Backward bifurcations in dengue transmission dynamics

A deterministic model for the transmission dynamics of a strain of dengue disease, which allows transmission by exposed humans and mosquitoes, is developed and rigorously analysed. The model, consisting of seven mutually-exclusive compartments representing the human and vector dynamics, has a locally-asymptotically stable disease-free equilibrium (DFE) whenever a certain epidemiological threshold, known as the basic reproduction number(R(0)) is less than unity. Further, the model exhibits the phenomenon of backward bifurcation, where the stable DFE coexists with a stable endemic equilibrium. The epidemiological consequence of this phenomenon is that the classical epidemiological requirement of making R(0) less than unity is no longer sufficient, although necessary, for effectively controlling the spread of dengue in a community. The model is extended to incorporate an imperfect vaccine against the strain of dengue. Using the theory of centre manifold, the extended model is also shown to undergo backward bifurcation. In both the original and the extended models, it is shown, using Lyapunov function theory and LaSalle Invariance Principle, that the backward bifurcation phenomenon can be removed by substituting the associated standard incidence function with a mass action incidence. In other words, in addition to establishing the presence of backward bifurcation in models of dengue transmission, this study shows that the use of standard incidence in modelling dengue disease causes the backward bifurcation phenomenon of dengue disease.     

Mechanism of vertical transmission of the dengue virus in mosquitoes

Both experimental and field data suggest that some tropical mosquito-borne flaviviruses, such as dengue and yellow fever, survive dry seasons by vertical (i.e. transgenerational) transmission in their mosquito hosts. Although vertical transmission of arboviruses in mosquitoes is considered to be transovarial in nature, observations reported here indicate that this is probably not true for dengue virus. Rather, infection of the next generation with this virus apparently takes place when the fully developed egg, enclosed in the chorion, is fertilized at the time of oviposition. In contrast to transovarial transmission, the latter mechanism permits the infection of progeny following a single maternal blood meal.     

Analysis of a dengue disease transmission model

A model for the transmission of dengue fever in a constant human population and variable vector population is discussed. A complete global analysis is given, which uses the results of the theory of competitive systems and stability of periodic orbits, to establish the global stability of the endemic equilibrium. The control measures of the vector population are discussed in terms of the threshold condition, which governs the existence and stability of the endemic equilibrium.     

Modeling the dynamic transmission of dengue fever: investigating disease persistence

Background

Dengue is a disease of great complexity, due to interactions between humans, mosquitoes and various virus serotypes as well as efficient vector survival strategies. Thus, understanding the factors influencing the persistence of the disease has been a challenge for scientists and policy makers. The aim of this study is to investigate the influence of various factors related to humans and vectors in the maintenance of viral transmission during extended periods.

Methodology/Principal Findings

We developed a stochastic cellular automata model to simulate the spread of dengue fever in a dense community. Each cell can correspond to a built area, and human and mosquito populations are individually monitored during the simulations. Human mobility and renewal, as well as vector infestation, are taken into consideration. To investigate the factors influencing the maintenance of viral circulation, two sets of simulations were performed: (1^st) varying human renewal rates and human population sizes and (2^nd) varying the house index (fraction of infested buildings) and vector per human ratio. We found that viral transmission is inhibited with the combination of small human populations with low renewal rates. It is also shown that maintenance of viral circulation for extended periods is possible at low values of house index. Based on the results of the model and on a study conducted in the city of Recife, Brazil, which associates vector infestation with Aedes aegytpi egg counts, we question the current methodology used in calculating the house index, based on larval survey.

Conclusions/Significance

This study contributed to a better understanding of the dynamics of dengue subsistence. Using basic concepts of metapopulations, we concluded that low infestation rates in a few neighborhoods ensure the persistence of dengue in large cities and suggested that better strategies should be implemented to obtain measures of house index values, in order to improve the dengue monitoring and control system.     

An apparent paradox of horizontal and vertical disease transmission

The question as to how the ratio of horizontal to vertical transmission depends on the coefficient of horizontal transmission is investigated in host-parasite models with one or two parasite strains. In an apparent paradox, this ratio decreases as the coefficient is increased provided that the ratio is taken at the equilibrium at which both host and parasite persist. Moreover, a completely vertically transmitted parasite strain that would go extinct on its own can coexist with a more harmful horizontally transmitted strain by protecting the host against it.     

An apparent paradox of horizontal and vertical disease transmission

The question as to how the ratio of horizontal to vertical transmission depends on the coefficient of horizontal transmission is investigated in host–parasite models with one or two parasite strains. In an apparent paradox, this ratio decreases as the coefficient is increased provided that the ratio is taken at the equilibrium at which both host and parasite persist. Moreover, a completely vertically transmitted parasite strain that would go extinct on its own can coexist with a more harmful horizontally transmitted strain by protecting the host against it.     

Non-linear transmission rates and the dynamics of infectious disease.

This study considers how non-linearities in the transmission of microparasitic infections affect the population dynamics of host-parasite systems in which the disease is potentially lethal to the host. Non-linearities can either lead to a locally stable or unstable host-parasite equilibrium point, depending on the respective contributions of healthy and infected hosts to the functional form of the transmission rate. Analysis of the non-linear transmission model results in a revealing pair of local stability criteria. Specifically, stability requires sufficient total levels of intrinsic growth of the host population and total levels of density-dependent transmission. The most stable systems occur when increases in the density of healthy hosts result in increases in transmission efficiency, and increases in the number of infected hosts result in small decreases in transmission efficiency. These appear to be very reasonable relationships for directly transmitted microparasites.     

Influence of the mechanical properties of a manipulandum on human operator dynamics

An active servo-system was used to change the stiffness of a manipulandum used in a positioncontrol pursuit-tracking task. The elastic stiffness of the manipulandum connected to the forearm was set by a computer at one of five levels ranging from 0 N/m to 2000 N/m. Subjects were required to track, either by moving their forearm or by generating a force isometrically, a visually presented target whose position changed randomly every second for 100 s. Nonparametric and parametric impulse response functions were calculated between the input (target) and output (force or position) in each tracking condition, and revealed that for all subjects force control was faster than position control when the stiffness of the manipulandum was set at 0 N/m. Subjects were also consistently faster in reaching the target when the stiffness was greater than zero, and were more accurate (steadystate response) when the stiffness of the manipulandum was set at lower rather than higher amplitudes. The parametric impulse response functions revealed that the human operator system was underdamped (0.7) with a natural frequency of approximately 8 rad/s. These findings were interpreted in terms of the responses of the various subsystems (visual, cognitive, contractile, limb mechanics) that comprise the human operator's response.     

Incorporating the process of vertical transmission into understanding of host–symbiont dynamics

Variation exists in the frequency of obligate, vertically transmitted symbiotic organisms within and among host populations; however, these patterns have not been adequately explained by variable fitness effects of symbionts on their hosts. In this forum, we call attention to another equally important, but overlooked mechanism to maintain variation in the frequency of symbioses in nature: the rate of vertical transmission. On ecological time scales, vertical transmission can affect the equilibrium frequencies of symbionts in host populations, with potential consequences for population and community dynamics. In addition, vertical transmission has the potential to influence the evolution of symbiosis, by affecting the probability of fixation of symbiosis (and therefore the evolution of complexity) and by allowing hosts to sanction against costly symbionts. Here we use grass–epichloae symbioses as a model system to explore the causes and consequences of variation in vertical transmission rates. We identify critical points for symbiont transmission that emerge from considering the host growth cycle devoted to reproduction (asexual vs sexual) and the host capability to maintain homeostasis. We also use information on the process of transmission to predict the environmental factors that would most likely affect transmission rates. Altogether, we aim to highlight the vertical transmission rate as an important process for understanding the ecology and evolution of symbiosis, using grass–epichloae interactions as a case study.     

Influence of inverse dynamics methods on the calculation of inter-segmental moments in vertical jumping and weightlifting

Background  

A vast number of biomechanical studies have employed inverse dynamics methods to calculate inter-segmental moments during movement. Although all inverse dynamics methods are rooted in classical mechanics and thus theoretically the same, there exist a number of distinct computational methods. Recent research has demonstrated a key influence of the dynamics computation of the inverse dynamics method on the calculated moments, despite the theoretical equivalence of the methods. The purpose of this study was therefore to explore the influence of the choice of inverse dynamics on the calculation of inter-segmental moments.     

Influence of spatial heterogeneity on an emerging infectious disease: the case of dengue epidemics

The importance of spatial heterogeneity and spatial scales (at a village or neighbourhood scale) has been explored with individual-based models. Our reasoning is based on the Chilean Easter Island (EI) case, where a first dengue epidemic occurred in 2002 among the relatively small population localized in one village. Even in this simple situation, the real epidemic is not consistent with homogeneous models. Conversely, including contact heterogeneity on different scales (intra-households, inter-house, inter-areas) allows the recovery of not only the EI epidemiological curve but also the qualitative patterns of Brazilian urban dengue epidemic in more complex situations.     

Stochastic eco-epidemiological model of dengue disease transmission by Aedes aegypti mosquito

We present a stochastic dynamical model for the transmission of dengue that takes into account seasonal and spatial dynamics of the vector Aedes aegypti. It describes disease dynamics triggered by the arrival of infected people in a city. We show that the probability of an epidemic outbreak depends on seasonal variation in temperature and on the availability of breeding sites. We also show that the arrival date of an infected human in a susceptible population dramatically affects the distribution of the final size of epidemics and that early outbreaks have a low probability. However, early outbreaks are likely to produce large epidemics because they have a longer time to evolve before the winter extinction of vectors. Our model could be used to estimate the risk and final size of epidemic outbreaks in regions with seasonal climatic variations.     

Optimal timing of insecticide fogging to minimize dengue cases: modeling dengue transmission among various seasonalities and transmission intensities

Background

Dengue infection is endemic in many regions throughout the world. While insecticide fogging targeting the vector mosquito Aedes aegypti is a major control measure against dengue epidemics, the impact of this method remains controversial. A previous mathematical simulation study indicated that insecticide fogging minimized cases when conducted soon after peak disease prevalence, although the impact was minimal, possibly because seasonality and population immunity were not considered. Periodic outbreak patterns are also highly influenced by seasonal climatic conditions. Thus, these factors are important considerations when assessing the effect of vector control against dengue. We used mathematical simulations to identify the appropriate timing of insecticide fogging, considering seasonal change of vector populations, and to evaluate its impact on reducing dengue cases with various levels of transmission intensity.

Methodology/Principal Findings

We created the Susceptible-Exposed-Infectious-Recovered (SEIR) model of dengue virus transmission. Mosquito lifespan was assumed to change seasonally and the optimal timing of insecticide fogging to minimize dengue incidence under various lengths of the wet season was investigated. We also assessed whether insecticide fogging was equally effective at higher and lower endemic levels by running simulations over a 500-year period with various transmission intensities to produce an endemic state. In contrast to the previous study, the optimal application of insecticide fogging was between the onset of the wet season and the prevalence peak. Although it has less impact in areas that have higher endemicity and longer wet seasons, insecticide fogging can prevent a considerable number of dengue cases if applied at the optimal time.

Conclusions/Significance

The optimal timing of insecticide fogging and its impact on reducing dengue cases were greatly influenced by seasonality and the level of transmission intensity. We suggest that these factors should be considered when planning a control strategy against dengue vectors.     

Life cycle and population dynamics of a protective insect symbiont reveal severe bottlenecks during vertical transmission

Insects engage in mutualistic relationships with a wide variety of microorganisms that are usually transmitted vertically to the next generation. During transmission, the symbiont populations often suffer significant bottlenecks that may entail major genetic and genomic consequences. Here we investigated the life-cycle and the severity of transmission bottlenecks in a symbiotic system with an unusual way of post-hatch vertical transmission by using quantitative PCRs and morphological 3D-reconstructions. European beewolves (Philanthus triangulum, Hymenoptera: Crabronidae) harbor symbiotic bacteria (‘Candidatus Streptomyces philanthi’) in specialized antennal gland reservoirs and secrete them into their subterranean brood cells. The symbionts are later taken up by the beewolf larva and incorporated into the cocoon material to provide protection against pathogenic microorganisms. Even after months of hibernation, the symbiont population on the cocoon is estimated to encompass around 1.4 × 10⁵ cells. However, our results indicate that only few of these bacterial cells (about 9.7 × 10²) are taken up from the cocoon by the emerging female. The symbiont population subsequently undergoes logistic growth within the antennal gland reservoirs and reaches a maximum of about 1.5 × 10⁷ cells 3–4 days after emergence. The maximum specific growth rate is estimated to be 0.084–0.105 h⁻¹. With a total reduction in cell numbers of about 6.7 × 10⁻⁵ during vertical transmission, the symbiont population experiences one of the most severe bottlenecks known for any symbiotic system to date. This extreme bottleneck may have significantly affected the evolution of the beewolf-Streptomyces symbiosis by increased genetic drift, an accumulation of mildly deleterious mutations and genome erosion.     

Phylogeography and population dynamics of dengue viruses in the Americas

Changes in Dengue virus (DENV) disease patterns in the Americas over recent decades have been attributed, at least in part, to repeated introduction of DENV strains from other regions, resulting in a shift from hypoendemicity to hyperendemicity. Using newly sequenced DENV-1 and DENV-3 envelope (E) gene isolates from 11 Caribbean countries, along with sequences available on GenBank, we sought to document the population genetic and spatiotemporal transmission histories of the four main invading DENV genotypes within the Americas and investigate factors that influence the rate and intensity of DENV transmission. For all genotypes, there was an initial invasion phase characterized by rapid increases in genetic diversity, which coincided with the first confirmed cases of each genotype in the region. Rapid geographic dispersal occurred upon each genotype's introduction, after which individual lineages were locally maintained, and gene flow was primarily observed among neighboring and nearby countries. There were, however, centers of viral diversity (Barbados, Puerto Rico, Colombia, Suriname, Venezuela, and Brazil) that were repeatedly involved in gene flow with more distant locations. For DENV-1 and DENV-2, we found that a "distance-informed" model, which posits that the intensity of virus movement between locations is inversely proportional to the distance between them, provided a better fit than a model assuming equal rates of movement between all pairs of countries. However, for DENV-3 and DENV-4, the more stochastic "equal rates" model was preferred.     

The chikungunya disease: modeling, vector and transmission global dynamics

Models for the transmission of the chikungunya virus to human population are discussed. The chikungunya virus is an alpha arbovirus, first identified in 1953. It is transmitted by Aedes mosquitoes and is responsible for a little documented uncommon acute tropical disease. Models describing the mosquito population dynamics and the virus transmission to the human population are discussed. Global analysis of equilibria are given, which use on the one hand Lyapunov functions and on the other hand results of the theory of competitive systems and stability of periodic orbits.     

On the dynamics of dengue epidemics from large-scale information

A model for the spatial and temporal dynamics of dengue fever is proposed in this article. The vector population dynamics is derived from a diffusion equation that is based on environmental parameters at the scale of a remote-sensing image. Vectors and hosts populations are then classically divided into compartments corresponding to their respective disease status. The transmission processes between hosts and vectors are described by a set of differential equations. The link between the vector population diffusion model and the compartmental model enables one to describe both the spatial and temporal dynamics of the disease. Simulations in artificial and actual landscapes show the advantage of using remotely sensed and complementary meteorological data for modelling in a realistic way the geographic spread of a vector-borne disease such as dengue fever.     

Influence of mechanical ventilation and pulmonary disease on pulmonary artery pressure monitoring.

Mechanical ventilation and respiratory disease impose both theoretical and practical limitations on the interpretation of hemodynamic measurements. To properly interpret such information a thorough understanding of the circulatory changes associated with normal breathing, mechanical ventilation and respiratory disease is vital. There are a variety of factors involved in patients with obstructive lung disease and those receiving mechanical ventilation that complicate the usual interpretation of hemodynamic data obtained from flow-directed catheters. An awareness of the potential pitfalls of hemodynamic monitoring in such situations is important in the efficient use of the hemodynamic data obtained.     

Influence of landscape and social interactions on transmission of disease in a social cervid

The mechanisms of pathogen transmission are often social behaviours. These occur at local scales and are affected by landscape-scale population structure. Host populations frequently exist in patchy and isolated environments that create a continuum of genetic and social familiarity. Such variability has an important multispatial effect on pathogen spread. We assessed elk dispersal (i.e. likelihood of interdeme pathogen transmission) through spatially explicit genetic analyses. At a landscape scale, the elk population was composed of one cluster within a southeast-to-northwest cline spanning three spatially discrete subpopulations of elk across two protected areas in Manitoba (Canada). Genetic data are consistent with spatial variability in apparent prevalence of bovine tuberculosis (TB) in elk. Given the existing population structure, between-subpopulation spread of disease because of elk dispersal is unlikely. Furthermore, to better understand the risk of spread and distribution of the TB, we used a combination of close-contact logging biotelemetry and genetic data, which highlights how social intercourse may affect pathogen transmission. Our results indicate that close-contact interaction rate and duration did not covary with genetic relatedness. Thus, direct elk-to-elk transmission of disease is unlikely to be constrained to related individuals. That social intercourse in elk is not limited to familial groups provides some evidence pathogen transmission may be density-dependent. We show that the combination of landscape-scale genetics, relatedness and local-scale social behaviours is a promising approach to understand and predict landscape-level pathogen transmission within our system and within all social ungulate systems affected by transmissible diseases.