On the uniqueness of endemic equilibria of an HIV/AIDS transmission model for a heterogeneous population

In this paper, we examine an HIV/AIDS transmission model which has been widely used for studying the spread of HIV/AIDS through sexual contact. Some sufficient conditions are obtained for the uniqueness of endemic equilibrium. We also present a two-group model whose no-disease equilibrium is unstable but it has at least three positive endemic equilibria.     

A dynamic model for tuberculosis transmission and optimal treatment strategies in South Korea

We have developed a dynamic model for tuberculosis (TB) transmission in South Korea using a SEIR model with the time-dependent parameters. South Korea ranked the highest TB incidence among members of the Organization for Economic Cooperation and Development (OECD) in 2005 yr. The observed data from the Korea Center for Disease Control and Prevention (KCDC) shows a certain rise of active-TB incidence individuals after 2001 yr. Because of this sudden jump, we have considered two different periods for best fitting the model: prior to 2001 yr and posterior to 2001 yr. The least-squares fitting has been used for estimating model parameters to the observed data of active-TB incidence. Our model agrees well with the observed data. In this work, we also propose optimal treatment strategies of TB model in South Korea for the future. We have considered three control mechanisms representing distancing, case finding and case holding efforts. Optimal control programs have been proposed in various scenarios, in order to minimize the number of exposed and infectious individuals and the cost of implementing the control treatment.     

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.     

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.     

Multiple sources and routes of information transmission: Implications for epidemic dynamics

In a recent paper [20], we proposed and analyzed a compartmental ODE-based model describing the dynamics of an infectious disease where the presence of the pathogen also triggers the diffusion of information about the disease. In this paper, we extend this previous work by presenting results based on pairwise and simulation models that are better suited for capturing the population contact structure at a local level. We use the pairwise model to examine the potential of different information generating mechanisms and routes of information transmission to stop disease spread or to minimize the impact of an epidemic. The individual-based simulation is used to better differentiate between the networks of disease and information transmission and to investigate the impact of different basic network topologies and network overlap on epidemic dynamics. The paper concludes with an individual-based semi-analytic calculation of R₀ at the non-trivial disease free equilibrium.     

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.     

On the evolutionary dynamics of pathogens with direct and environmental transmission

A number of ecologically and economically important pathogens exhibit a complex transmission dynamics that involves distinct transmission modes. In this paper, we study the evolutionary dynamics of pathogens for which transmission includes direct host-to-host as well as indirect environmental transmission. Different routes of infection spread require specific adaptations of the parasite, which may result in conflicting selection pressures. Using the framework of Adaptive dynamics, we investigate how these conflicting selection pressures are resolved in the course of evolution and determine the conditions for evolutionary diversification of pathogen strains. We show that evolutionary branching and subsequent evolution of specialist strains occurs in wide parameter regions but evolutionary bistability and evolution of generalist pathogens are possible as well. Our analysis reveals that the relative contributions of direct and environmental transmission, as well as the underlying ecological dynamics, play a crucial role in shaping the course of pathogen evolution. Our findings may explain the coexistence of high and low virulence strains observed in several pathogenic organisms using different transmission modes (e.g., influenza viruses) and highlight the importance of considering ecological dynamics in virulence management.     

Historical processes and environmental factors as determinants of inter-island differences in endemic faunas: the case of the Balearic Islands

Aim We describe current interisland similarities of endemic faunas, and elucidate the significance of historical factors and environmental ones in determining the pattern found. Location The six major islands of the Balearics (Western Mediterranean). Method An extensive review of all the endemic fauna ranging from platyhelminthes to mammals is made. From 568 presumed endemic species and subspecies, 230 full species with neither taxonomic nor distributional uncertainty are chosen. Inter-island similarities are determined using such a presence-absence matrix. Finally, relationships between the matrix of faunistic similarity and a number of matrices measuring environmental and historical factors are elucidated. Results Endemic fauna similarities depend clearly on historical factors. Dependence on environmental factors is unclear. Moreover, endemic fauna reveals two clear-cut clusters of islands within the Balearics: the Gymnesic Islands, in the NE, and the Pityusic Islands in the SW. Historical factors cluster the Balearic Islands in the same way. Contrasting, environmental variables show smoothed, no significant differences among the Gymnesics and the Pityusics. Main conclusions Pre-human flora (palynology) and fauna (bird and mammal fossil record) suggest that environmental differences among the Gymnesics and the Pityusics have now been reduced in comparison to the environmental differences at the Pleistocene and Holocene boundary. This environmental homogenization is likely related with human invasion. Historical effects of prehuman differences between Gymnesic and Pityusic Islands are still recognizable on endemic fauna. In contrast, there is no historical effects on interisland similarities using currently breeding birds (as an example of organisms well-dispersed and related to vegetation type). We explain the pattern of interisland similarities of endemic fauna as the result of the independent histories among the two islands groups. Contrasting, successive colonizations and extinctions would determine interisland similarities of breeding birds.     

A general model for the evolution of mutualisms

The evolution of mutualisms presents a puzzle. Why does selection favour cooperation among species rather than cheaters that accept benefits but provide nothing in return? Here we present a general model that predicts three key factors will be important in mutualism evolution: (i) high benefit to cost ratio, (ii) high within‐species relatedness and (iii) high between‐species fidelity. These factors operate by moderating three types of feedback benefit from mutualism: cooperator association, partner‐fidelity feedback and partner choice. In defining the relationship between these processes, our model also allows an assessment of their relative importance. Importantly, the model suggests that phenotypic feedbacks (partner‐fidelity feedback, partner choice) are a more important explanation for between‐species cooperation than the development of genetic correlations among species (cooperator association). We explain the relationship of our model to existing theories and discuss the empirical evidence for our predictions.     

The evolution of conformist transmission in social learning when the environment changes periodically

Conformity is often observed in human social learning. Social learners preferentially imitate the majority or most common behavior in many situations, though the strength of conformity varies with the situation. Why has such a psychological tendency evolved? I investigate this problem by extending a standard model of social learning evolution with infinite environmental states (Feldman, M.W., Aoki, K., Kumm, J., 1996. Individual versus social learning: evolutionary analysis in a fluctuating environment. Anthropol. Sci. 104, 209-231) to include conformity bias. I mainly focus on the relationship between the strength of conformity bias that evolves and environmental stability, which is one of the most important factors in the evolution of social learning. Using the evolutionarily stable strategy (ESS) approach, I show that conformity always evolves when environmental stability and the cost of adopting a wrong behavior are small, though environmental stability and the cost of individual learning both negatively affect the strength of conformity.     

Bacterial symbionts in the hepatopancreas of isopods: diversity and environmental transmission

The midgut glands (hepatopancreas) of terrestrial isopods contain bacterial symbionts. We analysed the phylogenetic diversity of hepatopancreatic bacteria in isopod species from various suborders colonizing marine, semiterrestrial, terrestrial and freshwater habitats. Hepatopancreatic bacteria were absent in the marine isopod Idotea balthica (Valvifera). The symbiotic bacteria present in the midgut glands of the freshwater isopod Asellus aquaticus (Asellota) were closely related to members of the proteobacterial genera Rhodobacter, Burkholderia, Aeromonas or Rickettsiella, but differed markedly between populations. By contrast, species of the suborder Oniscidea were consistently colonized by the same phylotypes of hepatopancreatic bacteria. While symbionts in the semiterrestrial isopod Ligia oceanica (Oniscidea) were close relatives of Pseudomonas sp. (Gammaproteobacteria), individuals of the terrestrial isopod Oniscus asellus (Oniscidea) harboured either 'Candidatus Hepatoplasma crinochetorum' (Mollicutes) or 'Candidatus Hepatincola porcellionum' (Rickettsiales), previously described as symbionts of another terrestrial isopod, Porcellio scaber. These two uncultivated bacterial taxa were consistently present in each population of six and three different species of terrestrial isopods, respectively, collected in different geographical locations. However, infection rates of individuals within a population ranged between 10% and 100%, rendering vertical transmission unlikely. Rather, feeding experiments suggest that 'Candidatus Hepatoplasma crinochetorum' is environmentally transmitted to the progeny.     

A model for influenza with vaccination and antiviral treatment

Compartmental models for influenza that include control by vaccination and antiviral treatment are formulated. Analytic expressions for the basic reproduction number, control reproduction number and the final size of the epidemic are derived for this general class of disease transmission models. Sensitivity and uncertainty analyses of the dependence of the control reproduction number on the parameters of the model give a comparison of the various intervention strategies. Numerical computations of the deterministic models are compared with those of recent stochastic simulation influenza models. Predictions of the deterministic compartmental models are in general agreement with those of the stochastic simulation models.     

A general kinetic model for biological nutrient removal activated sludge systems: model evaluation

Hu et al. (2007) presented a general kinetic model for biological nutrient removal (BNR) activated sludge (AS) systems in general, but for external nitrification (EN) BNRAS (ENBNRAS) systems in particular. In this article, this model is evaluated against a large number of experimental data sets. In this evaluation, the model is first used to simulate a wide variety of conventional internal nitrification (IN) BNRAS systems to evaluate its predictions and also evaluate the model parameters suggested by Hu et al. (2007), and to calibrate those constants for which values are not available in the literature. Simulation results indicate that the model, with appropriately calibrated parameters, is capable of predicting COD removal, nitrification and denitrification and two types of biological excess phosphorus removal (BEPR), namely aerobic and anoxic/aerobic P uptake BEPR. The model is then used to simulate the ENBNRAS systems to evaluate its capacity of simulating the behaviour of this system. Simulation results show that the model is capable of simulating the behaviour of the ENBNRAS systems, including COD, nitrification, denitrification and BEPR, particularly anoxic P uptake BEPR, with the values of kinetic and stoichiometric parameters obtained in modelling conventional BNRAS systems, except for micro(NIT), K(MP), eta(PAO) and eta(H) which required calibration.     

A simple model for predicting the effect of hygrothermal conditions on populations of house dust mite Dermatophagoides pteronyssinus (Acari: Pyroglyphidae)

A simple mite population index (MPI) model is presented which predicts the effect on house dust mite populations of any combination of temperature and relative humidity (RH). For each combination, the output is an index, or multiplication factor, such that 1.1 indicates 10% population growth and 0.9 indicates 10% population decline. To provide data for the model, laboratory experiments have been carried out using lab cultures of Dermatophagoides pteronyssinus. The population change was observed for mites held in steady-state conditions at different combinations of temperature and RH over 21 days. From the results, a best-fit equation has been derived which forms the basis of the MPI model. The results also enable a new term to be defined: the Population Equilibrium Humidity, PEH, the RH for a given temperature at which house dust mite populations neither grow nor decline. It is similar to Critical Equilibrium Humidity, the RH below which house dust mites are unable to maintain water balance, but relates to a population of mites (rather than a physiological phenomenon) and is more able to take account of the observed effects of extremes of temperature and RH. Compared with previous population models, the MPI model is potentially more accurate and comprehensive. It can be combined with other simple models (described in previous papers), such as BED, which simulates the average hygrothermal conditions in a bed, given room␣conditions, and Condensation Targeter II, which simulates room conditions given a range of easily obtainable inputs for climate, house type and occupant characteristics. In this way it is now possible, for any individual dwelling, to assess the most effective means of controlling mite populations by environmental means, such as by improving standards of ventilation and insulation, or by modifying the occupant behaviour that affects the hygrothermal environment within a dwelling. Although the MPI model requires further development and validation, it has already proved useful for understanding more clearly how the different hygrothermal conditions found in beds and bedrooms can affect mite populations. It has also demonstrated that there is considerable scope for controlling mites by environmental means in cold winter climates such as the UK.     

A general kinetic model for biological nutrient removal activated sludge systems: model development

In this article, a kinetic model is developed and presented for biological nutrient removal (BNR) activated sludge (BNRAS) systems in general, but for external nitrification (EN) BNRAS (ENBNRAS) systems in particular. The model is based on the UCTPHO model, but includes some significant modifications, such as anoxic P uptake and associated denitrification by phosphorus accumulating organisms (PAOs). Some key features of the model are described and discussed before the model is presented. Model evaluation will be addressed in another article (Hu et al., 2007).     

Estimating the environmental Kuznets curve for ecological footprint at the global level: A spatial econometric approach

The national ecological footprint of both consumption and production are significantly spatially autocorrelated at global level. This violates the assumption of independently distributed errors of most conventional estimation techniques. Using a spatial econometric approach, this paper re-examine the relationship between economic growth and environmental impact for indicator of ecological footprint. The results do not show evidence of inverted U-shape Environmental Kuznets Curve. The domestic ecological footprint of consumption (or production) was obviously influenced by the ecological footprint of consumption (or production), income and biocapacity in neighborhood countries. We also found that the consumption footprint is more sensitive to domestic income, while production footprint is more sensitive to domestic biocapacity, which is often unnoticed in EKC hypothesis analyses that focus exclusively on the consumption-based or production-based indictors.