2020) for the confirmed cases of a country, on a daily basis, as given by the Johns Hopkins University. We then use different types of networks (random Erdos-Rényi, Small World, and Barabási-Albert Scale-Free) with various characteristics in an effort to find the best fit with the real data for the same geographical regions as reported in Maier and Brockmann (2020). Our simulations show that the best fit comes with the Erdos-Rényi random networks. We then apply this method to several other countries, both for large-size countries, and small size ones. In all cases investigated we find the same result, i.e. best agreement for the evolution of the pandemic with time is for the Erdos-Rényi networks. Furthermore, our results indicate that the best fit occurs for a random network with an average degree of the order of 〈 k 〉 ≈ 10-25, for all countries tested. Scale Free and Small World networks fail to fit the real data convincingly.