On the definition and the computation of the type-reproduction number T for structured populations in heterogeneous environments

In the context of mathematical epidemiology, the type-reproduction number (TRN) for a specific host type is interpreted as the average number of secondary cases of that type produced by the primary cases of the same host type during the entire course of infection. Here, it must be noted that T takes into account not only the secondary cases directly transmitted from the specific host but also the cases indirectly transmitted by way of other types, who were infected from the primary cases of the specific host with no intermediate cases of the target host. Roberts and Heesterbeek (Proc R Soc Lond B 270:1359–1364, 2003) have shown that T is a useful measure when a particular single host type is targeted in the disease control effort in a community with various types of host, based on the fact that the sign relation sign(R ₀ ? 1) = sign(T ? 1) holds between the basic reproduction number R ₀ and T. In fact, T can be seen as an extension of R ₀ in a sense that the threshold condition of the total population growth can be formulated by the reproduction process of the target type only. However, the original formulation is limited to populations with discrete state space in constant environments. In this paper, based on a new perspective of R ₀ in heterogeneous environments (Inaba in J Math Biol 2011), we give a general definition of the TRN for continuously structured populations in heterogeneous environments and show some examples of its computation and applications.     

The type-reproduction number T in models for infectious disease control

A ubiquitous quantity in epidemic modelling is the basic reproduction number R(0). This became so popular in the 1990s that 'All you need know is R(0)!' became a familiar catch-phrase. The value of R(0) defines, among other things, the control effort needed to eliminate the infection from a homogeneous host population, but can be misleading when applied to a heterogeneous population for the same purpose. We have defined the type-reproduction number T for an infectious disease, and shown that this not only has the required threshold behaviour, but also correctly determines the critical control effort for heterogeneous populations. The two quantities coincide for homogeneous populations. In this paper we further develop the new threshold quantity as an indicator of control effort required in a system where multiple types of individuals are recognised when control targets a specific type.     

On the Role of Asymptomatic Infection in Transmission Dynamics of Infectious Diseases

We propose a compartmental disease transmission model with an asymptomatic (or subclinical) infective class to study the role of asymptomatic infection in the transmission dynamics of infectious diseases with asymptomatic infectives, e.g., influenza. Analytical results are obtained using the respective ratios of susceptible, exposed (incubating), and asymptomatic classes to the clinical symptomatic infective class. Conditions are given for bistability of equilibria to occur, where trajectories with distinct initial values could result in either a major outbreak where the disease spreads to the whole population or a lesser outbreak where some members of the population remain uninfected. This dynamic behavior did not arise in a SARS model without asymptomatic infective class studied by Hsu and Hsieh (SIAM J. Appl. Math. 66(2), 627–647, 2006). Hence, this illustrates that depending on the initial states, control of a disease outbreak with asymptomatic infections may involve more than simply reducing the reproduction number. Moreover, the presence of asymptomatic infections could result in either a positive or negative impact on the outbreak, depending on different sets of conditions on the parameters, as illustrated with numerical simulations. Biological interpretations of the analytical and numerical results are also given.     

Clinical Experience with Flexible Sigmoidoscopy in Asymptomatic and Symptomatic Patients

The purpose of this study was to evaluate the diagnostic yield of flexible sigmoidoscopy when performed as a routine procedure in asymptomatic patients over the age of 40 being referred for a complete physical examination. The preliminary results of this ongoing program are presented together with the diagnostic yield in 408 patients with symptoms and signs suggestive of colorectal disease who were of similar age (56.6 vs. 56.5 years) and sex distribution (79 percent male) to the asymptomatic population, and who underwent flexible sigmoidoscopy as an indicated part of their evaluation. In the 122 asymptomatic patients, the mean distance examined by the procedure was 50.8 cm with the instrument being advanced beyond the optimal rigid sigmoidoscopy distance of 20 cm in 100 percent of patients. Adenomatous and hyperplastic polyps were identified in 16 patients, 13.1 percent, in the asymptomatic group, a similar percentage to the symptomatic population, 15.4 percent. Adenomatous polyps were diagnosed in 7.4 percent of the asymptomatic subjects and 9.1 percent of the symptomatic group. Colonic cancer was diagnosed in 0.8 percent of asymptomatic patients vs. 3.2 percent of the symptomatic group (p < 0.05). Seventy-seven percent of the neoplastic polyps detected in the asymptomatic patients and 60 percent in the symptomatic group were beyond 20 cm from the anus. Diverticulosis was diagnosed in a similar percentage of patients, 13.1 percent in the asymptomatic and 10.0 percent in the symptomatic group. No complications were encountered and the procedure was well tolerated without analgesia. It is concluded that: (1) in an asymptomatic population over the age of 40, flexible sigmoidoscopy, as a routine examination, results in a diagnostic yield not possible with rigid proctosigmoidoscopy and which approaches that observed in a symptomatic population of similar age; (2) for the internist trained in this procedure, flexible sigmoidoscopy has a future role in the detection of colorectal lesions and as an interval screening examination for premalignant lesions and colorectal cancer in asymptomatic and symptomatic patients.     

The model of Kermack and McKendrick for the plague epidemic in Bombay and the type reproduction number with seasonality

The figure showing how the model of Kermack and McKendrick fits the data from the 1906 plague epidemic in Bombay is the most reproduced figure in books discussing mathematical epidemiology. In this paper we show that the assumption of constant parameters in the model leads to quite unrealistic numerical values for these parameters. Moreover the reports published at the time show that plague epidemics in Bombay occurred in fact with a remarkable seasonal pattern every year since 1897 and at least until 1911. So the 1906 epidemic is clearly not a good example of epidemic stopping because the number of susceptible humans has decreased under a threshold, as suggested by Kermack and McKendrick, but an example of epidemic driven by seasonality. We present a seasonal model for the plague in Bombay and compute the type reproduction numbers associated with rats and fleas, thereby extending to periodic models the notion introduced by Roberts and Heesterbeek.     

Disease‐structured N‐mixture models: A practical guide to model disease dynamics using count data

Obtaining inferences on disease dynamics (e.g., host population size, pathogen prevalence, transmission rate, host survival probability) typically requires marking and tracking individuals over time. While multistate mark–recapture models can produce high‐quality inference, these techniques are difficult to employ at large spatial and long temporal scales or in small remnant host populations decimated by virulent pathogens, where low recapture rates may preclude the use of mark–recapture techniques. Recently developed N‐mixture models offer a statistical framework for estimating wildlife disease dynamics from count data. N‐mixture models are a type of state‐space model in which observation error is attributed to failing to detect some individuals when they are present (i.e., false negatives). The analysis approach uses repeated surveys of sites over a period of population closure to estimate detection probability. We review the challenges of modeling disease dynamics and describe how N‐mixture models can be used to estimate common metrics, including pathogen prevalence, transmission, and recovery rates while accounting for imperfect host and pathogen detection. We also offer a perspective on future research directions at the intersection of quantitative and disease ecology, including the estimation of false positives in pathogen presence, spatially explicit disease‐structured N‐mixture models, and the integration of other data types with count data to inform disease dynamics. Managers rely on accurate and precise estimates of disease dynamics to develop strategies to mitigate pathogen impacts on host populations. At a time when pathogens pose one of the greatest threats to biodiversity, statistical methods that lead to robust inferences on host populations are critically needed for rapid, rather than incremental, assessments of the impacts of emerging infectious diseases.     

Threshold conditions for infection persistence in complex host-vectors interactions

As classically defined by Macdonald in the early 1950s, for the case of diseases with one vector and one host, the Basic Reproduction Number, R0, is defined as the number of secondary infections caused by a single infective of the same type (vector or host) during its infectiousness period in an entirely susceptible population. In the case of a disease which has one vector and one host, it is easy to show that R0 coincides with the threshold for the establishment of an endemic state: if R0 > 1 (< 1), the disease can invade (cannot invade) the host population. In this paper we examine various epidemic situations in which there are more than one vector and/or host. We show that in those more complex systems it is not possible to deduce a single R0 but rather a threshold for infection persistence which is a composite of several quantities closely related to the classical expression of R0. Another definition of R0 given by Diekmann, Heesterbeek and Metz, and denoted in this paper R0NGO is discussed and applied as an alternative to calculate the thresholds for infection establishment.     

A model of the Ebola epidemics in West Africa incorporating age of infection

A model of an Ebola epidemic is developed with infected individuals structured according to disease age. The transmission of the infection is tracked by disease age through an initial incubation (exposed) phase, followed by an infectious phase with variable transmission infectiousness. The removal of infected individuals is dependent on disease age, with three types of removal rates: (1) removal due to hospitalization (isolation), (2) removal due to mortality separate from hospitalization, and (3) removal due to recovery separate from hospitalization. The model is applied to the Ebola epidemics in Sierra Leone and Guinea. Model simulations indicate that successive stages of increased and earlier hospitalization of cases have resulted in mitigation of the epidemics.     

Age-related model for estimating the symptomatic and asymptomatic transmissibility of COVID-19 patients

Estimation of age-dependent transmissibility of COVID-19 patients is critical for effective policymaking. Although the transmissibility of symptomatic cases has been extensively studied, asymptomatic infection is understudied due to limited data. Using a dataset with reliably distinguished symptomatic and asymptomatic statuses of COVID-19 cases, we propose an ordinary differential equation model that considers age-dependent transmissibility in transmission dynamics. Under a Bayesian framework, multi-source information is synthesized in our model for identifying transmissibility. A shrinkage prior among age groups is also adopted to improve the estimation behavior of transmissibility from age-structured data. The added values of accounting for age-dependent transmissibility are further evaluated through simulation studies. In real-data analysis, we compare our approach with two basic models using the deviance information criterion (DIC) and its extension. We find that the proposed model is more flexible for our epidemic data. Our results also suggest that the transmissibility of asymptomatic infections is significantly lower (on average, 76.45% with a credible interval (27.38%, 88.65%)) than that of symptomatic cases. In both symptomatic and asymptomatic patients, the transmissibility mainly increases with age. Patients older than 30 years are more likely to develop symptoms with higher transmissibility. We also find that the transmission burden of asymptomatic cases is lower than that of symptomatic patients.     

Models of epidemics and endemicity in genetically variable host populations

A discrete time genetics model is developed for populations that are undergoing selection due to infectious disease. It is assumed that the generation time of the host and infectious agent are non-synchronous and that only the host population is evolving. Two classes of epidemic processes are considered. The first class is for infectious agents that confer immunity following infection, while the second class is for those that do not confer immunity. The necessary and sufficient conditions are found in order for the disease to persist in a stable polymorphic host population. These conditions are shown to depend on the density of susceptibles, the selection coefficients, and the severity and class of the disease process.     

Occurrence, quantification, and genotyping of Mycoplasma conjunctivae in wild Caprinae with and without infectious keratoconjunctivitis

Mycoplasma conjunctivae, the causative agent of infectious keratoconjunctivitis (IKC), was recently detected in asymptomatic Alpine ibex (Capra ibex ibex). This suggested that an external source of infection may not be required for an IKC outbreak in wildlife but might be initiated by healthy carriers, which contradicted previous serologic investigations in chamois. Our aims were to 1) assess the prevalence of M. conjunctivae among asymptomatic ibex and Alpine chamois (Rupicapra rupicapra rupicapra) and its frequency in IKC-affected animals, 2) determine mycoplasma loads in different disease stages, and 3) characterize the M. conjunctivae strains involved. Eye swabs from 654 asymptomatic and 204 symptomatic animals were collected in diverse Swiss regions between 2008 and 2010, and tested by TaqMan real-time PCR. Data analysis was performed considering various patterns of IKC occurrence in the respective sampling regions. Strains from 24 animals were compared by cluster analysis. Prevalence of M. conjunctivae was 5.6% (95% confidence interval [CI]: 3.7-8.1%) in asymptomatic ibex and 5.8% (CI: 3.0-9.9%) in asymptomatic chamois, with significant differences between years and regions in both species. Detection frequency in symptomatic animals was significantly higher during IKC outbreaks than in nonepidemic situations (i.e., regular but low incidence or sporadic occurrence). Mycoplasma load was significantly lower in eyes from healthy carriers and animals with mild signs than from animals with moderate and severe signs. Although some strains were found in both asymptomatic and diseased animals of the same species, others apparently differed in their pathogenic potential depending on the infected species. Overall, we found a widespread occurrence of M. conjunctivae in wild Caprinae with and without IKC signs. Our results confirm the central role of M. conjunctivae in outbreaks but suggest that other infectious agents may be involved in IKC cases in nonepidemic situations. Additionally, presence and severity of signs are related to the quantity of M. conjunctivae in the eyes rather than to the strain. We propose that individual or environmental factors influence the clinical expression of the disease and that persistence of M. conjunctivae in populations of wild Caprinae cannot be excluded.     

Inferential biases linked to unobservable states in complex occupancy models

Modeling of species distributions has undergone a shift from relying on equilibrium assumptions to recognizing transient system dynamics explicitly. This shift has necessitated more complex modeling techniques, but the performance of these dynamic models has not yet been assessed for systems where unobservable states exist. Our work is motivated by the impacts of the emerging infectious disease chytridiomycosis, a disease of amphibians that is associated with declines of many species worldwide. Using this host‐pathogen system as a general example, we first illustrate how misleading inferences can result from failing to incorporate pathogen dynamics into the modeling process, especially when the pathogen is difficult or impossible to survey in the absence of a host species. We found that traditional modeling techniques can underestimate the effect of a pathogen on host species occurrence and dynamics when the pathogen can only be detected in the host, and pathogen information is treated as a covariate. We propose a dynamic multistate modeling approach that is flexible enough to account for the detection structures that may be present in complex multistate systems, especially when the sampling design is limited by a species’ natural history or sampling technology. When multistate occupancy models are used and an unobservable state is present, parameter estimation can be influenced by model complexity, data sparseness, and the underlying dynamics of the system. We show that, even with large sample sizes, many models incorporating seasonal variation in vital rates may not generate reasonable estimates, indicating parameter redundancy. We found that certain types of missing data can greatly hinder inference, and we make study design recommendations to avoid these issues. Additionally, we advocate the use of time‐varying covariates to explain temporal trends in the data, and the development of sampling techniques that match the biology of the system to eliminate unobservable states when possible.     

Individual and Population-Level Impacts of an Emerging Poxvirus Disease in a Wild Population of Great Tits

Emerging infectious diseases of wildlife can have severe effects on host populations and constitute a pressing problem for biodiversity conservation. Paridae pox is an unusually severe form of avipoxvirus infection that has recently been identified as an emerging infectious disease particularly affecting an abundant songbird, the great tit (Parus major), in Great Britain. In this study, we study the invasion and establishment of Paridae pox in a long-term monitored population of wild great tits to (i) quantify the impact of this novel pathogen on host fitness and (ii) determine the potential threat it poses to population persistence. We show that Paridae pox significantly reduces the reproductive output of great tits by reducing the ability of parents to fledge young successfully and rear those young to independence. Our results also suggested that pathogen transmission from diseased parents to their offspring was possible, and that disease entails severe mortality costs for affected chicks. Application of multistate mark-recapture modelling showed that Paridae pox causes significant reductions to host survival, with particularly large effects observed for juvenile survival. Using an age-structured population model, we demonstrate that Paridae pox has the potential to reduce population growth rate, primarily through negative impacts on host survival rates. However, at currently observed prevalence, significant disease-induced population decline seems unlikely, although pox prevalence may be underestimated if capture probability of diseased individuals is low. Despite this, because pox-affected model populations exhibited lower average growth rates, this emerging infectious disease has the potential to reduce the resilience of populations to other environmental factors that reduce population size.     

Trichomonas vaginalis: random amplified polymorphic DNA analysis of isolates from symptomatic and asymptomatic women in India

Trichomonas vaginalis, the causative agent for human trichomoniasis, is a protozoan parasite. Trichomoniasis is the most common non-viral sexually transmitted disease. The infection in women may be asymptomatic or may lead to severe vaginitis, cervicitis and severe sequelae. Despite its high prevalence, the genetic variability and factors leading to symptomatic infection have been poorly understood. One thousand women in childbearing age group were screened for the presence of T vaginalis. Thirty-eight women were found positive for T vaginalis and out of these 22 (57.9%) were having symptomatic infection and 16 (42%) were asymptomatic. Fresh isolates from 15 symptomatic and 15 asymptomatic women were axenised and subjected to random amplified polymorphic DNA (RAPD) analysis with the use of five different random primers (OPD 1-OPD 5). The isolates with similar banding pattern were assigned as a single type. OPD 3 indicated least (nine types) while OPD 4 indicated highest typing (18 types) ability. Phylogenetic analysis using RAPD distance software indicated two distinct lineages; upper branch consisting of only seven symptomatic isolates while lower branch consisting of all the 15 asymptomatic isolates the other eight symptomatic isolates were recorded in separate cluster. The study indicated that RAPD technique might be helpful to delineate the pathogenic mechanism(s) for its virulence; however, further studies on large number of isolates are desired to elucidate the findings.     

In Vitro Detection of prionemia in TSE-Infected Cervids and Hamsters

Blood-borne transmission of infectious prions during the symptomatic and asymptomatic stages of disease occurs for both human and animal transmissible spongiform encephalopathies (TSEs). The geographical distribution of the cervid TSE, chronic wasting disease (CWD), continues to spread across North America and the prospective number of individuals harboring an asymptomatic infection of human variant Creutzfeldt-Jakob Disease (vCJD) in the United Kingdom has been projected to be ~1 in 3000 residents. Thus, it is important to monitor cervid and human blood products to ensure herd health and human safety. Current methods for detecting blood-associated prions rely primarily upon bioassay in laboratory animals. While bioassay provides high sensitivity and specificity, it requires many months, animals, and it is costly. Here we report modification of the real time quaking-induced conversion (RT-QuIC) assay to detect blood-borne prions in whole blood from prion-infected preclinical white-tailed deer, muntjac deer, and Syrian hamsters, attaining sensitivity of >90% while maintaining 100% specificity. Our results indicate that RT-QuIC methodology as modified can provide consistent and reliable detection of blood-borne prions in preclinical and symptomatic stages of two animal TSEs, offering promise for prionemia detection in other species, including humans.     

The prevalence of Campylobacter pylori gastritis among asymptomatic adults.

To determine the prevalence of Campylobacter pylori colonization in the healthy population we studied 54 asymptomatic volunteers and 65 patients referred because of gastrointestinal symptoms. All subjects underwent gastroscopy and gastric biopsy. C. pylori was isolated from 6 volunteers (11%) and 36 patients (55%). Histologic evidence of inflammation was present in 98% of the culture-positive subjects. Linear regression analysis revealed that the prevalence of C. pylori colonization increased with age. There was no difference in the isolation rate between the two groups when adjusted for age. Four of the six culture-positive volunteers underwent repeat endoscopy and gastric biopsy 1 year later; despite remaining asymptomatic, all still had positive culture results and histologic evidence of gastritis. We conclude that the prevalence of C. pylori-associated gastritis among symptomatic patients increases with age and that the organism may be present in the gastrointestinal tract for prolonged periods without symptoms or evidence of disease progression.     

Detecting Presymptomatic Infection Is Necessary to Forecast Major Epidemics in the Earliest Stages of Infectious Disease Outbreaks

We assess how presymptomatic infection affects predictability of infectious disease epidemics. We focus on whether or not a major outbreak (i.e. an epidemic that will go on to infect a large number of individuals) can be predicted reliably soon after initial cases of disease have appeared within a population. For emerging epidemics, significant time and effort is spent recording symptomatic cases. Scientific attention has often focused on improving statistical methodologies to estimate disease transmission parameters from these data. Here we show that, even if symptomatic cases are recorded perfectly, and disease spread parameters are estimated exactly, it is impossible to estimate the probability of a major outbreak without ambiguity. Our results therefore provide an upper bound on the accuracy of forecasts of major outbreaks that are constructed using data on symptomatic cases alone. Accurate prediction of whether or not an epidemic will occur requires records of symptomatic individuals to be supplemented with data concerning the true infection status of apparently uninfected individuals. To forecast likely future behavior in the earliest stages of an emerging outbreak, it is therefore vital to develop and deploy accurate diagnostic tests that can determine whether asymptomatic individuals are actually uninfected, or instead are infected but just do not yet show detectable symptoms.