Generalizations of the 'Linear Chain Trick': incorporating more flexible dwell time distributions into mean field ODE models

GI-NemaTracker - A farm system-level mathematical model to predict the consequences of gastrointestinal parasite control strategies in sheep

Gastro-intestinal nematode infections are considered one of the major endemic diseases of sheep on the grounds of animal health and economic burden, both in the British Isles and globally. Parasites are increasingly developing resistance to commonly used anthelmintic treatments meaning that alternative control strategies that reduce or replace the use of anthelmintics are required. We present GI-NemaTracker, a systems-level mathematical model of the full host-parasite-environment system governing gastro-intestinal nematode transmission on a sheep farm. The model is based on a series of time-varying delay-differential equations that explicitly capture environmentally-driven time delays in nematode development. By taking a farm systems-level approach we represent both in-host and environmentally-driven free-living parasite dynamics and their interaction with a population of individually modelled lambs with diverse trait parameters assigned at birth. Thus we capture seasonally varying rates of parasite transmission and consequently variable weight gain of individual lambs throughout the season. The model is parameterised for Teladorsagia circumcincta, although the framework described could be applied to a range of nematode parasite species. We validate the model against experimental and field data and apply it to study the efficacy of four different anthelmintic treatment regimes (neo-suppresive treatment, strategic prophylactic treatment, treatment based on faecal egg counts and a regime which leaves 10% of the animals untreated) on lamb weight gain and pasture contamination. The model predicts that similar body weights at a flock level can be achieved while reducing the number of treatments administered, thus supporting a health plan that reduces anthelmintic treatments. As the model is capable of combining parasitic and free-living stages of the parasite with host performance, it is well suited to predict complex system responses under non-stationary conditions. The implications of the model and its potential as a tool in the development of sustainable control strategies in sheep are discussed.

Modelling the effects of diurnal temperature variation on malaria infection dynamics in mosquitoes

Mosquito infection experiments that characterise how sporogony changes with temperature are increasingly being used to parameterise malaria transmission models. In these experiments, mosquitoes are exposed to a range of temperatures, with each group experiencing a single temperature. Diurnal temperature variation can, however, affect the sporogonic cycle of Plasmodium parasites. Mosquito dissection data is not available for all temperature profiles, so we investigate whether mathematical models of mosquito infection parameterised with constant temperature thermal performance curves can predict the effects of diurnal temperature variation. We use this model to predict two key parameters governing disease transmission: the human-to-mosquito transmission probability and extrinsic incubation period - and, embed this model into a malaria transmission model to simulate sporozoite prevalence with and without the effects of diurnal and seasonal temperature variation for a single site in Burkina Faso. Simulations incorporating diurnal temperature variation better predict changes in sporogony in laboratory mosquitoes, indicating that constant temperature experiments can be used to predict the effects of fluctuating temperatures. Including the effects of diurnal temperature variation, however, did not substantially improve the predictive ability of the transmission model to predict changes in sporozoite prevalence in wild mosquitoes, indicating further research is needed in more settings.

Differentiating Contact with Symptomatic and Asymptomatic Infectious Individuals in a SEIR Epidemic Model

This manuscript introduces a new Erlang-distributed SEIR model. The model incorporates asymptomatic spread through a subdivided exposed class, distinguishing between asymptomatic ( E a ) and symptomatic ( E s ) cases. The model identifies two key parameters: relative infectiousness, β SA , and the percentage of people who become asymptomatic after being infected by a symptomatic individual, κ . Lower values of these parameters reduce the peak magnitude and duration of the infectious period, highlighting the importance of isolation measures. Additionally, the model underscores the need for strategies addressing both symptomatic and asymptomatic transmissions.

Multi-strain phage induced clearance of bacterial infections

Bacteriophage (or 'phage' - viruses that infect and kill bacteria) are increasingly considered as a therapeutic alternative to treat antibiotic-resistant bacterial infections. However, bacteria can evolve resistance to phage, presenting a significant challenge to the near- and long-term success of phage therapeutics. Application of mixtures of multiple phages (i.e., 'cocktails') has been proposed to limit the emergence of phage-resistant bacterial mutants that could lead to therapeutic failure. Here, we combine theory and computational models of in vivo phage therapy to study the efficacy of a phage cocktail, composed of two complementary phages motivated by the example of Pseudomonas aeruginosa facing two phages that exploit different surface receptors, LUZ19v and PAK_P1. As confirmed in a Luria-Delbrück fluctuation test, this motivating example serves as a model for instances where bacteria are extremely unlikely to develop simultaneous resistance mutations against both phages. We then quantify therapeutic outcomes given single- or double-phage treatment models, as a function of phage traits and host immune strength. Building upon prior work showing monophage therapy efficacy in immunocompetent hosts, here we show that phage cocktails comprised of phage targeting independent bacterial receptors can improve treatment outcome in immunocompromised hosts and reduce the chance that pathogens simultaneously evolve resistance against phage combinations. The finding of phage cocktail efficacy is qualitatively robust to differences in virus-bacteria interactions and host immune dynamics. Altogether, the combined use of theory and computational analysis highlights the influence of viral life history traits and receptor complementarity when designing and deploying phage cocktails in immunocompetent and immunocompromised hosts.

The Effect of Vaccination on the Competitive Advantage of Two Strains of an Infectious Disease

We investigate the impact of differential vaccine effectiveness, waning immunity, and natural cross-immunity on the capacity for vaccine-induced strain replacement in two-strain models of infectious disease spread. We focus specifically on the case where the first strain is more transmissible but the second strain is more immune-resistant. We consider two cases on vaccine-induced immunity: (1) a monovalent model where the second strain has immune escape with respect to vaccination; and (2) a bivalent model where the vaccine remains equally effective against both strains. Our analysis reaffirms the capacity for vaccine-induced strain replacement under a variety of circumstances; surprisingly, however, we find that which strain is preferred depends sensitively on the degree of differential vaccine effectiveness. In general, the monovalent model favors the more immune-resistant strain at high vaccination levels while the bivalent model favors the more transmissible strain at high vaccination levels. To further investigate this phenomenon, we parametrize the bifurcation space between the monovalent and bivalent model.

Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them

Our paper reviews some key concepts in chemical reaction network theory and mathematical epidemiology, and examines their intersection, with three goals. The first is to make the case that mathematical epidemiology (ME), and also related sciences like population dynamics, virology, ecology, etc., could benefit by adopting the universal language of essentially non-negative kinetic systems as developed by chemical reaction network (CRN) researchers. In this direction, our investigation of the relations between CRN and ME lead us to propose for the first time a definition of ME models, stated in Open Problem 1. Our second goal is to inform researchers outside ME of the convenient next generation matrix (NGM) approach for studying the stability of boundary points, which do not seem sufficiently well known. Last but not least, we want to help students and researchers who know nothing about either ME or CRN to learn them quickly, by offering them a Mathematica package "bootcamp", including illustrating notebooks (and certain sections below will contain associated suggested notebooks; however, readers with experience may safely skip the bootcamp). We hope that the files indicated in the titles of various sections will be helpful, though of course improvement is always possible, and we ask the help of the readers for that.

Overcoming bias in estimating epidemiological parameters with realistic history-dependent disease spread dynamics

Epidemiological parameters such as the reproduction number, latent period, and infectious period provide crucial information about the spread of infectious diseases and directly inform intervention strategies. These parameters have generally been estimated by mathematical models that involve an unrealistic assumption of history-independent dynamics for simplicity. This assumes that the chance of becoming infectious during the latent period or recovering during the infectious period remains constant, whereas in reality, these chances vary over time. Here, we find that conventional approaches with this assumption cause serious bias in epidemiological parameter estimation. To address this bias, we developed a Bayesian inference method by adopting more realistic history-dependent disease dynamics. Our method more accurately and precisely estimates the reproduction number than the conventional approaches solely from confirmed cases data, which are easy to obtain through testing. It also revealed how the infectious period distribution changed throughout the COVID-19 pandemic during 2020 in South Korea. We also provide a user-friendly package, IONISE, that automates this method.

Multi-strain phage induced clearance of bacterial infections

Bacteriophage (or 'phage' - viruses that infect and kill bacteria) are increasingly considered as a therapeutic alternative to treat antibiotic-resistant bacterial infections. However, bacteria can evolve resistance to phage, presenting a significant challenge to the near- and long-term success of phage therapeutics. Application of mixtures of multiple phage (i.e., 'cocktails') have been proposed to limit the emergence of phage-resistant bacterial mutants that could lead to therapeutic failure. Here, we combine theory and computational models of in vivo phage therapy to study the efficacy of a phage cocktail, composed of two complementary phages motivated by the example of Pseudomonas aeruginosa facing two phages that exploit different surface receptors, LUZ19v and PAK_P1. As confirmed in a Luria-Delbrück fluctuation test, this motivating example serves as a model for instances where bacteria are extremely unlikely to develop simultaneous resistance mutations against both phages. We then quantify therapeutic outcomes given single- or double-phage treatment models, as a function of phage traits and host immune strength. Building upon prior work showing monophage therapy efficacy in immunocompetent hosts, here we show that phage cocktails comprised of phage targeting independent bacterial receptors can improve treatment outcome in immunocompromised hosts and reduce the chance that pathogens simultaneously evolve resistance against phage combinations. The finding of phage cocktail efficacy is qualitatively robust to differences in virus-bacteria interactions and host immune dynamics. Altogether, the combined use of theory and computational analysis highlights the influence of viral life history traits and receptor complementarity when designing and deploying phage cocktails in immunocompetent and immunocompromised hosts.

Transoceanic pathogen transfer in the age of sail and steam

In the centuries following Christopher Columbus's 1492 voyage to the Americas, transoceanic travel opened unprecedented pathways in global pathogen circulation. Yet no biological transfer is a single, discrete event. We use mathematical modeling to quantify historical risk of shipborne pathogen introduction, exploring the respective contributions of journey time, ship size, population susceptibility, transmission intensity, density dependence, and pathogen biology. We contextualize our results using port arrivals data from San Francisco, 1850 to 1852, and from a selection of historically significant voyages, 1492 to 1918. We offer numerical estimates of introduction risk across historically realistic ranges of journey time and ship population size, and show that both steam travel and shipping regimes that involved frequent, large-scale movement of people substantially increased risk of transoceanic pathogen circulation.

Analytic delay distributions for a family of gene transcription models

Models intended to describe the time evolution of a gene network must somehow include transcription, the DNA-templated synthesis of RNA, and translation, the RNA-templated synthesis of proteins. In eukaryotes, the DNA template for transcription can be very long, often consisting of tens of thousands of nucleotides, and lengthy pauses may punctuate this process. Accordingly, transcription can last for many minutes, in some cases hours. There is a long history of introducing delays in gene expression models to take the transcription and translation times into account. Here we study a family of detailed transcription models that includes initiation, elongation, and termination reactions. We establish a framework for computing the distribution of transcription times, and work out these distributions for some typical cases. For elongation, a fixed delay is a good model provided elongation is fast compared to initiation and termination, and there are no sites where long pauses occur. The initiation and termination phases of the model then generate a nontrivial delay distribution, and elongation shifts this distribution by an amount corresponding to the elongation delay. When initiation and termination are relatively fast, the distribution of elongation times can be approximated by a Gaussian. A convolution of this Gaussian with the initiation and termination time distributions gives another analytic approximation to the transcription time distribution. If there are long pauses during elongation, because of the modularity of the family of models considered, the elongation phase can be partitioned into reactions generating a simple delay (elongation through regions where there are no long pauses), and reactions whose distribution of waiting times must be considered explicitly (initiation, termination, and motion through regions where long pauses are likely). In these cases, the distribution of transcription times again involves a nontrivial part and a shift due to fast elongation processes.

flepiMoP: The evolution of a flexible infectious disease modeling pipeline during the COVID-19 pandemic

The COVID-19 pandemic led to an unprecedented demand for projections of disease burden and healthcare utilization under scenarios ranging from unmitigated spread to strict social distancing policies. In response, members of the Johns Hopkins Infectious Disease Dynamics Group developed flepiMoP (formerly called the COVID Scenario Modeling Pipeline), a comprehensive open-source software pipeline designed for creating and simulating compartmental models of infectious disease transmission and inferring parameters through these models. The framework has been used extensively to produce short-term forecasts and longer-term scenario projections of COVID-19 at the state and county level in the US, for COVID-19 in other countries at various geographic scales, and more recently for seasonal influenza. In this paper, we highlight how the flepiMoP has evolved throughout the COVID-19 pandemic to address changing epidemiological dynamics, new interventions, and shifts in policy-relevant model outputs. As the framework has reached a mature state, we provide a detailed overview of flepiMoP's key features and remaining limitations, thereby distributing flepiMoP and its documentation as a flexible and powerful tool for researchers and public health professionals to rapidly build and deploy large-scale complex infectious disease models for any pathogen and demographic setup.

Stochastic modeling of Dalbulus maidis, vector of maize diseases

We developed a simple linear stochastic model for Dalbulus maidis dependent exclusively on temperature, whose parameters were determined from published field and laboratory studies performed at different temperatures. This model takes into account the principal stages and events of the life cycle of this pest, which is vector of maize diseases. We implemented the effect of distributed delays or Linear Chain Trick (LCT) considering a fixed number of sub-stages for egg and nymph stages of Dalbulus maidis in order to accurately represent what is observed in nature. A sensitivity analysis allows us to observe that the speed of the dynamics is sensitive to changes in the development rates, but not to the longevity of each stage or the fecundity, which almost exclusively affect insect abundance. We used our model to study its predictive and explanatory capacity considering a published experiment as a case study. Although the simulation results show a behavior qualitatively equivalent to that observed in the experimental results it is not possible to explain accurately the magnitude, nor the times in which the maximum abundances of second-generation nymphs and adults are reached. Therefore, we evaluated three possible scenarios for the insect that allow us to glimpse some of the advantages of having a computational model in order to find out what processes, taken into account in the model, may explain the differences observed between published experimental results and model results. The three proposed scenarios, based on variations in the parameterized rates of the model, can satisfactorily explain the experimental observations. We observed that in order to better simulate the experimental results it is not necessary to modify fecundity or mortality rates. However, it is necessary to accelerate the average development rates of our model by 20 to 40 %, compatible with extreme values of the rates close to the upper edges of the confidence bands of our parameterization rate curves, according to insects with faster development rates already reported in literature.

A data-driven semi-parametric model of SARS-CoV-2 transmission in the United States

To support decision-making and policy for managing epidemics of emerging pathogens, we present a model for inference and scenario analysis of SARS-CoV-2 transmission in the USA. The stochastic SEIR-type model includes compartments for latent, asymptomatic, detected and undetected symptomatic individuals, and hospitalized cases, and features realistic interval distributions for presymptomatic and symptomatic periods, time varying rates of case detection, diagnosis, and mortality. The model accounts for the effects on transmission of human mobility using anonymized mobility data collected from cellular devices, and of difficult to quantify environmental and behavioral factors using a latent process. The baseline transmission rate is the product of a human mobility metric obtained from data and this fitted latent process. We fit the model to incident case and death reports for each state in the USA and Washington D.C., using likelihood Maximization by Iterated particle Filtering (MIF). Observations (daily case and death reports) are modeled as arising from a negative binomial reporting process. We estimate time-varying transmission rate, parameters of a sigmoidal time-varying fraction of hospitalized cases that result in death, extra-demographic process noise, two dispersion parameters of the observation process, and the initial sizes of the latent, asymptomatic, and symptomatic classes. In a retrospective analysis covering March-December 2020, we show how mobility and transmission strength became decoupled across two distinct phases of the pandemic. The decoupling demonstrates the need for flexible, semi-parametric approaches for modeling infectious disease dynamics in real-time.

A Time for Every Purpose: Using Time-Dependent Sensitivity Analysis to Help Understand and Manage Dynamic Ecological Systems

AbstractSensitivity analysis is often used to help understand and manage ecological systems by assessing how a constant change in vital rates or other model parameters might affect the management outcome. This allows the manager to identify the most favorable course of action. However, realistic changes are often localized in time-for example, a short period of culling leads to a temporary increase in the mortality rate over the period. Hence, knowing when to act may be just as important as knowing what to act on. In this article, we introduce the method of time-dependent sensitivity analysis (TDSA) that simultaneously addresses both questions. We illustrate TDSA using three case studies: transient dynamics in static disease transmission networks, disease dynamics in a reservoir species with seasonal life history events, and endogenously driven population cycles in herbivorous invertebrate forest pests. We demonstrate how TDSA often provides useful biological insights, which are understandable on hindsight but would not have been easily discovered without the help of TDSA. However, as a caution, we also show how TDSA can produce results that mainly reflect uncertain modeling choices and are therefore potentially misleading. We provide guidelines to help users maximize the utility of TDSA while avoiding pitfalls.

Distribution modeling quantifies collective TH cell decision circuits in chronic inflammation

Immune responses are tightly regulated by a diverse set of interacting immune cell populations. Alongside decision-making processes such as differentiation into specific effector cell types, immune cells initiate proliferation at the beginning of an inflammation, forming two layers of complexity. Here, we developed a general mathematical framework for the data-driven analysis of collective immune cell dynamics. We identified qualitative and quantitative properties of generic network motifs, and we specified differentiation dynamics by analysis of kinetic transcriptome data. Furthermore, we derived a specific, data-driven mathematical model for T helper 1 versus T follicular helper cell-fate decision dynamics in acute and chronic lymphocytic choriomeningitis virus infections in mice. The model recapitulates important dynamical properties without model fitting and solely by using measured response-time distributions. Model simulations predict different windows of opportunity for perturbation in acute and chronic infection scenarios, with potential implications for optimization of targeted immunotherapy.

Anchoring the mean generation time in the SEIR to mitigate biases in ℜ0 estimates due to uncertainty in the distribution of the epidemiological delays

The basic reproduction number, ℜ 0 , is of paramount importance in the study of infectious disease dynamics. Primarily, ℜ 0 serves as an indicator of the transmission potential of an emerging infectious disease and the effort required to control the invading pathogen. However, its estimates from compartmental models are strongly conditioned by assumptions in the model structure, such as the distributions of the latent and infectious periods (epidemiological delays). To further complicate matters, models with dissimilar delay structures produce equivalent incidence dynamics. Following a simulation study, we reveal that the nature of such equivalency stems from a linear relationship between ℜ 0 and the mean generation time, along with adjustments to other parameters in the model. Leveraging this knowledge, we propose and successfully test an alternative parametrization of the SEIR model that produces accurate ℜ 0 estimates regardless of the distribution of the epidemiological delays, at the expense of biases in other quantities deemed of lesser importance. We further explore this approach's robustness by testing various transmissibility levels, generation times and data fidelity (overdispersion). Finally, we apply the proposed approach to data from the 1918 influenza pandemic. We anticipate that this work will mitigate biases in estimating ℜ 0 .

Analysis and modeling of cancer drug responses using cell cycle phase-specific rate effects

Identifying effective therapeutic treatment strategies is a major challenge to improving outcomes for patients with breast cancer. To gain a comprehensive understanding of how clinically relevant anti-cancer agents modulate cell cycle progression, here we use genetically engineered breast cancer cell lines to track drug-induced changes in cell number and cell cycle phase to reveal drug-specific cell cycle effects that vary across time. We use a linear chain trick (LCT) computational model, which faithfully captures drug-induced dynamic responses, correctly infers drug effects, and reproduces influences on specific cell cycle phases. We use the LCT model to predict the effects of unseen drug combinations and confirm these in independent validation experiments. Our integrated experimental and modeling approach opens avenues to assess drug responses, predict effective drug combinations, and identify optimal drug sequencing strategies.

The relationship between controllability, optimal testing resource allocation, and incubation-latent period mismatch as revealed by COVID-19

The severe shortfall in testing supplies during the initial COVID-19 outbreak and ensuing struggle to manage the pandemic have affirmed the critical importance of optimal supply-constrained resource allocation strategies for controlling novel disease epidemics. To address the challenge of constrained resource optimization for managing diseases with complications like pre- and asymptomatic transmission, we develop an integro partial differential equation compartmental disease model which incorporates realistic latent, incubation, and infectious period distributions along with limited testing supplies for identifying and quarantining infected individuals. Our model overcomes the limitations of typical ordinary differential equation compartmental models by decoupling symptom status from model compartments to allow a more realistic representation of symptom onset and presymptomatic transmission. To analyze the influence of these realistic features on disease controllability, we find optimal strategies for reducing total infection sizes that allocate limited testing resources between 'clinical' testing, which targets symptomatic individuals, and 'non-clinical' testing, which targets non-symptomatic individuals. We apply our model not only to the original, delta, and omicron COVID-19 variants, but also to generically parameterized disease systems with varying mismatches between latent and incubation period distributions, which permit varying degrees of presymptomatic transmission or symptom onset before infectiousness. We find that factors that decrease controllability generally call for reduced levels of non-clinical testing in optimal strategies, while the relationship between incubation-latent mismatch, controllability, and optimal strategies is complicated. In particular, though greater degrees of presymptomatic transmission reduce disease controllability, they may increase or decrease the role of non-clinical testing in optimal strategies depending on other disease factors like transmissibility and latent period length. Importantly, our model allows a spectrum of diseases to be compared within a consistent framework such that lessons learned from COVID-19 can be transferred to resource constrained scenarios in future emerging epidemics and analyzed for optimality.

Multiple cohort study of hospitalized SARS-CoV-2 in-host infection dynamics: Parameter estimates, identifiability, sensitivity and the eclipse phase profile

Within-host SARS-CoV-2 modelling studies have been published throughout the COVID-19 pandemic. These studies contain highly variable numbers of individuals and capture varying timescales of pathogen dynamics; some studies capture the time of disease onset, the peak viral load and subsequent heterogeneity in clearance dynamics across individuals, while others capture late-time post-peak dynamics. In this study, we curate multiple previously published SARS-CoV-2 viral load data sets, fit these data with a consistent modelling approach, and estimate the variability of in-host parameters including the basic reproduction number, R0, as well as the best-fit eclipse phase profile. We find that fitted dynamics can be highly variable across data sets, and highly variable within data sets, particularly when key components of the dynamic trajectories (e.g. peak viral load) are not represented in the data. Further, we investigated the role of the eclipse phase time distribution in fitting SARS-CoV-2 viral load data. By varying the shape parameter of an Erlang distribution, we demonstrate that models with either no eclipse phase, or with an exponentially-distributed eclipse phase, offer significantly worse fits to these data, whereas models with less dispersion around the mean eclipse time (shape parameter two or more) offered the best fits to the available data across all data sets used in this work. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

A time for every purpose: using time-dependent sensitivity analysis to help understand and manage dynamic ecological systems

Sensitivity analysis is often used to help understand and manage ecological systems, by assessing how a constant change in vital rates or other model parameters might affect the management outcome. This allows the manager to identify the most favorable course of action. However, realistic changes are often localized in time-for example, a short period of culling leads to a temporary increase in the mortality rate over the period. Hence, knowing when to act may be just as important as knowing what to act upon. In this article, we introduce the method of time-dependent sensitivity analysis (TDSA) that simultaneously addresses both questions. We illustrate TDSA using three case studies: transient dynamics in static disease transmission networks, disease dynamics in a reservoir species with seasonal life-history events, and endogenously-driven population cycles in herbivorous invertebrate forest pests. We demonstrate how TDSA often provides useful biological insights, which are understandable on hindsight but would not have been easily discovered without the help of TDSA. However, as a caution, we also show how TDSA can produce results that mainly reflect uncertain modeling choices and are therefore potentially misleading. We provide guidelines to help users maximize the utility of TDSA while avoiding pitfalls.

Uncertainty and error in SARS-CoV-2 epidemiological parameters inferred from population-level epidemic models

During the SARS-CoV-2 pandemic, epidemic models have been central to policy-making. Public health responses have been shaped by model-based projections and inferences, especially related to the impact of various non-pharmaceutical interventions. Accompanying this has been increased scrutiny over model performance, model assumptions, and the way that uncertainty is incorporated and presented. Here we consider a population-level model, focusing on how distributions representing host infectiousness and the infection-to-death times are modelled, and particularly on the impact of inferred epidemic characteristics if these distributions are mis-specified. We introduce an SIR-type model with the infected population structured by 'infected age', i.e. the number of days since first being infected, a formulation that enables distributions to be incorporated that are consistent with clinical data. We show that inference based on simpler models without infected age, which implicitly mis-specify these distributions, leads to substantial errors in inferred quantities relevant to policy-making, such as the reproduction number and the impact of interventions. We consider uncertainty quantification via a Bayesian approach, implementing this for both synthetic and real data focusing on UK data in the period 15 Feb-14 Jul 2020, and emphasising circumstances where it is misleading to neglect uncertainty. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Integration of quantitative methods and mathematical approaches for the modeling of cancer cell proliferation dynamics

Physiological processes rely on the control of cell proliferation, and the dysregulation of these processes underlies various pathological conditions, including cancer. Mathematical modeling can provide new insights into the complex regulation of cell proliferation dynamics. In this review, we first examine quantitative experimental approaches for measuring cell proliferation dynamics in vitro and compare the various types of data that can be obtained in these settings. We then explore the toolbox of common mathematical modeling frameworks that can describe cell behavior, dynamics, and interactions of proliferation. We discuss how these wet-laboratory studies may be integrated with different mathematical modeling approaches to aid the interpretation of the results and to enable the prediction of cell behaviors, specifically in the context of cancer.

A generalized distributed delay model of COVID-19: An endemic model with immunity waning

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been spreading worldwide for over two years, with millions of reported cases and deaths. The deployment of mathematical modeling in the fight against COVID-19 has recorded tremendous success. However, most of these models target the epidemic phase of the disease. The development of safe and effective vaccines against SARS-CoV-2 brought hope of safe reopening of schools and businesses and return to pre-COVID normalcy, until mutant strains like the Delta and Omicron variants, which are more infectious, emerged. A few months into the pandemic, reports of the possibility of both vaccine- and infection-induced immunity waning emerged, thereby indicating that COVID-19 may be with us for longer than earlier thought. As a result, to better understand the dynamics of COVID-19, it is essential to study the disease with an endemic model. In this regard, we developed and analyzed an endemic model of COVID-19 that incorporates the waning of both vaccine- and infection-induced immunities using distributed delay equations. Our modeling framework assumes that the waning of both immunities occurs gradually over time at the population level. We derived a nonlinear ODE system from the distributed delay model and showed that the model could exhibit either a forward or backward bifurcation depending on the immunity waning rates. Having a backward bifurcation implies that $ R_c < 1 $ is not sufficient to guarantee disease eradication, and that the immunity waning rates are critical factors in eradicating COVID-19. Our numerical simulations show that vaccinating a high percentage of the population with a safe and moderately effective vaccine could help in eradicating COVID-19.

Numerical methods and hypoexponential approximations for gamma distributed delay differential equations

Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic gamma distributed DDEs have not previously been implemented. Modellers have therefore resorted to approximating the gamma distribution with an Erlang distribution and using the linear chain technique to derive an equivalent system of ordinary differential equations (ODEs). In this work, we address the lack of appropriate numerical tools for gamma distributed DDEs in two ways. First, we develop a functional continuous Runge-Kutta (FCRK) method to numerically integrate the gamma distributed DDE without resorting to Erlang approximation. We prove the fourth-order convergence of the FCRK method and perform numerical tests to demonstrate the accuracy of the new numerical method. Nevertheless, FCRK methods for infinite delay DDEs are not widely available in existing scientific software packages. As an alternative approach to solving gamma distributed DDEs, we also derive a hypoexponential approximation of the gamma distributed DDE. This hypoexponential approach is a more accurate approximation of the true gamma distributed DDE than the common Erlang approximation but, like the Erlang approximation, can be formulated as a system of ODEs and solved numerically using standard ODE software. Using our FCRK method to provide reference solutions, we show that the common Erlang approximation may produce solutions that are qualitatively different from the underlying gamma distributed DDE. However, the proposed hypoexponential approximations do not have this limitation. Finally, we apply our hypoexponential approximations to perform statistical inference on synthetic epidemiological data to illustrate the utility of the hypoexponential approximation.

On predicting heterogeneity in nanoparticle dosage

Nanoparticles are increasingly employed as a vehicle for the targeted delivery of therapeutics to specific cell types. However, much remains to be discovered about the fundamental biology that dictates the interactions between nanoparticles and cells. Accordingly, few nanoparticle-based targeted therapeutics have succeeded in clinical trials. One element that hinders our understanding of nanoparticle-cell interactions is the presence of heterogeneity in nanoparticle dosage data obtained from standard experiments. It is difficult to distinguish between heterogeneity that arises from stochasticity in nanoparticle-cell interactions, and that which arises from heterogeneity in the cell population. Mathematical investigations have revealed that both sources of heterogeneity contribute meaningfully to the heterogeneity in nanoparticle dosage. However, these investigations have relied on simplified models of nanoparticle internalisation. Here we present a stochastic mathematical model of nanoparticle internalisation that incorporates a suite of relevant biological phenomena such as multistage internalisation, cell division, asymmetric nanoparticle inheritance and nanoparticle saturation. Critically, our model provides information about nanoparticle dosage at an individual cell level. We perform model simulations to examine the influence of specific biological phenomena on the heterogeneity in nanoparticle dosage in the absence of heterogeneity in the cell population. Under certain modelling assumptions, we derive analytic approximations of the nanoparticle dosage distribution. We demonstrate that the analytic approximations are accurate, and show that nanoparticle dosage can be described by a Poisson mixture distribution with rate parameters that are a function of Beta-distributed random variables. We discuss the implications of the analytic results with respect to parameter estimation and model identifiability from standard experimental data. Finally, we highlight extensions and directions for future research.

Why the Spectral Radius? An intuition-building introduction to the basic reproduction number

The basic reproduction number [Formula: see text] is a fundamental concept in mathematical epidemiology and infectious disease modeling. Loosely speaking, it describes the number of people that an infectious person is expected to infect. The basic reproduction number has profound implications for epidemic trajectories and disease control strategies. It is well known that the basic reproduction number can be calculated as the spectral radius of the next generation matrix, but why this is the case may not be intuitively obvious. Here, we walk through how the discrete, next generation process connects to the ordinary differential equation disease system of interest, linearized at the disease-free equilibrium. Then, we use linear algebra to develop a geometric explanation of why the spectral radius of the next generation matrix is an epidemic threshold. Finally, we work through a series of examples that help to build familiarity with the kinds of patterns that arise in parameter combinations produced by the next generation method. This article is intended to help new infectious disease modelers develop intuition for the form and interpretation of the basic reproduction number in their disease systems of interest.

Hyper-radiosensitivity affects low-dose acute myeloid leukemia incidence in a mathematical model

In vitro experiments show that the cells possibly responsible for radiation-induced acute myeloid leukemia (rAML) exhibit low-dose hyper-radiosensitivity (HRS). In these cells, HRS is responsible for excess cell killing at low doses. Besides the endpoint of cell killing, HRS has also been shown to stimulate the low-dose formation of chromosomal aberrations such as deletions. Although HRS has been investigated extensively, little is known about the possible effect of HRS on low-dose cancer risk. In CBA mice, rAML can largely be explained in terms of a radiation-induced Sfpi1 deletion and a point mutation in the remaining Sfpi1 gene copy. The aim of this paper is to present and quantify possible mechanisms through which HRS may influence low-dose rAML incidence in CBA mice. To accomplish this, a mechanistic rAML CBA mouse model was developed to study HRS-dependent AML onset after low-dose photon irradiation. The rAML incidence was computed under the assumptions that target cells: (1) do not exhibit HRS; (2) HRS only stimulates cell killing; or (3) HRS stimulates cell killing and the formation of the Sfpi1 deletion. In absence of HRS (control), the rAML dose-response curve can be approximated with a linear-quadratic function of the absorbed dose. Compared to the control, the assumption that HRS stimulates cell killing lowered the rAML incidence, whereas increased incidence was observed at low doses if HRS additionally stimulates the induction of the Sfpi1 deletion. In conclusion, cellular HRS affects the number of surviving pre-leukemic cells with an Sfpi1 deletion which, depending on the HRS assumption, directly translates to a lower/higher probability of developing rAML. Low-dose HRS may affect cancer risk in general by altering the probability that certain mutations occur/persist.

A data-validated temporary immunity model of COVID-19 spread in Michigan

We introduce a distributed-delay differential equation disease spread model for COVID-19 spread. The model explicitly incorporates the population's time-dependent vaccine uptake and incorporates a gamma-distributed temporary immunity period for both vaccination and previous infection. We validate the model on COVID-19 cases and deaths data from the state of Michigan and use the calibrated model to forecast the spread and impact of the disease under a variety of realistic booster vaccine strategies. The model suggests that the mean immunity duration for individuals after vaccination is 350 days and after a prior infection is 242 days. Simulations suggest that both high population-wide adherence to vaccination mandates and a more-than-annually frequency of booster doses will be required to contain outbreaks in the future.

A dynamically structured matrix population model for insect life histories observed under variable environmental conditions

Various environmental drivers influence life processes of insect vectors that transmit human disease. Life histories observed under experimental conditions can reveal such complex links; however, designing informative experiments for insects is challenging. Furthermore, inferences obtained under controlled conditions often extrapolate poorly to field conditions. Here, we introduce a pseudo-stage-structured population dynamics model to describe insect development as a renewal process with variable rates. The model permits representing realistic life stage durations under constant and variable environmental conditions. Using the model, we demonstrate how random environmental variations result in fluctuating development rates and affect stage duration. We apply the model to infer environmental dependencies from the life history observations of two common disease vectors, the southern (Culex quinquefasciatus) and northern (Culex pipiens) house mosquito. We identify photoperiod, in addition to temperature, as pivotal in regulating larva stage duration, and find that carefully timed life history observations under semi-field conditions accurately predict insect development throughout the year. The approach we describe augments existing methods of life table design and analysis, and contributes to the development of large-scale climate- and environment-driven population dynamics models for important disease vectors.

New Results and Open Questions for SIR-PH Epidemic Models with Linear Birth Rate, Loss of Immunity, Vaccination, and Disease and Vaccination Fatalities

Our paper presents three new classes of models: SIR-PH, SIR-PH-FA, and SIR-PH-IA, and states two problems we would like to solve about them. Recall that deterministic mathematical epidemiology has one basic general law, the “R0 alternative” of Van den Driessche and Watmough, which states that the local stability condition of the disease-free equilibrium may be expressed as R0<1, where R0 is the famous basic reproduction number, which also plays a major role in the theory of branching processes. The literature suggests that it is impossible to find general laws concerning the endemic points. However, it is quite common that 1. When R0>1, there exists a unique fixed endemic point, and 2. the endemic point is locally stable when R0>1. One would like to establish these properties for a large class of realistic epidemic models (and we do not include here epidemics without casualties). We have introduced recently a “simple” but broad class of “SIR-PH models” with varying populations, with the express purpose of establishing for these processes the two properties above. Since that seemed still hard, we have introduced a further class of “SIR-PH-FA” models, which may be interpreted as approximations for the SIR-PH models, and which include simpler models typically studied in the literature (with constant population, without loss of immunity, etc.). For this class, the first “endemic law” above is “almost established”, as explicit formulas for a unique endemic point are available, independently of the number of infectious compartments, and it only remains to check its belonging to the invariant domain. This may yet turn out to be always verified, but we have not been able to establish that. However, the second property, the sufficiency of R0>1 for the local stability of an endemic point, remains open even for SIR-PH-FA models, despite the numerous particular cases in which it was checked to hold (via Routh–Hurwitz time-onerous computations, or Lyapunov functions). The goal of our paper is to draw attention to the two open problems above, for the SIR-PH and SIR-PH-FA, and also for a second, more refined “intermediate approximation” SIR-PH-IA. We illustrate the current status-quo by presenting new results on a generalization of the SAIRS epidemic model.

The role of time-varying viral shedding in modelling environmental surveillance for public health: revisiting the 2013 poliovirus outbreak in Israel

Environmental pathogen surveillance is a sensitive tool that can detect early-stage outbreaks, and it is being used to track poliovirus and other pathogens. However, interpretation of longitudinal environmental surveillance signals is difficult because the relationship between infection incidence and viral load in wastewater depends on time-varying shedding intensity. We developed a mathematical model of time-varying poliovirus shedding intensity consistent with expert opinion across a range of immunization states. Incorporating this shedding model into an infectious disease transmission model, we analysed quantitative, polymerase chain reaction data from seven sites during the 2013 Israeli poliovirus outbreak. Compared to a constant shedding model, our time-varying shedding model estimated a slower peak (four weeks later), with more of the population reached by a vaccination campaign before infection and a lower cumulative incidence. We also estimated the population shed virus for an average of 29 days (95% CI 28-31), longer than expert opinion had suggested for a population that was purported to have received three or more inactivated polio vaccine (IPV) doses. One explanation is that IPV may not substantially affect shedding duration. Using realistic models of time-varying shedding coupled with longitudinal environmental surveillance may improve our understanding of outbreak dynamics of poliovirus, SARS-CoV-2, or other pathogens.

Understanding dynamics of Plasmodium falciparum gametocytes production: Insights from an age-structured model

Many models of within-host malaria infection dynamics have been formulated since the pioneering work of Anderson et al. in 1989. Biologically, the goal of these models is to understand what governs the severity of infections, the patterns of infectiousness, and the variation thereof across individual hosts. Mathematically, these models are based on dynamical systems, with standard approaches ranging from K-compartments ordinary differential equations (ODEs) to delay differential equations (DDEs), to capture the relatively constant duration of replication and bursting once a parasite infects a host red blood cell. Using malariatherapy data, which offers fine-scale resolution on the dynamics of infection across a number of individual hosts, we compare the fit and robustness of one of these standard approaches (K-compartments ODE) with a partial differential equations (PDEs) model, which explicitly tracks the "age" of an infected cell. While both models perform quite similarly in terms of goodness-of-fit for suitably chosen K, the K-compartments ODE model particularly overestimates parasite densities early on in infections when the number of repeated compartments is not large enough. Finally, the K-compartments ODE model (for suitably chosen K) and the PDE model highlight a strong qualitative connection between the density of transmissible parasite stages (i.e., gametocytes) and the density of host-damaging (and asexually-replicating) parasite stages. This finding provides a simple tool for predicting which hosts are most infectious to mosquitoes -vectors of Plasmodium parasites- which is a crucial component of global efforts to control and eliminate malaria.

Structural identifiability analysis of age-structured PDE epidemic models

Computational and mathematical models rely heavily on estimated parameter values for model development. Identifiability analysis determines how well the parameters of a model can be estimated from experimental data. Identifiability analysis is crucial for interpreting and determining confidence in model parameter values and to provide biologically relevant predictions. Structural identifiability analysis, in which one assumes data to be noiseless and arbitrarily fine-grained, has been extensively studied in the context of ordinary differential equation (ODE) models, but has not yet been widely explored for age-structured partial differential equation (PDE) models. These models present additional difficulties due to increased number of variables and partial derivatives as well as the presence of boundary conditions. In this work, we establish a pipeline for structural identifiability analysis of age-structured PDE models using a differential algebra framework and derive identifiability results for specific age-structured models. We use epidemic models to demonstrate this framework because of their wide-spread use in many different diseases and for the corresponding parallel work previously done for ODEs. In our application of the identifiability analysis pipeline, we focus on a Susceptible-Exposed-Infected model for which we compare identifiability results for a PDE and corresponding ODE system and explore effects of age-dependent parameters on identifiability. We also show how practical identifiability analysis can be applied in this example.

Mathematical modelling of SARS-CoV-2 infection of human and animal host cells reveals differences in the infection rates and delays in viral particle production by infected cells

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV -2), a causative agent of COVID-19 disease, poses a significant threat to public health. Since its outbreak in December 2019, Wuhan, China, extensive collection of diverse data from cell culture and animal infections as well as population level data from an ongoing pandemic, has been vital in assessing strategies to battle its spread. Mathematical modelling plays a key role in quantifying determinants that drive virus infection dynamics, especially those relevant for epidemiological investigations and predictions as well as for proposing efficient mitigation strategies. We utilized a simple mathematical model to describe and explain experimental results on viral replication cycle kinetics during SARS-CoV-2 infection of animal and human derived cell lines, green monkey kidney cells, Vero-E6, and human lung epithelium cells, A549-ACE2, respectively. We conducted cell infections using two distinct initial viral concentrations and quantified viral loads over time. We then fitted the model to our experimental data and quantified the viral parameters. We showed that such cellular tropism generates significant differences in the infection rates and incubation times of SARS-CoV-2, that is, the times to the first release of newly synthesised viral progeny by SARS-CoV-2-infected cells. Specifically, the rate at which A549-ACE2 cells were infected by SARS-CoV-2 was 15 times lower than that in the case of Vero-E6 cell infection and the duration of latent phase of A549-ACE2 cells was 1.6 times longer than that of Vero-E6 cells. On the other hand, we found no statistically significant differences in other viral parameters, such as viral production rate or infected cell death rate. Since in vitro infection assays represent the first stage in the development of antiviral treatments against SARS-CoV-2, discrepancies in the viral parameter values across different cell hosts have to be identified and quantified to better target vaccine and antiviral research.

A generalized differential equation compartmental model of infectious disease transmission

For decades, mathematical models of disease transmission have provided researchers and public health officials with critical insights into the progression, control, and prevention of disease spread. Of these models, one of the most fundamental is the SIR differential equation model. However, this ubiquitous model has one significant and rarely acknowledged shortcoming: it is unable to account for a disease's true infectious period distribution. As the misspecification of such a biological characteristic is known to significantly affect model behavior, there is a need to develop new modeling approaches that capture such information. Therefore, we illustrate an innovative take on compartmental models, derived from their general formulation as systems of nonlinear Volterra integral equations, to capture a broader range of infectious period distributions, yet maintain the desirable formulation as systems of differential equations. Our work illustrates a compartmental model that captures any Erlang distributed duration of infection with only 3 differential equations, instead of the typical inflated model sizes required by traditional differential equation compartmental models, and a compartmental model that captures any mean, standard deviation, skewness, and kurtosis of an infectious period distribution with 4 differential equations. The significance of our work is that it opens up a new class of easy-to-use compartmental models to predict disease outbreaks that do not require a complete overhaul of existing theory, and thus provides a starting point for multiple research avenues of investigation under the contexts of mathematics, public health, and evolutionary biology.

Host Controls of Within-Host Disease Dynamics: Insight from an Invertebrate System

AbstractWithin-host processes (representing the entry, establishment, growth, and development of a parasite inside its host) may play a key role in parasite transmission but remain challenging to observe and quantify. We develop a general model for measuring host defenses and within-host disease dynamics. Our stochastic model breaks the infection process down into the stages of parasite exposure, entry, and establishment and provides associated probabilities for a host's ability to resist infections with barriers and clear internal infections. We tested our model on Daphnia dentifera and the parasitic fungus Metschnikowia bicuspidata and found that when faced with identical levels of parasite exposure, Daphnia patent (transmitting) infections depended on the strength of internal clearance. Applying a Gillespie algorithm to the model-estimated probabilities allowed us to visualize within-host dynamics, within which signatures of host defense could be clearly observed. We also found that early within-host stages were the most vulnerable to internal clearance, suggesting that hosts have a limited window during which recovery can occur. Our study demonstrates how pairing longitudinal infection data with a simple model can reveal new insight into within-host dynamics and mechanisms of host defense. Our model and methodological approach may be a powerful tool for exploring these properties in understudied host-parasite interactions.

Epidemic models with discrete state structures

The state of an infectious disease can represent the degree of infectivity of infected individuals, or susceptibility of susceptible individuals, or immunity of recovered individuals, or a combination of these measures. When the disease progression is long such as for HIV, individuals often experience switches among different states. We derive an epidemic model in which infected individuals have a discrete set of states of infectivity and can switch among different states. The model also incorporates a general incidence form in which new infections are distributed among different disease states. We discuss the importance of the transmission-transfer network for infectious diseases. Under the assumption that the transmission-transfer network is strongly connected, we establish that the basic reproduction numberR 0 is a sharp threshold parameter: ifR 0 ≤ 1 , the disease-free equilibrium is globally asymptotically stable and the disease always dies out; ifR 0 > 1 , the disease-free equilibrium is unstable, the system is uniformly persistent and initial outbreaks lead to persistent disease infection. For a restricted class of incidence functions, we prove that there is a unique endemic equilibrium and it is globally asymptotically stable whenR 0 > 1 . Furthermore, we discuss the impact of different state structures onR 0 , on the distribution of the disease states at the unique endemic equilibrium, and on disease control and preventions. Implications to the COVID-19 pandemic are also discussed.

Dynamics of SARS-CoV-2 with waning immunity in the UK population

The dynamics of immunity are crucial to understanding the long-term patterns of the SARS-CoV-2 pandemic. Several cases of reinfection with SARS-CoV-2 have been documented 48-142 days after the initial infection and immunity to seasonal circulating coronaviruses is estimated to be shorter than 1 year. Using an age-structured, deterministic model, we explore potential immunity dynamics using contact data from the UK population. In the scenario where immunity to SARS-CoV-2 lasts an average of three months for non-hospitalized individuals, a year for hospitalized individuals, and the effective reproduction number after lockdown ends is 1.2 (our worst-case scenario), we find that the secondary peak occurs in winter 2020 with a daily maximum of 387 000 infectious individuals and 125 000 daily new cases; threefold greater than in a scenario with permanent immunity. Our models suggest that longitudinal serological surveys to determine if immunity in the population is waning will be most informative when sampling takes place from the end of the lockdown in June until autumn 2020. After this period, the proportion of the population with antibodies to SARS-CoV-2 is expected to increase due to the secondary wave. Overall, our analysis presents considerations for policy makers on the longer-term dynamics of SARS-CoV-2 in the UK and suggests that strategies designed to achieve herd immunity may lead to repeated waves of infection as immunity to reinfection is not permanent. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

A Review of Matrix SIR Arino Epidemic Models

Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain subclass of compartmental models whose classes may be divided into three “(x,y,z)” groups, which we will call respectively “susceptible/entrance, diseased, and output” (in the classic SIR case, there is only one class of each type). Roughly, the ODE dynamics of these models contains only linear terms, with the exception of products between x and y terms. It has long been noticed that the reproduction number R has a very simple Formula in terms of the matrices which define the model, and an explicit first integral Formula is also available. These results can be traced back at least to Arino, Brauer, van den Driessche, Watmough, and Wu (2007) and to Feng (2007), respectively, and may be viewed as the “basic laws of SIR-type epidemics”. However, many papers continue to reprove them in particular instances. This motivated us to redraw attention to these basic laws and provide a self-contained reference of related formulas for (x,y,z) models. For the case of one susceptible class, we propose to use the name SIR-PH, due to a simple probabilistic interpretation as SIR models where the exponential infection time has been replaced by a PH-type distribution. Note that to each SIR-PH model, one may associate a scalar quantity Y(t) which satisfies “classic SIR relations”,which may be useful to obtain approximate control policies.

Building mean field ODE models using the generalized linear chain trick & Markov chain theory

The well known linear chain trick (LCT) allows modellers to derive mean field ODEs that assume gamma (Erlang) distributed passage times, by transitioning individuals sequentially through a chain of sub-states. The time spent in these sub-states is the sum of k exponentially distributed random variables, and is thus gamma distributed. The generalized linear chain trick (GLCT) extends this technique to the broader phase-type family of distributions, which includes exponential, Erlang, hypoexponential, and Coxian distributions. Phase-type distributions are the family of matrix exponential distributions on [0,∞) that represent the absorption time distributions for finite-state, continuous time Markov chains (CTMCs). Here we review CTMCs and phase-type distributions, then illustrate how to use the GLCT to efficiently build ODE models from underlying stochastic model assumptions. We introduce two novel model families by using the GLCT to generalize the Rosenzweig-MacArthur predator-prey model, and the SEIR model. We illustrate the kinds of complexity that can be captured by such models through multiple examples. We also show the benefits of using a GLCT-based model formulation to speed up the computation of numerical solutions to such models. These results highlight the intuitive nature, and utility, of using the GLCT to derive ODE models from first principles.

A process-based, stage-structured model of potato cyst nematode population dynamics: Effects of temperature and resistance

Potato cyst nematodes (PCN) are responsible for large losses in potato yields in many of the world's potato-growing regions. As soil temperatures increase due to climate change, there is potential for faster growth rates of PCN, allowing development of multiple generations in a growing season. We develop a process-based temperature-dependent model representing the life cycle of Globodera pallida, comprising juvenile, adult and cyst/diapause stages. To incorporate variability in the amount of time spent in each stage caused by genetic/environmental variation, the model is based on a mix of ordinary differential equations (ODEs) with sub-stages, and delay differential equations (DDEs). The effect of climate change is incorporated through the influence of soil temperature on the rate of development and survival in the hatching and juvenile stages. The level of the plant resistance to PCN is incorporated via the proportion of juveniles which become adults. After comparing the model with field data we run simulations to explore the effects of temperature and resistance on PCN populations. We find that with higher temperatures and longer growing seasons multiple generations of PCN can develop within a season, provided any required diapause period is short. Despite this, we show that growing resistant potatoes is a very effective control strategy and planting potatoes with even moderate levels of resistance can counter the effects of climate change.

Modeling the efficiency of filovirus entry into cells in vitro: Effects of SNP mutations in the receptor molecule

Interaction between filovirus glycoprotein (GP) and the Niemann-Pick C1 (NPC1) protein is essential for membrane fusion during virus entry. Some single-nucleotide polymorphism (SNPs) in two surface-exposed loops of NPC1 are known to reduce viral infectivity. However, the dependence of differences in entry efficiency on SNPs remains unclear. Using vesicular stomatitis virus pseudotyped with Ebola and Marburg virus GPs, we investigated the cell-to-cell spread of viruses in cultured cells expressing NPC1 or SNP derivatives. Eclipse and virus-producing phases were assessed by in vitro infection experiments, and we developed a mathematical model describing spatial-temporal virus spread. This mathematical model fit the plaque radius data well from day 2 to day 6. Based on the estimated parameters, we found that SNPs causing the P424A and D508N substitutions in NPC1 most effectively reduced the entry efficiency of Ebola and Marburg viruses, respectively. Our novel approach could be broadly applied to other virus plaque assays.

Ebola (EBOV) and Marburg (MARV) viruses, which are included viruses of the family Filoviridae, cause severe hemorrhagic fever in humans. Filovirus particles is adsorbed to the cell through glycoprotein (GP), which is the only viral surface protein. Interaction between the filovirus sugar protein (GP) and the Niemann-Pick C1 (NPC1) protein plays a key role in membrane fusion during virus entry. Although some single-nucleotide polymorphism (SNPs) in two surface-exposed loops of NPC1 are known to reduce viral infectivity, the dependence of differences in entry efficiency on SNPs has not been studied. We therefore investigated the cell-to-cell spread of viruses in cultured cells expressing NPC1 or SNP derivatives. Using a mathematical model describing spatial-temporal virus spread, we quantitatively analyze viral entry efficiency and how this affected cell-to-cell spread. Our approach may be applied to not only understanding the roles of genetic polymorphisms in human susceptibility to filoviruses, but also other virus plaque assays.

Using compartmental models to simulate directed acyclic graphs to explore competing causal mechanisms underlying epidemiological study data

Accurately estimating the effect of an exposure on an outcome requires understanding how variables relevant to a study question are causally related to each other. Directed acyclic graphs (DAGs) are used in epidemiology to understand causal processes and determine appropriate statistical approaches to obtain unbiased measures of effect. Compartmental models (CMs) are also used to represent different causal mechanisms, by depicting flows between disease states on the population level. In this paper, we extend a mapping between DAGs and CMs to show how DAG-derived CMs can be used to compare competing causal mechanisms by simulating epidemiological studies and conducting statistical analyses on the simulated data. Through this framework, we can evaluate how robust simulated epidemiological study results are to different biases in study design and underlying causal mechanisms. As a case study, we simulated a longitudinal cohort study to examine the obesity paradox: the apparent protective effect of obesity on mortality among diabetic ever-smokers, but not among diabetic never-smokers. Our simulations illustrate how study design bias (e.g. reverse causation), can lead to the obesity paradox. Ultimately, we show the utility of transforming DAGs into in silico laboratories within which researchers can systematically evaluate bias, and inform analyses and study design.

Hitchhiking, collapse, and contingency in phage infections of migrating bacterial populations

Natural bacterial populations are subjected to constant predation pressure by bacteriophages. Bacteria use a variety of molecular mechanisms to defend themselves from phage predation. However, since phages are nonmotile, perhaps the simplest defense against phage is for bacteria to move faster than phages. In particular, chemotaxis, the active migration of bacteria up attractant gradients, may help the bacteria escape slowly diffusing phages. Here we study phage infection dynamics in migrating bacterial populations driven by chemotaxis through low viscosity agar plates. We find that expanding phage-bacteria populations supports two moving fronts, an outermost bacterial front driven by nutrient uptake and chemotaxis and an inner phage front at which the bacterial population collapses due to phage predation. We show that with increasing adsorption rate and initial phage population, the speed of the moving phage front increases, eventually overtaking the bacterial front and driving the system across a transition from a regime where bacterial front speed exceeds that of the phage front to one where bacteria must evolve phage resistance to survive. Our data support the claim that this process requires phage to hitchhike with moving bacteria. A deterministic model recapitulates the transition under the assumption that phage virulence declines with host growth rate which we confirm experimentally. Finally, near the transition between regimes we observe macroscopic fluctuations in bacterial densities at the phage front. Our work opens a new, spatio-temporal, line of investigation into the eco-evolutionary struggle between bacteria and phage.