Some remarks on definition and validity of terms used in models for infectious disease spread.

The epidemiology of infectious diseases makes use of a number of terms, such as exposure, infected, carrier, attack rate, and immunity. Researchers who intend to model the spread of epidemics should be aware of the problems with some of these terms. The role played by inapparent, or subclinical, infections is receiving increased attention in infectious disease epidemiology. Patients with such infections may never be reported as cases, which could give rise to problems when, for example, data from national surveillance bodies are being used for modeling. The assignment of patients to different transmission groups must, in most cases, rely on self-reported data from the medical interview. This possible source of bias should be recognized.     

Problems of determinacy in compartmental modeling with application to Bilirubin Kinetics

A new concept, called determinacy, is introduced. The concept is applied to compartmental modeling of the metabolism of bilirubin in the human biological system. Necessarily gross simplifications must be made in deriving the model. This paper treats the consequent problems of determinacy: (a) selection of model structure from a finite set of alternatives; (b) selection of parameter values from a finite set of solutions (resolution of ambiguities); (c) selection of parameter values from a continuum of solutions.     

The effects of asymptomatic attacks on the spread of infectious disease: A deterministic model

A deterministic model for a multi-agent disease epidemic with asymptomatic attacks is proposed and investigated. The limitations inherent in the assumptions of the model are discussed in connection with specific agents of disease. The mathematical treatment of the model is separated into analyses of the equilibrium situation and the transient behavior of the disease outbreak. Explicit formulas are derived for the number of susceptibles in the population as well as for the numbers of each type of infective—those with and without symptoms. These theoretical results are followed by a discussion of the practical considerations which must be taken into account to obtain useful information from the model. This work was supported in part by National Library of Medicine Training Grant Number 5 T01 LM00160 and in part by National Institutes of Health National Research Service Award Number 1 F32 GMO 5839 from the Institute of General Medical Sciences.     

A branching model for the spread of infectious animal diseases in varying environments

This paper is concerned with a stochastic model, describing outbreaks of infectious diseases that have potentially great animal or human health consequences, and which can result in such severe economic losses that immediate sets of measures need to be taken to curb the spread. During an outbreak of such a disease, the environment that the infectious agent experiences is therefore changing due to the subsequent control measures taken. In our model, we introduce a general branching process in a changing (but not random) environment. With this branching process, we estimate the probability of extinction and the expected number of infected individuals for different control measures. We also use this branching process to calculate the generating function of the number of infected individuals at any given moment. The model and methods are designed using important infections of farmed animals, such as classical swine fever, foot-and-mouth disease and avian influenza as motivating examples, but have a wider application, for example to emerging human infections that lead to strict quarantine of cases and suspected cases (e.g. SARS) and contact and movement restrictions.     

The spread and persistence of infectious diseases in structured populations

A basic assumption of many epidemic models is that populations are composed of a homogeneous group of randomly mixing individuals. This is not a realistic assumption. Most actual populations are divided into a number of subpopulations, within which there may be relatively random mixing, but among which there is nonrandom mixing. As a consequence of the structuring of the population, there are several sources of heterogeneity within populations that can affect the course of an infection through the population. Two of these sources of heterogeneity are differences in contact number between subpopulations, and differences in the patterns of contact among subpopulations. A model for the spread of a disease in such a population is described. The model considers two levels of interaction: interactions between individuals within a subpopulation because of geographic proximity, and interactions between individuals of the same or different subpopulations because of attendance at common social functions. Because of this structure, it is possible to analyze with the model both heterogeneity in contact number and variation in the patterns of contact. A stability analysis of the model is presented which shows that there is a unique threshold for disease maintenance. Below the threshold the disease goes extinct, and the equilibrium is globally asymptotically stable. Above the threshold, the extinction equilibrium is unstable, and there is a unique endemic equilibrium. The analysis presents a sufficient condition for disease maintenance, which determines critical subpopulation sizes above which the disease cannot go extinct. The condition is a simple inequality relating the removal rate of infectives to the infection rate of susceptibles. In addition, bounds on the actual threshold and the effect of symmetry in the interaction matrix on the threshold are presented.     

Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission

A precise definition of the basic reproduction number, , is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if , then the disease free equilibrium is locally asymptotically stable; whereas if , then it is unstable. Thus, is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for near one. This criterion, together with the definition of , is illustrated by treatment, multigroup, staged progression, multistrain and vector–host models and can be applied to more complex models. The results are significant for disease control.     

Bioprinting technologies for disease modeling

There is a great need for the development of biomimetic human tissue models that allow elucidation of the pathophysiological conditions involved in disease initiation and progression. Conventional two-dimensional (2D) in vitro assays and animal models have been unable to fully recapitulate the critical characteristics of human physiology. Alternatively, three-dimensional (3D) tissue models are often developed in a low-throughput manner and lack crucial native-like architecture. The recent emergence of bioprinting technologies has enabled creating 3D tissue models that address the critical challenges of conventional in vitro assays through the development of custom bioinks and patient derived cells coupled with well-defined arrangements of biomaterials. Here, we provide an overview on the technological aspects of 3D bioprinting technique and discuss how the development of bioprinted tissue models have propelled our understanding of diseases’ characteristics (i.e. initiation and progression). The future perspectives on the use of bioprinted 3D tissue models for drug discovery application are also highlighted.     

Empowering African genomics for infectious disease control

At present, African scientists can only participate minimally in the genomics revolution that is transforming the understanding, surveillance and clinical treatment of infectious diseases. We discuss new initiatives to equip African scientists with knowledge of cutting-edge genomics tools, and build a sustainable critical mass of well-trained African infectious diseases genomics scientists.     

Serendipity and new drugs for infectious disease

Serendipity, in various shades of semantic legitimacy, is abundantly evident in the history of the chemotherapy of infectious disease. We may be on the threshold of a new era of rational drug design, but most medications for infectious diseases have arisen, and continue to arise, from chance observation, clinical experience, and the empirical search for substances active against pathogens. Chance does not produce drugs; but where chance has played a pivotal role in drug discovery, the event may be considered serendipitous to a greater or lesser degree. In a deliberate search for new drugs, it is often difficult to assess the degree to which any resulting discovery is serendipitous, and the usefulness of the term becomes debatable. Many therapeutic advances emerge from research involving animals, and a triggering "happy accident" may reside in the most basic aspects of animal care or in the most arcane knowledge of animals. The examples discussed in this article deal mostly with parasitic disease and the use of animal models in the discovery of antiparasitic agents. In this area, as in others, chance has laid the groundwork for scientific advancement and practical benefit. Although the applicability of the word serendipity to drug discovery may often be uncertain, the role played by chance should be recognized and welcomed.     

Advances in microfluidic PCR for point-of-care infectious disease diagnostics

Global burdens from existing or emerging infectious diseases emphasize the need for point-of-care (POC) diagnostics to enhance timely recognition and intervention. Molecular approaches based on PCR methods have made significant inroads by improving detection time and accuracy but are still largely hampered by resource-intensive processing in centralized laboratories, thereby precluding their routine bedside- or field-use. Microfluidic technologies have enabled miniaturization of PCR processes onto a chip device with potential benefits including speed, cost, portability, throughput, and automation. In this review, we provide an overview of recent advances in microfluidic PCR technologies and discuss practical issues and perspectives related to implementing them into infectious disease diagnostics.     

Analytic models for the patchy spread of plant disease

Plant epidemiologists have long been concerned with the patchy nature of plant disease epidemics. This paper presents a new analytical model for patchy plant epidemics (and patchy dynamics in general), using a second-order approximation to capture the spatial dynamics in terms of the densities and spatial covariances of healthy and infected hosts. Using these spatial moment equations helps us to explain the dynamic growth of patchiness during the early phase of the epidemic, and how the patchiness feeds back on the growth rate of the epidemic. Both underlying heterogeneity in the host spatial arrangement and dynamically generated heterogeneity in the spatial arrangement of infected plants initially accelerate but later decelerate the epidemic.