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

The progression of an infection within a host determines the ability of a pathogen to transmit to new hosts and to maintain itself in the population. While the general connection between the infection dynamics within a host and the population-level transmission dynamics of pathogens is widely acknowledged, a comprehensive and quantitative understanding that would allow full integration of the two scales is still lacking. Here, we provide a brief discussion of both models and data that have attempted to provide quantitative mappings from within-host infection dynamics to transmission fitness. We present a conceptual framework and provide examples of studies that have taken first steps towards development of a quantitative framework that scales from within-host infections to population-level fitness of different pathogens. We hope to illustrate some general themes, summarize some of the recent advances and—maybe most importantly—discuss gaps in our ability to bridge these scales, and to stimulate future research on this important topic.     

A mathematical model for Chagas disease with infection-age-dependent infectivity

In this paper we develop a mathematical model for Chagas disease with infection-age-dependent infectivity. The effects of vector and blood transfusion transmission are considered, and the infected population is structured by the infection age (the time elapsed from infection). The authors identify the basic reproduction ratio R0 and show that the disease can invade into the susceptible population and unique endemic steady state exists if R0 > 1, whereas the disease dies out if R0 is small enough. We show that depending on parameters, backward bifurcation of endemic steady state can occur, so even if R0 < 1, there could exist endemic steady states. We also discuss local and global stability of steady states.     

在有限资源条件下的肺结核模型研究

讨论了有限资源下的肺结核模型,得到了基本再生数,考虑了模型的双稳定性,用第二加型复合矩阵研究了模型平衡点的全局渐近稳定性．最后数值模拟验证理论结果．     

Dynamic phenomena arising from an extended Core Group model

In order to obtain a reasonably accurate model for the spread of a particular infectious disease through a population, it may be necessary for this model to possess some degree of structural complexity. Many such models have, in recent years, been found to exhibit a phenomenon known as backward bifurcation, which generally implies the existence of two subcritical endemic equilibria. It is often possible to refine these models yet further, and we investigate here the influence such a refinement may have on the dynamic behaviour of a system in the region of the parameter space near R₀=1.We consider a natural extension to a so-called Core Group model for the spread of a sexually transmitted disease, arguing that this may in fact give rise to a more realistic model. From the deterministic viewpoint we study the possible shapes of the resulting bifurcation diagrams and the associated stability patterns. Stochastic versions of both the original and the extended models are also developed so that the probability of extinction and time to extinction may be examined, allowing us to gain further insights into the complex system dynamics near R₀=1. A number of interesting phenomena are observed, for which heuristic explanations are provided.     

Forward hysteresis and backward bifurcation caused by culling in an avian influenza model

The emerging threat of a human pandemic caused by the H5N1 avian influenza virus strain magnifies the need for controlling the incidence of H5N1 infection in domestic bird populations. Culling is one of the most widely used control measures and has proved effective for isolated outbreaks. However, the socio-economic impacts of mass culling, in the face of a disease which has become endemic in many regions of the world, can affect the implementation and success of culling as a control measure. We use mathematical modeling to understand the dynamics of avian influenza under different culling approaches. We incorporate culling into an SI model by considering the per capita culling rates to be general functions of the number of infected birds. Complex dynamics of the system, such as backward bifurcation and forward hysteresis, along with bi-stability, are detected and analyzed for two distinct culling scenarios. In these cases, employing other control measures temporarily can drastically change the dynamics of the solutions to a more favorable outcome for disease control.     

The minimum effort required to eradicate infections in models with backward bifurcation

We study an epidemiological model which assumes that the susceptibility after a primary infection is r times the susceptibility before a primary infection. For r = 0 (r = 1) this is the SIR (SIS) model. For r > 1 + (μ/α) this model shows backward bifurcations, where μ is the death rate and α is the recovery rate. We show for the first time that for such models we can give an expression for the minimum effort required to eradicate the infection if we concentrate on control measures affecting the transmission rate constant β. This eradication effort is explicitly expressed in terms of α,r, and μ As in models without backward bifurcation it can be interpreted as a reproduction number, but not necessarily as the basic reproduction number. We define the relevant reproduction numbers for this purpose. The eradication effort can be estimated from the endemic steady state. The classical basic reproduction number R ₀ is smaller than the eradication effort for r > 1 + (μ/α) and equal to the effort for other values of r. The method we present is relevant to the whole class of compartmental models with backward bifurcation.Dedicated to Karl Peter Hadeler on the occasion of his 70th birthday.     

Poverty trap formed by the ecology of infectious diseases

While most of the world has enjoyed exponential economic growth, more than one-sixth of the world is today roughly as poor as their ancestors were many generations ago. Widely accepted general explanations for the persistence of such poverty have been elusive and are needed by the international development community. Building on a well-established model of human infectious diseases, we show how formally integrating simple economic and disease ecology models can naturally give rise to poverty traps, where initial economic and epidemiological conditions determine the long-term trajectory of the health and economic development of a society. This poverty trap may therefore be broken by improving health conditions of the population. More generally, we demonstrate that simple human ecological models can help explain broad patterns of modern economic organization.     

Examining the Links between Biodiversity and Human Health: An Interdisciplinary Research Initiative at the U.S. Environmental Protection Agency

Under the U.S. Environmental Protection Agency’s mission to protect human health and the environment, the agency seeks to conduct research on the structure and function of ecosystems and to improve our understanding of the processes that contribute to the sustained health of the nation’s ecosystems and the well-being of human populations. Changes in biodiversity can profoundly impact the ability of ecosystems to provide clean water, energy, food, recreation, and other services that contribute to human well-being. In addition, changes in biodiversity can affect the transmission of infectious disease to humans, particularly vectorborne diseases such as malaria and Lyme disease. The Environmental Protection Agency’s new initiative supports interdisciplinary research to characterize the mechanisms that link biodiversity and human health and to use this knowledge to develop integrative tools and approaches for quantifying and predicting these relationships. Research on these links can have an important impact on our view of biodiversity and how we manage resources to protect human and ecosystem health. Disclaimer: This work was funded in part under Grant #CX3-832328 with the American Association for the Advance of Science (AAAS). The views expressed do not necessarily reflect the views of the Environmental Protection Agency.     

Distribution and Impacts of Tasmanian Devil Facial Tumor Disease

The Tasmanian devil, Sarcophilus harrisii, is the largest extant marsupial carnivore. In 1996, a debilitating facial tumor was reported. It is now clear that this is an invariably lethal infectious cancer. The disease has now spread across the majority of the range of the species and is likely to occur across the entire range within 5 to 10 years. The disease has lead to continuing declines of up to 90% and virtual disappearance of older age classes. Mark-recapture analysis and a preliminary epidemiological model developed for the population with the best longitudinal data both project local extinction in that area over a timeframe of 10 to 15 years from disease emergence. However, the prediction of extinction from the model is sensitive to the estimate of the latent period, which is poorly known. As transmission appears to occur by biting, much of which happens during sexual encounters, the dynamics of the disease may be typical of sexually transmitted diseases. This means that transmission is likely to be frequency-dependent with no threshold density for disease maintenance. Extinction over the entire current range of the devil is therefore a real possibility and an unacceptable risk.     

Source-sink dynamics shape the evolution of antibiotic resistance and its pleiotropic fitness cost

Understanding the conditions that favour the evolution and maintenance of antibiotic resistance is the central goal of epidemiology. A crucial feature explaining the adaptation to harsh, or 'sink', environments is the supply of beneficial mutations via migration from a 'source' population. Given that antibiotic resistance is frequently associated with antagonistic pleiotropic fitness costs, increased migration rate is predicted not only to increase the rate of resistance evolution but also to increase the probability of fixation of resistance mutations with minimal fitness costs. Here we report in vitro experiments using the nosocomial pathogenic bacterium Pseudomonas aeruginosa that support these predictions: increasing rate of migration into environments containing antibiotics increased the rate of resistance evolution and decreased the associated costs of resistance. Consistent with previous theoretical work, we found that resistance evolution arose more rapidly in the presence of a single antibiotic than two. Evolution of resistance was also more rapid when bacteria were subjected to sequential exposure with two antibiotics (cycling therapy) compared with simultaneous exposure (bi-therapy). Furthermore, pleiotropic fitness costs of resistance to two antibiotics were higher than for one antibiotic, and were also higher under bi-therapy than cycling therapy, although the cost of resistance depended on the order of the antibiotics through time. These results may be relevant to the clinical setting where immigration is known to be important between chemotherapeutically treated patients, and demonstrate the importance of ecological and evolutionary dynamics in the control of antibiotic resistance.     

The probability of extinction in a bovine respiratory syncytial virus epidemic model

Backward bifurcation is a relatively recent yet well-studied phenomenon associated with deterministic epidemic models. It allows for the presence of multiple subcritical endemic equilibria, and is generally found only in models possessing a reasonable degree of complexity. One particular aspect of backward bifurcation that appears to have been virtually overlooked in the literature is the potential influence its presence might have on the behaviour of any analogous stochastic model. Indeed, the primary aim of this paper is to investigate this possibility. Our approach is to compare the theoretical probabilities of extinction, calculated via a particular stochastic formulation of a deterministic model exhibiting backward bifurcation, with those obtained from a series of stochastic simulations. We have found some interesting links in the behaviour between the deterministic and stochastic models, and are able to offer plausible explanations for our observations.     

Influence of backward bifurcation in a model of hepatitis B and C viruses

In the 1990s, liver transplantation for hepatitis B and C virus (HBV and HCV) related-liver diseases was a very controversial issue since recurrent infection of the graft was inevitable. Significant progress has been made in the prophylaxis and treatment of recurrent hepatitis B/C (or HBV/HCV infection) after liver transplantation. In this paper, we propose a mathematical model of ordinary differential equations describing the dynamics of the HBV/HCV and its interaction with both liver and blood cells. A single model is used to describe infection of either virus since the dynamics in-host (infected of the liver) are similar. Analyzing the model, we observe that the system shows either a transcritical or a backward bifurcation. Explicit conditions on the model parameters are given for the backward bifurcation to be present. Consequently, we investigate possible factors that are responsible for HBV/HCV infection and assess control strategies to reduce HBV/HCV reinfection and improve graft survival after liver transplantation.     

Inferring patterns of influenza transmission in swine from multiple streams of surveillance data

Swine populations are known to be an important source of new human strains of influenza A, including those responsible for global pandemics. Yet our knowledge of the epidemiology of influenza in swine is dismayingly poor, as highlighted by the emergence of the 2009 pandemic strain and the paucity of data describing its origins. Here, we analyse a unique dataset arising from surveillance of swine influenza at a Hong Kong abattoir from 1998 to 2010. We introduce a state–space model that estimates disease exposure histories by joint inference from multiple modes of surveillance, integrating both virological and serological data. We find that an observed decrease in virus isolation rates is not due to a reduction in the regional prevalence of influenza. Instead, a more likely explanation is increased infection of swine in production farms, creating greater immunity to disease early in life. Consistent with this, we find that the weekly risk of exposure on farms equals or exceeds the exposure risk during transport to slaughter. We discuss potential causes for these patterns, including competition between influenza strains and shifts in the Chinese pork industry, and suggest opportunities to improve knowledge and reduce prevalence of influenza in the region.     

Backward bifurcations and multiple equilibria in epidemic models with structured immunity

Many disease pathogens stimulate immunity in their hosts, which then wanes over time. To better understand the impact of this immunity on epidemiological dynamics, we propose an epidemic model structured according to immunity level that can be applied in many different settings. Under biologically realistic hypotheses, we find that immunity alone never creates a backward bifurcation of the disease-free steady state. This does not rule out the possibility of multiple stable equilibria, but we provide two sufficient conditions for the uniqueness of the endemic equilibrium, and show that these conditions ensure uniqueness in several common special cases. Our results indicate that the within-host dynamics of immunity can, in principle, have important consequences for population-level dynamics, but also suggest that this would require strong non-monotone effects in the immune response to infection. Neutralizing antibody titer data for measles are used to demonstrate the biological application of our theory.     

Enemies and turncoats: bovine tuberculosis exposes pathogenic potential of Rift Valley fever virus in a common host,African buffalo (Syncerus caffer)

The ubiquity and importance of parasite co-infections in populations of free-living animals is beginning to be recognized, but few studies have demonstrated differential fitness effects of single infection versus co-infection in free-living populations. We investigated interactions between the emerging bacterial disease bovine tuberculosis (BTB) and the previously existing viral disease Rift Valley fever (RVF) in a competent reservoir host, African buffalo, combining data from a natural outbreak of RVF in captive buffalo at a buffalo breeding facility in 2008 with data collected from a neighbouring free-living herd of African buffalo in Kruger National Park. RVF infection was twice as likely in individual BTB+ buffalo as in BTB− buffalo, which, according to a mathematical model, may increase RVF outbreak size at the population level. In addition, co-infection was associated with a far higher rate of fetal abortion than other infection states. Immune interactions between BTB and RVF may underlie both of these interactions, since animals with BTB had decreased innate immunity and increased pro-inflammatory immune responses. This study is one of the first to demonstrate how the consequences of emerging infections extend beyond direct effects on host health, potentially altering the dynamics and fitness effects of infectious diseases that had previously existed in the ecosystem on free-ranging wildlife populations.