Crossing the scale from within-host infection dynamics to between-host transmission fitness: a discussion of current assumptions and knowledge

Quantifying the relationship between within-host dynamics and transmission for viral diseases of livestock

Understanding the population dynamics of an infectious disease requires linking within-host dynamics and between-host transmission in a quantitative manner, but this is seldom done in practice. Here a simple phenomenological model for viral dynamics within a host is linked to between-host transmission by assuming that the probability of transmission is related to log viral titre. Data from transmission experiments for two viral diseases of livestock, foot-and-mouth disease virus in cattle and swine influenza virus in pigs, are used to parametrize the model and, importantly, test the underlying assumptions. The model allows the relationship between within-host parameters and transmission to be determined explicitly through their influence on the reproduction number and generation time. Furthermore, these critical within-host parameters (time and level of peak titre, viral growth and clearance rates) can be computed from more complex within-host models, raising the possibility of assessing the impact of within-host processes on between-host transmission in a more detailed quantitative manner.

Public Health Impact of Paxlovid as Treatment for COVID-19, United States

We evaluated the population-level benefits of expanding treatment with the antiviral drug Paxlovid (nirmatrelvir/ritonavir) in the United States for SARS-CoV-2 Omicron variant infections. Using a multiscale mathematical model, we found that treating 20% of symptomatic case-patients with Paxlovid over a period of 300 days beginning in January 2022 resulted in life and cost savings. In a low-transmission scenario (effective reproduction number of 1.2), this approach could avert 0.28 million (95% CI 0.03-0.59 million) hospitalizations and save US $56.95 billion (95% CI US $2.62-$122.63 billion). In a higher transmission scenario (effective reproduction number of 3), the benefits increase, potentially preventing 0.85 million (95% CI 0.36-1.38 million) hospitalizations and saving US $170.17 billion (95% CI US $60.49-$286.14 billion). Our findings suggest that timely and widespread use of Paxlovid could be an effective and economical approach to mitigate the effects of COVID-19.

An agent-based nested model integrating within-host and between-host mechanisms to predict an epidemic

The COVID-19 pandemic has remarkably heightened concerns regarding the prediction of communicable disease spread. This study introduces an innovative agent-based modeling approach. In this model, the quantification of human-to-human transmission aligns with the dynamic variations in the viral load within an individual, termed "within-host" and adheres to the susceptible-infected-recovered (SIR) process, referred to as "between-host." Variations in the viral load over time affect the infectivity between individual agents. This model diverges from the traditional SIR model, which employs a constant transmission probability, by incorporating a dynamic, time-dependent transmission probability influenced by the viral load in a host agent. The proposed model retains the time-integrated transmission probability characteristic of the conventional SIR model. As observed in this model, the overall epidemic size remains consistent with the predictions of the standard SIR model. Nonetheless, compared to predictions based on the classical SIR process, notable differences existed in the peak number of the infected individuals and the timing of this peak. These nontrivial differences are induced by the direct correlation between the time-evolving transmission probability and the viral load within a host agent. The developed model can inform targeted intervention strategies and public health policies by providing detailed insights into disease spread dynamics, crucial for effectively managing epidemics.

Mathematical methods for scaling from within-host to population-scale in infectious disease systems

Mathematical modellers model infectious disease dynamics at different scales. Within-host models represent the spread of pathogens inside an individual, whilst between-host models track transmission between individuals. However, pathogen dynamics at one scale affect those at another. This has led to the development of multiscale models that connect within-host and between-host dynamics. In this article, we systematically review the literature on multiscale infectious disease modelling according to PRISMA guidelines, dividing previously published models into five categories governing their methodological approaches (Garira (2017)), explaining their benefits and limitations. We provide a primer on developing multiscale models of infectious diseases.

The public health impact of Paxlovid COVID-19 treatment in the United States

The antiviral drug Paxlovid has been shown to rapidly reduce viral load. Coupled with vaccination, timely administration of safe and effective antivirals could provide a path towards managing COVID-19 without restrictive non-pharmaceutical measures. Here, we estimate the population-level impacts of expanding treatment with Paxlovid in the US using a multi-scale mathematical model of SARS-CoV-2 transmission that incorporates the within-host viral load dynamics of the Omicron variant. We find that, under a low transmission scenario R e ∼ 1.2 treating 20% of symptomatic cases would be life and cost saving, leading to an estimated 0.26 (95% CrI: 0.03, 0.59) million hospitalizations averted, 30.61 (95% CrI: 1.69, 71.15) thousand deaths averted, and US$52.16 (95% CrI: 2.62, 122.63) billion reduction in health- and treatment-related costs. Rapid and broad use of the antiviral Paxlovid could substantially reduce COVID-19 morbidity and mortality, while averting socioeconomic hardship.

Within- and between-host dynamics of producer and non-producer pathogens

For infections to be maintained in a population, pathogens must compete to colonize hosts and transmit between them. We use an experimental approach to investigate within-and-between host dynamics using the pathogen Pseudomonas aeruginosa and the animal host Caenorhabditis elegans. Within-host interactions can involve the production of goods that are beneficial to all pathogens in the local environment but susceptible to exploitation by non-producers. We exposed the nematode host to ‘producer’ and two ‘non-producer’ bacterial strains (specifically for siderophore production and quorum sensing), in single infections and coinfections, to investigate within-host colonization. Subsequently, we introduced infected nematodes to pathogen-naive populations to allow natural transmission between hosts. We find that producer pathogens are consistently better at colonizing hosts and transmitting between them than non-producers during coinfection and single infection. Non-producers were poor at colonizing hosts and between-host transmission, even when coinfecting with producers. Understanding pathogen dynamics across these multiple levels will ultimately help us predict and control the spread of infections, as well as contribute to explanations for the persistence of cooperative genotypes in natural populations.

Simplified within-host and Dose-response Models of SARS-CoV-2

Understanding the mechanistic dynamics of transmission is key to designing more targeted and effective interventions to limit the spread of infectious diseases. A well-described within-host model allows explicit simulation of how infectiousness changes over time at an individual level. This can then be coupled with dose-response models to investigate the impact of timing on transmission. We collected and compared a range of within-host models used in previous studies and identified a minimally-complex model that provides suitable within-host dynamics while keeping a reduced number of parameters to allow inference and limit unidentifiability issues. Furthermore, non-dimensionalised models were developed to further overcome the uncertainty in estimates of the size of the susceptible cell population, a common problem in many of these approaches. We will discuss these models, and their fit to data from the human challenge study (see Killingley et al. (2022)) for SARS-CoV-2 and the model selection results, which has been performed using ABC-SMC. The parameter posteriors have then used to simulate viral-load based infectiousness profiles via a range of dose-response models, which illustrate the large variability of the periods of infection window observed for COVID-19.

Compositional modelling of immune response and virus transmission dynamics

Transmission models for infectious diseases are typically formulated in terms of dynamics between individuals or groups with processes such as disease progression or recovery for each individual captured phenomenologically, without reference to underlying biological processes. Furthermore, the construction of these models is often monolithic: they do not allow one to readily modify the processes involved or include the new ones, or to combine models at different scales. We show how to construct a simple model of immune response to a respiratory virus and a model of transmission using an easily modifiable set of rules allowing further refining and merging the two models together. The immune response model reproduces the expected response curve of PCR testing for COVID-19 and implies a long-tailed distribution of infectiousness reflective of individual heterogeneity. This immune response model, when combined with a transmission model, reproduces the previously reported shift in the population distribution of viral loads along an epidemic trajectory. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Scaling effects of temperature on parasitism from individuals to populations

Parasitism is expected to change in a warmer future, but whether warming leads to substantial increases in parasitism remains unclear. Understanding how warming effects on parasitism in individual hosts (e.g. parasite load) translate to effects on population-level parasitism (e.g. prevalence, R0 ) remains a major knowledge gap. We conducted a literature review and identified 24 host-parasite systems that had information on the temperature dependence of parasitism at both individual host and host population levels: 13 vector-borne systems and 11 environmentally transmitted systems. We found a strong positive correlation between the thermal optima of individual- and population-level parasitism, although several of the environmentally transmitted systems exhibited thermal optima >5°C apart between individual and population levels. Parasitism thermal optima were close to vector performance thermal optima in vector-borne systems but not hosts in environmentally transmitted systems, suggesting these thermal mismatches may be more common in certain types of host-parasite systems. We also adapted and simulated simple models for both types of transmission modes and found the same pattern across the two modes: thermal optima were more strongly correlated across scales when there were more traits linking individual- to population-level processes. Generally, our results suggest that information on the temperature dependence, and specifically the thermal optimum, at either the individual or population level should provide a useful-although not quantitatively exact-baseline for predicting temperature dependence at the other level, especially in vector-borne parasite systems. Environmentally transmitted parasitism may operate by a different set of rules, in which temperature dependence is decoupled in some systems, requiring the need for trait-based studies of temperature dependence at individual and population levels.

Managing host-parasite interactions in humans and wildlife in times of global change

Global change in the Anthropocene has modified the environment of almost any species on earth, be it through climate change, habitat modifications, pollution, human intervention in the form of mass drug administration (MDA), or vaccination. This can have far-reaching consequences on all organisational levels of life, including eco-physiological stress at the cell and organism level, individual fitness and behaviour, population viability, species interactions and biodiversity. Host-parasite interactions often require highly adapted strategies by the parasite to survive and reproduce within the host environment and ensure efficient transmission among hosts. Yet, our understanding of the system-level outcomes of the intricate interplay of within host survival and among host parasite spread is in its infancy. We shed light on how global change affects host-parasite interactions at different organisational levels and address challenges and opportunities to work towards better-informed management of parasite control. We argue that global change affects host-parasite interactions in wildlife inhabiting natural environments rather differently than in humans and invasive species that benefit from anthropogenic environments as habitat and more deliberate rather than erratic exposure to therapeutic drugs and other control efforts.

Variation in within-host replication kinetics among virus genotypes provides evidence of specialist and generalist infection strategies across three salmonid host species

Theory of the evolution of pathogen specialization suggests that a specialist pathogen gains high fitness in one host, but this comes with fitness loss in other hosts. By contrast, a generalist pathogen does not achieve high fitness in any host, but gains ecological fitness by exploiting different hosts, and has higher fitness than specialists in nonspecialized hosts. As a result, specialist pathogens are predicted to have greater variation in fitness across hosts, and generalists would have lower fitness variation across hosts. We test these hypotheses by measuring pathogen replicative fitness as within-host viral loads from the onset of infection to the beginning of virus clearance, using the rhabdovirus infectious hematopoietic necrosis virus (IHNV) in salmonid fish. Based on field prevalence and virulence studies, the IHNV subgroups UP, MD, and L are specialists, causing infection and mortality in sockeye salmon, steelhead, and Chinook salmon juveniles, respectively. The UC subgroup evolved naturally from a UP ancestor and is a generalist infecting all three host species but without causing severe disease. We show that the specialist subgroups had the highest peak and mean viral loads in the hosts in which they are specialized, and they had low viral loads in nonspecialized hosts, resulting in large variation in viral load across hosts. Viral kinetics show that the mechanisms of specialization involve the ability to both maximize early virus replication and avoid clearance at later times, with different mechanisms of specialization evident in different host-virus combinations. Additional nuances in the data included different fitness levels for nonspecialist interactions, reflecting different trade-offs for specialist viruses in other hosts. The generalist UC subgroup reached intermediate viral loads in all hosts and showed the smallest variation in fitness across hosts. The evolution of the UC generalist from an ancestral UP sockeye specialist was associated with fitness increases in steelhead and Chinook salmon, but only slight decreases in fitness in sockeye salmon, consistent with low- or no-cost generalism. Our results support major elements of the specialist-generalist theory, providing evidence of a specialist-generalist continuum in a vertebrate pathogen. These results also quantify within-host replicative fitness trade-offs resulting from the natural evolution of specialist and generalist virus lineages in multi-host ecosystems.

Capturing complex interactions in disease ecology with simplicial sets

Network approaches have revolutionized the study of ecological interactions. Social, movement and ecological networks have all been integral to studying infectious disease ecology. However, conventional (dyadic) network approaches are limited in their ability to capture higher-order interactions. We present simplicial sets as a tool that addresses this limitation. First, we explain what simplicial sets are. Second, we explain why their use would be beneficial in different subject areas. Third, we detail where these areas are: social, transmission, movement/spatial and ecological networks and when using them would help most in each context. To demonstrate their application, we develop a novel approach to identify how pathogens persist within a host population. Fourth, we provide an overview of how to use simplicial sets, highlighting specific metrics, generative models and software. Finally, we synthesize key research questions simplicial sets will help us answer and draw attention to methodological developments that will facilitate this.

Within-host dynamics of SARS-CoV-2 infection: A systematic review and meta-analysis

Within-host model specified by viral dynamic parameters is a mainstream tool to understand SARS-CoV-2 replication cycle in infected patients. The parameter uncertainty further affects the output of the model, such as the efficacy of potential antiviral drugs. However, gathering empirical data on these parameters is challenging. Here, we aim to conduct a systematic review of viral dynamic parameters used in within-host models by calibrating the model to the viral load data measured from upper respiratory specimens. We searched the PubMed, Embase and Web of Science databases (between 1 December 2019 and 10 February 2022) for within-host modelling studies. We identified seven independent within-host models from the above nine studies, including Type I interferon, innate response, humoral immune response or cell-mediated immune response. From these models, we extracted and analyse seven widely used viral dynamic parameters including the viral load at the point of infection or symptom onset, the rate of viral particles infecting susceptible cells, the rate of infected cells releasing virus, the rate of virus particles cleared, the rate of infected cells cleared and the rate of cells in the eclipse phase can become productively infected. We identified seven independent within-host models from nine eligible studies. The viral load at symptom onset is 4.78 (95% CI:2.93, 6.62) log(copies/ml), and the viral load at the point of infection is -1.00 (95% CI:-1.94, -0.05) log(copies/ml). The rate of viral particles infecting susceptible cells and the rate of infected cells cleared have the pooled estimates as -6.96 (95% CI:-7.66, -6.25) log([copies/ml]^-1 day^-1 ) and 0.92 (95% CI:-0.09, 1.93) day^-1 , respectively. We found that the rate of infected cells cleared was associated with the reported model in the meta-analysis by including the model type as a categorical variable (p < .01). Joint viral dynamic parameters estimates when parameterizing within-host models have been published for SARS-CoV-2. The reviewed viral dynamic parameters can be used in the same within-host model to understand SARS-CoV-2 replication cycle in infected patients and assess the impact of pharmaceutical interventions.

A model for leveraging animal movement to understand spatio-temporal disease dynamics

The ongoing explosion of fine-resolution movement data in animal systems provides a unique opportunity to empirically quantify spatial, temporal and individual variation in transmission risk and improve our ability to forecast disease outbreaks. However, we lack a generalizable model that can leverage movement data to quantify transmission risk and how it affects pathogen invasion and persistence on heterogeneous landscapes. We developed a flexible model 'Movement-driven modelling of spatio-temporal infection risk' (MoveSTIR) that leverages diverse data on animal movement to derive metrics of direct and indirect contact by decomposing transmission into constituent processes of contact formation and duration and pathogen deposition and acquisition. We use MoveSTIR to demonstrate that ignoring fine-scale animal movements on actual landscapes can mis-characterize transmission risk and epidemiological dynamics. MoveSTIR unifies previous work on epidemiological contact networks and can address applied and theoretical questions at the nexus of movement and disease ecology.

The role of a programmatic immune response on the evolution of pathogen traits

In modelling pathogen evolution during epidemics, it is important to understand the interactions between within-host infection dynamics and between-host pathogen transmission. Multiscale models often assume an immune response that is highly responsive to pathogen dynamics. Empirical evidence, however, suggests that the immune response in acute infections is triggered and programmatic. This leads to somewhat more predictable infection trajectories where transition times and, consequently, the infectious window are non-exponentially distributed. Here, we develop a within-host model where the immune response is triggered by pathogen growth but otherwise develops independently, and use this to obtain analytic expressions for the infectious period and peak pathogen load. This allows us to model the basic reproductive number in terms of explicit functional relationships among within-host traits including the growth rate of the pathogen. We find that the dependence of pathogen load and the infectious window on within-host parameters constrains the evolution of the pathogen growth rate. At low growth rate, selection favours a higher pathogen load and therefore increasing pathogen growth rate. At high growth rates, selection for a longer infectious window trades off against selection against the effects of virulence. At intermediate growth rates the basic reproductive number is relatively insensitive to changes in the growth rate. The resulting "flat" region of the pathogen fitness landscape is due to the stability of the programmatic immune response in clearing the infection.

Sensitivity Analysis in an Immuno-Epidemiological Vector-Host Model

Sensitivity Analysis (SA) is a useful tool to measure the impact of changes in model parameters on the infection dynamics, particularly to quantify the expected efficacy of disease control strategies. SA has only been applied to epidemic models at the population level, ignoring the effect of within-host virus-with-immune-system interactions on the disease spread. Connecting the scales from individual to population can help inform drug and vaccine development. Thus the value of understanding the impact of immunological parameters on epidemiological quantities. Here we consider an age-since-infection structured vector-host model, in which epidemiological parameters are formulated as functions of within-host virus and antibody densities, governed by an ODE system. We then use SA for these immuno-epidemiological models to investigate the impact of immunological parameters on population-level disease dynamics such as basic reproduction number, final size of the epidemic or the infectiousness at different phases of an outbreak. As a case study, we consider Rift Valley Fever Disease utilizing parameter estimations from prior studies. SA indicates that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1\%$$\end{document}1% increase in within-host pathogen growth rate can lead up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$8\%$$\end{document}8% increase in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal R_0,$$\end{document}R0, up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1 \%$$\end{document}1% increase in steady-state infected host abundance, and up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\%$$\end{document}4% increase in infectiousness of hosts when the reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal R_0$$\end{document}R0 is larger than one. These significant increases in population-scale disease quantities suggest that control strategies that reduce the within-host pathogen growth can be important in reducing disease prevalence.

In vivo kinetics of SARS-CoV-2 infection and its relationship with a person's infectiousness

The within-host viral kinetics of SARS-CoV-2 infection and how they relate to a person's infectiousness are not well understood. This limits our ability to quantify the impact of interventions on viral transmission. Here, we develop viral dynamic models of SARS-CoV-2 infection and fit them to data to estimate key within-host parameters such as the infected cell half-life and the within-host reproductive number. We then develop a model linking viral load (VL) to infectiousness and show a person's infectiousness increases sublinearly with VL and that the logarithm of the VL in the upper respiratory tract is a better surrogate of infectiousness than the VL itself. Using data on VL and the predicted infectiousness, we further incorporated data on antigen and RT-PCR tests and compared their usefulness in detecting infection and preventing transmission. We found that RT-PCR tests perform better than antigen tests assuming equal testing frequency; however, more frequent antigen testing may perform equally well with RT-PCR tests at a lower cost but with many more false-negative tests. Overall, our models provide a quantitative framework for inferring the impact of therapeutics and vaccines that lower VL on the infectiousness of individuals and for evaluating rapid testing strategies.

Decomposing the sources of SARS-CoV-2 fitness variation in the United States

The fitness of a pathogen is a composite phenotype determined by many different factors influencing growth rates both within and between hosts. Determining what factors shape fitness at the host population-level is especially challenging because both intrinsic factors like pathogen genetics and extrinsic factors such as host behavior influence between-host transmission potential. This challenge has been highlighted by controversy surrounding the population-level fitness effects of mutations in the SARS-CoV-2 genome and their relative importance when compared against non-genetic factors shaping transmission dynamics. Building upon phylodynamic birth-death models, we develop a new framework to learn how hundreds of genetic and non-genetic factors have shaped the fitness of SARS-CoV-2. We estimate the fitness effects of all amino acid variants and several structural variants that have circulated in the United States between February 2020 and March 2021 from viral phylogenies. We also estimate how much fitness variation among pathogen lineages is attributable to genetic versus non-genetic factors such as spatial heterogeneity in transmission rates. Before September 2020, most fitness variation between lineages can be explained by background spatial heterogeneity in transmission rates across geographic regions. Starting in late 2020, genetic variation in fitness increased dramatically with the emergence of several new lineages including B.1.1.7, B.1.427, B.1.429 and B.1.526. Our analysis also indicates that genetic variants in less well-explored genomic regions outside of Spike may be contributing significantly to overall fitness variation in the viral population.

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.

Towards an ecosystem model of infectious disease

Increasingly intimate associations between human society and the natural environment are driving the emergence of novel pathogens, with devastating consequences for humans and animals alike. Prior to emergence, these pathogens exist within complex ecological systems that are characterized by trophic interactions between parasites, their hosts and the environment. Predicting how disturbance to these ecological systems places people and animals at risk from emerging pathogens-and the best ways to manage this-remains a significant challenge. Predictive systems ecology models are powerful tools for the reconstruction of ecosystem function but have yet to be considered for modelling infectious disease. Part of this stems from a mistaken tendency to forget about the role that pathogens play in structuring the abundance and interactions of the free-living species favoured by systems ecologists. Here, we explore how developing and applying these more complete systems ecology models at a landscape scale would greatly enhance our understanding of the reciprocal interactions between parasites, pathogens and the environment, placing zoonoses in an ecological context, while identifying key variables and simplifying assumptions that underly pathogen host switching and animal-to-human spillover risk. As well as transforming our understanding of disease ecology, this would also allow us to better direct resources in preparation for future pandemics.

In vivo kinetics of SARS-CoV-2 infection and its relationship with a person's infectiousness

The within-host viral kinetics of SARS-CoV-2 infection and how they relate to a person's infectiousness are not well understood. This limits our ability to quantify the impact of interventions on viral transmission. Here, we develop data-driven viral dynamic models of SARS-CoV-2 infection and estimate key within-host parameters such as the infected cell half-life and the within-host reproductive number. We then develop a model linking VL to infectiousness, showing that a person's infectiousness increases sub-linearly with VL. We show that the logarithm of the VL in the upper respiratory tract (URT) is a better surrogate of infectiousness than the VL itself. Using data on VL and the predicted infectiousness, we further incorporated data on antigen and reverse transcription polymerase chain reaction (RT-PCR) tests and compared their usefulness in detecting infection and preventing transmission. We found that RT-PCR tests perform better than antigen tests assuming equal testing frequency; however, more frequent antigen testing may perform equally well with RT-PCR tests at a lower cost, but with many more false-negative tests. Overall, our models provide a quantitative framework for inferring the impact of therapeutics and vaccines that lower VL on the infectiousness of individuals and for evaluating rapid testing strategies.

SIGNIFICANCE

Quantifying the kinetics of SARS-CoV-2 infection and individual infectiousness is key to quantitatively understanding SARS-CoV-2 transmission and evaluating intervention strategies. Here we developed data-driven within-host models of SARS-CoV-2 infection and by fitting them to clinical data we estimated key within-host viral dynamic parameters. We also developed a mechanistic model for viral transmission and show that the logarithm of the viral load in the upper respiratory tract serves an appropriate surrogate for a person's infectiousness. Using data on how viral load changes during infection, we further evaluated the effectiveness of PCR and antigen-based testing strategies for averting transmission and identifying infected individuals.

The roles of environmental variation and parasite survival in virulence-transmission relationships

Disease outbreaks are a consequence of interactions among the three components of a host-parasite system: the infectious agent, the host and the environment. While virulence and transmission are widely investigated, most studies of parasite life-history trade-offs are conducted with theoretical models or tractable experimental systems where transmission is standardized and the environment controlled. Yet, biotic and abiotic environmental factors can strongly affect disease dynamics, and ultimately, host-parasite coevolution. Here, we review research on how environmental context alters virulence-transmission relationships, focusing on the off-host portion of the parasite life cycle, and how variation in parasite survival affects the evolution of virulence and transmission. We review three inter-related 'approaches' that have dominated the study of the evolution of virulence and transmission for different host-parasite systems: (i) evolutionary trade-off theory, (ii) parasite local adaptation and (iii) parasite phylodynamics. These approaches consider the role of the environment in virulence and transmission evolution from different angles, which entail different advantages and potential biases. We suggest improvements to how to investigate virulence-transmission relationships, through conceptual and methodological developments and taking environmental context into consideration. By combining developments in life-history evolution, phylogenetics, adaptive dynamics and comparative genomics, we can improve our understanding of virulence-transmission relationships across a diversity of host-parasite systems that have eluded experimental study of parasite life history.

Transient disease dynamics across ecological scales

Analyses of transient dynamics are critical to understanding infectious disease transmission and persistence. Identifying and predicting transients across scales, from within-host to community-level patterns, plays an important role in combating ongoing epidemics and mitigating the risk of future outbreaks. Moreover, greater emphases on non-asymptotic processes will enable timely evaluations of wildlife and human diseases and lead to improved surveillance efforts, preventive responses, and intervention strategies. Here, we explore the contributions of transient analyses in recent models spanning the fields of epidemiology, movement ecology, and parasitology. In addition to their roles in predicting epidemic patterns and endemic outbreaks, we explore transients in the contexts of pathogen transmission, resistance, and avoidance at various scales of the ecological hierarchy. Examples illustrate how (i) transient movement dynamics at the individual host level can modify opportunities for transmission events over time; (ii) within-host energetic processes often lead to transient dynamics in immunity, pathogen load, and transmission potential; (iii) transient connectivity between discrete populations in response to environmental factors and outbreak dynamics can affect disease spread across spatial networks; and (iv) increasing species richness in a community can provide transient protection to individuals against infection. Ultimately, we suggest that transient analyses offer deeper insights and raise new, interdisciplinary questions for disease research, consequently broadening the applications of dynamical models for outbreak preparedness and management.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s12080-021-00514-w.

Testing the multiple stressor hypothesis: chlorothalonil exposure alters transmission potential of a bumblebee pathogen but not individual host health

Numerous threats are putting pollinator health and essential ecosystem pollination services in jeopardy. Although individual threats are widely studied, their co-occurrence may exacerbate negative effects, as posited by the multiple stressor hypothesis. A prominent branch of this hypothesis concerns pesticide-pathogen co-exposure. A landscape analysis demonstrated a positive association between local chlorothalonil fungicide use and microsporidian pathogen (Nosema bombi) prevalence in declining bumblebee species (Bombus spp.), suggesting an interaction deserving further investigation. We tested the multiple stressor hypothesis with field-realistic chlorothalonil and N. bombi exposures in worker-produced B. impatiens microcolonies. Chlorothalonil was not avoided in preference assays, setting the stage for pesticide-pathogen co-exposure. However, contrary to the multiple stressor hypothesis, co-exposure did not affect survival. Bees showed surprising tolerance to Nosema infection, which was also unaffected by chlorothalonil exposure. However, previously fungicide-exposed infected bees carried more transmission-ready spores. Our use of a non-declining bumblebee and potential higher chlorothalonil exposures under some scenarios could mean stronger individual or interactive effects in certain field settings. Yet, our results alone suggest consequences of pesticide co-exposure for pathogen dynamics in host communities. This underlies the importance of considering both within- and between-host processes when addressing the multiple stressor hypothesis in relation to pathogens.

Mechanistic Modeling of SARS-CoV-2 and Other Infectious Diseases and the Effects of Therapeutics

Modern viral kinetic modeling and its application to therapeutics is a field that attracted the attention of the medical, pharmaceutical, and modeling communities during the early days of the AIDS epidemic. Its successes led to applications of modeling methods not only to HIV but a plethora of other viruses, such as hepatitis C virus (HCV), hepatitis B virus and cytomegalovirus, which along with HIV cause chronic diseases, and viruses such as influenza, respiratory syncytial virus, West Nile virus, Zika virus, and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which generally cause acute infections. Here we first review the historical development of mathematical models to understand HIV and HCV infections and the effects of treatment by fitting the models to clinical data. We then focus on recent efforts and contributions of applying these models towards understanding SARS-CoV-2 infection and highlight outstanding questions where modeling can provide crucial insights and help to optimize nonpharmaceutical and pharmaceutical interventions of the coronavirus disease 2019 (COVID-19) pandemic. The review is written from our personal perspective emphasizing the power of simple target cell limited models that provided important insights and then their evolution into more complex models that captured more of the virology and immunology. To quote Albert Einstein, "Everything should be made as simple as possible, but not simpler," and this idea underlies the modeling we describe below.

Initial Inoculum and the Severity of COVID-19: A Mathematical Modeling Study of the Dose-Response of SARS-CoV-2 Infections

SARS-CoV-2 (Severe acute respiratory syndrome coronavirus 2) causes a variety of responses in those who contract the virus, ranging from asymptomatic infections to acute respiratory failure and death. While there are likely multiple mechanisms triggering severe disease, one potential cause of severe disease is the size of the initial inoculum. For other respiratory diseases, larger initial doses lead to more severe outcomes. We investigate whether there is a similar link for SARS-CoV-2 infections using the combination of an agent-based model (ABM) and a partial differential equation model (PDM). We use the model to examine the viral time course for different sizes of initial inocula, generating dose-response curves for peak viral load, time of viral peak, viral growth rate, infection duration, and area under the viral titer curve. We find that large initial inocula lead to short infections, but with higher viral titer peaks; and that smaller initial inocula lower the viral titer peak, but make the infection last longer.

In-host Mathematical Modelling of COVID-19 in Humans

COVID-19 pandemic has underlined the impact of emergent pathogens as a major threat to human health. The development of quantitative approaches to advance comprehension of the current outbreak is urgently needed to tackle this severe disease. Considering different starting times of infection, mathematical models are proposed to represent SARS-CoV-2 dynamics in infected patients. Based on the target cell limited model, the within-host reproductive number for SARS-CoV-2 is consistent with the broad values of human influenza infection. The best model to fit the data was including immune cell response, which suggests a slow immune response peaking between 5 to 10 days post-onset of symptoms. The model with the eclipse phase, time in a latent phase before becoming productively infected cells, was not supported. Interestingly, model simulations predict that SARS-CoV-2 may replicate very slowly in the first days after infection, and viral load could be below detection levels during the first 4 days post infection. A quantitative comprehension of SARS-CoV-2 dynamics and the estimation of standard parameters of viral infections is the key contribution of this pioneering work. These models can serve for future evaluation of control theoretical approaches to tailor new drugs against COVID-19.

Host nutrition mediates interactions between plant viruses, altering transmission and predicted disease spread

Interactions among co-infecting pathogens are common across host taxa and can affect infectious disease dynamics. Host nutrition can mediate these among-pathogen interactions, altering the establishment and growth of pathogens within hosts. It is unclear, however, how nutrition-mediated among-pathogen interactions affect transmission and the spread of disease through populations. We manipulated the nitrogen (N) and phosphorus (P) supplies to oat plants in growth chambers and evaluated interactions between two aphid-vectored Barley and Cereal Yellow Dwarf Viruses: PAV and RPV. We quantified the effect of each virus on the other's establishment, within-plant density, and transmission. Co-inoculation significantly increased PAV density when N and P supplies were low and tended to increase RPV density when N supply was high. Co-infection increased PAV transmission when N and P supplies were low and tended to increase RPV transmission when N supply was high. Despite the parallels between the effects of among-pathogen interactions on density and transmission, changes in virus density only partially explained changes in transmission, suggesting that virus density-independent processes contribute to transmission. A mathematical model describing the spread of two viruses through a plant population, parameterized with empirically derived transmission values, demonstrated that nutrition-mediated among-pathogen interactions could affect disease spread. Interactions that altered transmission through virus density-independent processes determined overall disease dynamics. Our work suggests that host nutrition alters disease spread through among-pathogen interactions that modify transmission.

AN IMMUNO-EPIDEMIOLOGICAL VECTOR–HOST MODEL WITH WITHIN-VECTOR VIRAL KINETICS

A current challenge for disease modeling and public health is understanding pathogen dynamics across scales since their ecology and evolution ultimately operate on several coupled scales. This is particularly true for vector-borne diseases, where within-vector, within-host, and between vector–host populations all play crucial roles in diversity and distribution of the pathogen. Despite recent modeling efforts to determine the effect of within-host virus-immune response dynamics on between-host transmission, the role of within-vector viral dynamics on disease spread is overlooked. Here, we formulate an age-since-infection-structured epidemic model coupled to nonlinear ordinary differential equations describing within-host immune-virus dynamics and within-vector viral kinetics, with feedbacks across these scales. We first define the within-host viral-immune response and within-vector viral kinetics-dependent basic reproduction number [Formula: see text] Then we prove that whenever [Formula: see text] the disease-free equilibrium is locally asymptotically stable, and under certain biologically interpretable conditions, globally asymptotically stable. Otherwise, if [Formula: see text] it is unstable and the system has a unique positive endemic equilibrium. In the special case of constant vector to host inoculum size, we show the positive equilibrium is locally asymptotically stable and the disease is weakly uniformly persistent. Furthermore, numerical results suggest that within-vector-viral kinetics and dynamic inoculum size may play a substantial role in epidemics. Finally, we address how the model can be utilized to better predict the success of control strategies such as vaccination and drug treatment.

A theoretical framework for transitioning from patient-level to population-scale epidemiological dynamics: influenza A as a case study

Multi-scale epidemic forecasting models have been used to inform population-scale predictions with within-host models and/or infection data collected in longitudinal cohort studies. However, most multi-scale models are complex and require significant modelling expertise to run. We formulate an alternative multi-scale modelling framework using a compartmental model with multiple infected stages. In the large-compartment limit, our easy-to-use framework generates identical results compared to previous more complicated approaches. We apply our framework to the case study of influenza A in humans. By using a viral dynamics model to generate synthetic patient-level data, we explore the effects of limited and inaccurate patient data on the accuracy of population-scale forecasts. If infection data are collected daily, we find that a cohort of at least 40 patients is required for a mean population-scale forecasting error below 10%. Forecasting errors may be reduced by including more patients in future cohort studies or by increasing the frequency of observations for each patient. Our work, therefore, provides not only an accessible epidemiological modelling framework but also an insight into the data required for accurate forecasting using multi-scale models.

Virulence-mediated infectiousness and activity trade-offs and their impact on transmission potential of influenza patients

Communicable diseases are often virulent, i.e. they cause morbidity symptoms in those infected. While some symptoms may be transmission-enhancing, other symptoms are likely to reduce transmission potential. For human diseases, the reduction in transmission opportunities is commonly caused by reduced activity. There is limited data regarding the potential impact of virulence on transmission potential. We performed an exploratory data analysis of 324 influenza patients at a university health centre during the 2016/2017 influenza season. We classified symptoms as infectiousness-related or morbidity-related and calculated two scores. The scores were used to explore the relationship between infectiousness, morbidity (virulence), and activity level. We found a decrease in the activity level with increasing morbidity scores. There was no consistent pattern between an activity level and an infectiousness score. We also found a positive correlation between morbidity and infectiousness scores. Overall, we find that increasing virulence leads to increased infectiousness and reduced activity, suggesting a trade-off that can impact overall transmission potential. Our findings indicate that a reduction of systemic symptoms may increase host activity without reducing infectiousness. Therefore, interventions should target both systemic- and infectiousness-related symptoms to reduce overall transmission potential. Our findings can also inform simulation models that investigate the impact of different interventions on transmission.

A Mathematical Framework for Predicting Lifestyles of Viral Pathogens

Despite being similar in structure, functioning, and size, viral pathogens enjoy very different, usually well-defined ways of life. They occupy their hosts for a few days (influenza), for a few weeks (measles), or even lifelong (HCV), which manifests in acute or chronic infections. The various transmission routes (airborne, via direct physical contact, etc.), degrees of infectiousness (referring to the viral load required for transmission), antigenic variation/immune escape and virulence define further aspects of pathogenic lifestyles. To survive, pathogens must infect new hosts; the success determines their fitness. Infection happens with a certain likelihood during contact of hosts, where contact can also be mediated by vectors. Besides structural aspects of the host-contact network, three parameters appear to be key: the contact rate and the infectiousness during contact, which encode the mode of transmission, and third the immunity of susceptible hosts. On these grounds, what can be said about the reproductive success of viral pathogens? This is the biological question addressed in this paper. The answer extends earlier results of the author and makes explicit connection to another basic work on the evolution of pathogens. A mathematical framework is presented that models intra- and inter-host dynamics in a minimalistic but unified fashion covering a broad spectrum of viral pathogens, including those that cause flu-like infections, childhood diseases, and sexually transmitted infections. These pathogens turn out as local maxima of numerically simulated fitness landscapes. The models involve differential and integral equations, agent-based simulation, networks, and probability.

Parasite-Mediated Anorexia and Nutrition Modulate Virulence Evolution

Temporary but substantial reductions in voluntary food intake routinely accompany parasite infection in hosts ranging from insects to humans. This "parasite-mediated anorexia" drives dynamic nutrient-dependent feedbacks within and among hosts, which should alter the fitness of both hosts and parasites. Yet, few studies have examined the evolutionary and epidemiological consequences of this ubiquitous but overlooked component of infection. Moreover, numerous biomedical, veterinary, and farming practices (e.g., rapid biomass production via high-calorie or high-fat diets, low-level antibiotics to promote growth, nutritional supplementation, nonsteroidal anti-inflammatory drugs like Ibuprofen) directly or indirectly alter the magnitude of host anorexia-while also controlling host diet and therefore the nutrients available to hosts and parasites. Here, we show that anorexia can enhance or diminish disease severity, depending on whether the current dietary context provides nutrients that bolster or inhibit immune function. Feedbacks driven by nutrition-mediated competition between host immune function and parasite production can create a unimodal relationship between anorexia and parasite fitness. Subsequently, depending on the host's diet, medical or husbandry practices that suppress anorexia could backfire, and inadvertently select for more virulent parasites and larger epidemics. These findings carry implications for the development of integrated treatment programs that consider links between host feeding behavior, nutrition, and disease severity.

Modeling the Effects of Resource-Driven Immune Defense on Parasite Transmission in Heterogeneous Host Populations

Individuals experience heterogeneous environmental conditions that can affect within-host processes such as immune defense against parasite infection. Variation among individuals in parasite shedding can cause some hosts to contribute disproportionately to population-level transmission, but we currently lack mechanistic theory that predicts when environmental conditions can result in large disease outbreaks through the formation of immunocompromised superspreading individuals. Here, I present a within-host model of a microparasite's interaction with the immune system that links an individual host's resource intake to its infectious period. For environmental scenarios driving population-level heterogeneity in resource intake (resource scarcity and resource subsidy relative to baseline availability), I generate a distribution of infectious periods and simulate epidemics on these heterogeneous populations. I find that resource scarcity can result in large epidemics through creation of superspreading individuals, while resource subsidies can reduce or prevent transmission of parasites close to their invasion threshold by homogenizing resource allocation to immune defense. Importantly, failure to account for heterogeneity in competence can result in under-prediction of outbreak size, especially when parasites are close to their invasion threshold. More generally, this framework suggests that differences in conditions experienced by individual hosts can lead to superspreading via differences in resource allocation to immune defense alone, even in the absence of other heterogeneites such as host contacts.

Multi-Scale Drivers of Immunological Variation and Consequences for Infectious Disease Dynamics

The immune system is the primary barrier to parasite infection, replication, and transmission following exposure, and variation in immunity can accordingly manifest in heterogeneity in traits that govern population-level infectious disease dynamics. While much work in ecoimmunology has focused on individual-level determinants of host immune defense (e.g., reproductive status and body condition), an ongoing challenge remains to understand the broader evolutionary and ecological contexts of this variation (e.g., phylogenetic relatedness and landscape heterogeneity) and to connect these differences into epidemiological frameworks. Ultimately, such efforts could illuminate general principles about the drivers of host defense and improve predictions and control of infectious disease. Here, we highlight recent work that synthesizes the complex drivers of immunological variation across biological scales of organization and scales these within-host differences to population-level infection outcomes. Such studies note the limitations involved in making species-level comparisons of immune phenotypes, stress the importance of spatial scale for immunology research, showcase several statistical tools for translating within-host data into epidemiological parameters, and provide theoretical frameworks for linking within- and between-host scales of infection processes. Building from these studies, we highlight several promising avenues for continued work, including the application of machine learning tools and phylogenetically controlled meta-analyses to immunology data and quantifying the joint spatial and temporal dependencies in immune defense using range expansions as model systems. We also emphasize the use of organismal traits (e.g., host tolerance, competence, and resistance) as a way to interlink various scales of analysis. Such continued collaboration and disciplinary cross-talk among ecoimmunology, disease ecology, and mathematical modeling will facilitate an improved understanding of the multi-scale drivers and consequences of variation in host defense.

Infection severity across scales in multi-strain immuno-epidemiological Dengue model structured by host antibody level

Infection by distinct Dengue virus serotypes and host immunity are intricately linked. In particular, certain levels of cross-reactive antibodies in the host may actually enhance infection severity leading to Dengue hemorrhagic fever (DHF). The coupled immunological and epidemiological dynamics of Dengue calls for a multi-scale modeling approach. In this work, we formulate a within-host model which mechanistically recapitulates characteristics of antibody dependent enhancement in Dengue infection. The within-host scale is then linked to epidemiological spread by a vector-host partial differential equation model structured by host antibody level. The coupling allows for dynamic population-wide antibody levels to be tracked through primary and secondary infections by distinct Dengue strains, along with waning of cross-protective immunity after primary infection. Analysis of both the within-host and between-host systems are conducted. Stability results in the epidemic model are formulated via basic and invasion reproduction numbers as a function of immunological variables. Additionally, we develop numerical methods in order to simulate the multi-scale model and assess the influence of parameters on disease spread and DHF prevalence in the population.

Survival dynamical systems: individual-level survival analysis from population-level epidemic models

In this paper, we show that solutions to ordinary differential equations describing the large-population limits of Markovian stochastic epidemic models can be interpreted as survival or cumulative hazard functions when analysing data on individuals sampled from the population. We refer to the individual-level survival and hazard functions derived from population-level equations as a survival dynamical system (SDS). To illustrate how population-level dynamics imply probability laws for individual-level infection and recovery times that can be used for statistical inference, we show numerical examples based on synthetic data. In these examples, we show that an SDS analysis compares favourably with a complete-data maximum-likelihood analysis. Finally, we use the SDS approach to analyse data from a 2009 influenza A(H1N1) outbreak at Washington State University.

Linking community assembly and structure across scales in a wild mouse parasite community

Understanding what processes drive community structure is fundamental to ecology. Many wild animals are simultaneously infected by multiple parasite species, so host-parasite communities can be valuable tools for investigating connections between community structures at multiple scales, as each host can be considered a replicate parasite community. Like free-living communities, within-host-parasite communities are hierarchical; ecological interactions between hosts and parasites can occur at multiple scales (e.g., host community, host population, parasite community within the host), therefore, both extrinsic and intrinsic processes can determine parasite community structure. We combine analyses of community structure and assembly at both the host population and individual scales using extensive datasets on wild wood mice (Apodemus sylvaticus) and their parasite community. An analysis of parasite community nestedness at the host population scale provided predictions about the order of infection at the individual scale, which were then tested using parasite community assembly data from individual hosts from the same populations. Nestedness analyses revealed parasite communities were significantly more structured than random. However, observed nestedness did not differ from null models in which parasite species abundance was kept constant. We did not find consistency between observed community structure at the host population scale and within-host order of infection. Multi-state Markov models of parasite community assembly showed that a host's likelihood of infection with one parasite did not consistently follow previous infection by a different parasite species, suggesting there is not a deterministic order of infection among the species we investigated in wild wood mice. Our results demonstrate that patterns at one scale (i.e., host population) do not reliably predict processes at another scale (i.e., individual host), and that neutral or stochastic processes may be driving the patterns of nestedness observed in these communities. We suggest that experimental approaches that manipulate parasite communities are needed to better link processes at multiple ecological scales.

Starving the Enemy? Feeding Behavior Shapes Host-Parasite Interactions

The loss of appetite that typically accompanies infection or mere exposure to parasites is traditionally considered a negative byproduct of infection, benefitting neither the host nor the parasite. Numerous medical and veterinary practices directly or indirectly subvert this 'illness-mediated anorexia'. However, the ecological factors that influence it, its effects on disease outcomes, and why it evolved remain poorly resolved. We explore how hosts use anorexia to defend against infection and how parasites manipulate anorexia to enhance transmission. Then, we use a coevolutionary model to illustrate how shifts in the magnitude of anorexia (e.g., via drugs) affect disease dynamics and virulence evolution. Anorexia could be exploited to improve disease management; we propose an interdisciplinary approach to minimize unintended consequences.

Improving risk assessment of the emergence of novel influenza A viruses by incorporating environmental surveillance

Reassortment is an evolutionary mechanism by which influenza A viruses (IAV) generate genetic novelty. Reassortment is an important driver of host jumps and is widespread according to retrospective surveillance studies. However, predicting the epidemiological risk of reassortant emergence in novel hosts from surveillance data remains challenging. IAV strains persist and co-occur in the environment, promoting co-infection during environmental transmission. These conditions offer opportunity to understand reassortant emergence in reservoir and spillover hosts. Specifically, environmental RNA could provide rich information for understanding the evolutionary ecology of segmented viruses, and transform our ability to quantify epidemiological risk to spillover hosts. However, significant challenges with recovering and interpreting genomic RNA from the environment have impeded progress towards predicting reassortant emergence from environmental surveillance data. We discuss how the fields of genomics, experimental ecology and epidemiological modelling are well positioned to address these challenges. Coupling quantitative disease models and natural transmission studies with new molecular technologies, such as deep-mutational scanning and single-virus sequencing of environmental samples, should dramatically improve our understanding of viral co-occurrence and reassortment. We define observable risk metrics for emerging molecular technologies and propose a conceptual research framework for improving accuracy and efficiency of risk prediction. This article is part of the theme issue 'Dynamic and integrative approaches to understanding pathogen spillover'.

How parasite interaction strategies alter virulence evolution in multi-parasite communities

The majority of organisms host multiple parasite species, each of which can interact with hosts and competitors through a diverse range of direct and indirect mechanisms. These within-host interactions can directly alter the mortality rate of coinfected hosts and alter the evolution of virulence (parasite-induced host mortality). Yet we still know little about how within-host interactions affect the evolution of parasite virulence in multi-parasite communities. Here, we modeled the virulence evolution of two coinfecting parasites in a host population in which parasites interacted through cross immunity, immune suppression, immunopathology, or spite. We show (1) that these within-host interactions have different effects on virulence evolution when all parasites interact with each other in the same way versus when coinfecting parasites have unique interaction strategies, (2) that these interactions cause the evolution of lower virulence in some hosts, and higher virulence in other hosts, depending on the hosts infection status, and (3) that for cross immunity and spite, whether parasites increase or decrease the evolutionarily stable virulence in coinfected hosts depended on interaction strength. These results improve our understanding of virulence evolution in complex parasite communities, and show that virulence evolution must be understood at the community scale.

Linked within-host and between-host models and data for infectious diseases: a systematic review

The observed dynamics of infectious diseases are driven by processes across multiple scales. Here we focus on two: within-host, that is, how an infection progresses inside a single individual (for instance viral and immune dynamics), and between-host, that is, how the infection is transmitted between multiple individuals of a host population. The dynamics of each of these may be influenced by the other, particularly across evolutionary time. Thus understanding each of these scales, and the links between them, is necessary for a holistic understanding of the spread of infectious diseases. One approach to combining these scales is through mathematical modeling. We conducted a systematic review of the published literature on multi-scale mathematical models of disease transmission (as defined by combining within-host and between-host scales) to determine the extent to which mathematical models are being used to understand across-scale transmission, and the extent to which these models are being confronted with data. Following the PRISMA guidelines for systematic reviews, we identified 24 of 197 qualifying papers across 30 years that include both linked models at the within and between host scales and that used data to parameterize/calibrate models. We find that the approach that incorporates both modeling with data is under-utilized, if increasing. This highlights the need for better communication and collaboration between modelers and empiricists to build well-calibrated models that both improve understanding and may be used for prediction.

The effect of the infection within the individual host on its propagation in the population

We consider nested or multiscale models to study the effect of the temporal evolution of the disease within the host in the population dynamics of the disease, for one and two infectious agents. We assumed a coupling between the within-host infection rate and the between-host transmission rate. The age of infection within each individual in a population affects the probability of transmission of the disease to a susceptible host and this will affect the temporal evolution of the disease in the host population. To analyze the infection within the host, we consider bacterial-like and viral-like infections. In the model for two infectious agents, we found that, when strain 2 has a basic reproduction number R 02 greater than the basic reproduction number R 01 of strain 1, strain 2 replaces strain 1 in the population. However, if R 02 > R 01 but the values are closer, the replacement does not occur immediately and both strains can coexist for a long time. We applied the model to a scenario in which patients infected with the hepatitis C virus (HCV) are cleared of HCV when super-infected with the hepatitis A virus (HAV). We compared the time for the replacement of HCV by HAV in the population considering instantaneous and non-instantaneous replacement within the individuals. The model developed can be generalized for more than two infectious agents.

Resource-driven changes to host population stability alter the evolution of virulence and transmission

What drives the evolution of parasite life-history traits? Recent studies suggest that linking within- and between-host processes can provide key insight into both disease dynamics and parasite evolution. Still, it remains difficult to understand how to pinpoint the critical factors connecting these cross-scale feedbacks, particularly under non-equilibrium conditions; many natural host populations inherently fluctuate and parasites themselves can strongly alter the stability of host populations. Here, we develop a general model framework that mechanistically links resources to parasite evolution across a gradient of stable and unstable conditions. First, we dynamically link resources and between-host processes (host density, stability, transmission) to virulence evolution, using a 'non-nested' model. Then, we consider a 'nested' model where population-level processes (transmission and virulence) depend on resource-driven changes to individual-level (within-host) processes (energetics, immune function, parasite production). Contrary to 'non-nested' model predictions, the 'nested' model reveals complex effects of host population dynamics on parasite evolution, including regions of evolutionary bistability; evolution can push parasites towards strongly or weakly stabilizing strategies. This bistability results from dynamic feedbacks between resource-driven changes to host density, host immune function and parasite production. Together, these results highlight how cross-scale feedbacks can provide key insights into the structuring role of parasites and parasite evolution.This article is part of the theme issue 'Anthropogenic resource subsidies and host-parasite dynamics in wildlife'.

Extreme Competence: Keystone Hosts of Infections

Individual hosts differ extensively in their competence for parasites, but traditional research has discounted this variation, partly because modeling such heterogeneity is difficult. This discounting has diminished as tools have improved and recognition has grown that some hosts, the extremely competent, can have exceptional impacts on disease dynamics. Most prominent among these hosts are the superspreaders, but other forms of extreme competence (EC) exist and others await discovery; each with potentially strong but distinct implications for disease emergence and spread. Here, we propose a framework for the study and discovery of EC, suitable for different host-parasite systems, which we hope enhances our understanding of how parasites circulate and evolve in host communities.

Coupling multiscale within-host dynamics and between-host transmission with recovery (SIR) dynamics

Multiscale models that link within-host infection to between-host transmission are valuable tools to progress understanding of viral infectious diseases. In this paper, we present two multiscale models that couple within-host infection to a susceptible-infected-recovered (SIR) model. A disease-induced transmission rate bridges the scales from within to between-host. Our stability analysis on the first model (influenza infection) reveals two equilibrium points for the SIR model that describe endemic scenarios where both susceptible and infected cases maintain nonzero population sizes. Consequently, the between-host system has two bifurcations determined by the corresponding basic reproduction number of the within-host and the size of the infected population at the interior equilibrium point. Analysis on the second model (Ebola infection) reveals the limited transient inhibitory effect of antibodies on viral replication, which influences the time window from infection to a potential outbreak. Simulations numerically illustrate our results.