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.     

Natural vertical transmission of dengue viruses by Aedes aegypti in Bolivia

The natural transmission of dengue virus from an infected female mosquito to its progeny, namely the vertical transmission, was researched in wild caught Aedes aegypti during an important outbreak in the town of Santa Cruz de la Sierra, Bolivia. Mosquitoes were collected at the preimaginal stages (eggs, larvae and pupae) then reared up to adult stage for viral detection using molecular methods. Dengue virus serotypes 1 and 3 were found to be co-circulating with significant higher prevalence in male than in female mosquitoes. Of the 97 pools of Ae. aegypti (n = 635 male and 748 female specimens) screened, 14 pools, collected in February-May in 2007, were found positive for dengue virus infection: five DEN-1 and nine DEN-3. The average true infection rate (TIR) and minimum infection rate (MIR) were respectively 1.08% and 1.01%. These observations suggest that vertical transmission of dengue virus may be detected in vectors at the peak of an outbreak as well as several months before an epidemic occurs in human population.     

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.     

Disease-driven reduction in human mobility influences human-mosquito contacts and dengue transmission dynamics

Heterogeneous exposure to mosquitoes determines an individual’s contribution to vector-borne pathogen transmission. Particularly for dengue virus (DENV), there is a major difficulty in quantifying human-vector contacts due to the unknown coupled effect of key heterogeneities. To test the hypothesis that the reduction of human out-of-home mobility due to dengue illness will significantly influence population-level dynamics and the structure of DENV transmission chains, we extended an existing modeling framework to include social structure, disease-driven mobility reductions, and heterogeneous transmissibility from different infectious groups. Compared to a baseline model, naïve to human pre-symptomatic infectiousness and disease-driven mobility changes, a model including both parameters predicted an increase of 37% in the probability of a DENV outbreak occurring; a model including mobility change alone predicted a 15.5% increase compared to the baseline model. At the individual level, models including mobility change led to a reduction of the importance of out-of-home onward transmission (R, the fraction of secondary cases predicted to be generated by an individual) by symptomatic individuals (up to -62%) at the expense of an increase in the relevance of their home (up to +40%). An individual’s positive contribution to R could be predicted by a GAM including a non-linear interaction between an individual’s biting suitability and the number of mosquitoes in their home (>10 mosquitoes and 0.6 individual attractiveness significantly increased R). We conclude that the complex fabric of social relationships and differential behavioral response to dengue illness cause the fraction of symptomatic DENV infections to concentrate transmission in specific locations, whereas asymptomatic carriers (including individuals in their pre-symptomatic period) move the virus throughout the landscape. Our findings point to the difficulty of focusing vector control interventions reactively on the home of symptomatic individuals, as this approach will fail to contain virus propagation by visitors to their house and asymptomatic carriers.     

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.     

Modelling the effect of temperature on transmission of dengue

The main entomological parameters involved in the rate of dengue virus transmission include the longevity of female mosquitoes, the time interval between bites and the extrinsic incubation period of the virus. Field and laboratory data provide estimates for these parameters, but their interactions with other factors (e.g. host population density and environmental parameters) make their integration into a transmission model quite complex. To estimate the impact of these parameters on transmission, we developed a model of virus transmission by a vector population which predicts the number of potentially infective bites under a range of temperatures and entomological parameters, including the daily survival rate of females, the interval between bites and the extrinsic incubation period. Results show that in a stable population, an increase in mosquito longevity disproportionately enhances the number of potential transmissions (e.g. by as much as five times when the survival rate rises from 0.80 to 0.95). Halving the length of the biting interval with a 10-°C rise in temperature increases the transmission rate by at least 2.4 times. Accordingly, the model can predict changes in dengue transmission associated with short-term variation in seasonal temperature and also with potentially long-lasting increases in global temperatures.     

Effect of pathogen-resistant vectors on the transmission dynamics of a vector-borne disease

A model is introduced for the transmission dynamics of a vector-borne disease with two vector strains, one wild and one pathogen-resistant; resistance comes at the cost of reduced reproductive fitness. The model, which assumes that vector reproduction can lead to the transmission or loss of resistance (reversion), is analyzed in a particular case with specified forms for the birth and force of infection functions. The vector component can have, in the absence of disease, a coexistence equilibrium where both strains survive. In the case where reversion is possible, this coexistence equilibrium is globally asymptotically stable when it exists. This equilibrium is still present in the full vector-host system, leading to a reduction of the associated reproduction number, thereby making elimination of the disease more feasible. When reversion is not possible, there can exist an additional equilibrium with only resistant vectors.     

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.     

Natural vertical transmission of dengue viruses in Aedes aegypti in selected sites in Cebu City,Philippines

We attempted to determine the vertical transmission of dengue virus (DENV) in Aedes aegypti in selected sites in Cebu City, Philippines. Mosquito sub‐adults were collected monthly from households and the field during the wet‐dry‐wet season from November, 2011 to July, 2012 and were laboratory‐reared to adults. Viral RNA extracts in mosquitoes were assayed by hemi‐nested RT‐PCR. Results showed that 62 (36.26%; n=679) out of 171 mosquito pools (n=2,871) were DENV+. The minimum infection rate (MIR) of DENV ranged from 0 in wet months to 48.22/1,000 mosquitoes in April, 2012 (mid‐dry). DENVs were detected in larvae, pupae, and male and female adults, with DENV‐4, DENV‐3, and DENV‐1, in that rank of prevalence. DENV‐1 co‐infected with either DENV‐3 or ?4 or with both in April, 2012; DENV‐3 and ?4 were present in both seasons. More DENV+ mosquitoes were collected from households than in field premises (p<0.001) and in the dry than in the wet season (p<0.05), with significant interaction (p<0.05) between sites and premises but no interaction between sites and seasons (p>0.05). By Generalized Linear Mixed models, the type of premises nested in sites and monthly total rainfall were significant predictors of monthly dengue cases (p<0.05) and not MIR, season, temperature, and relative humidity. Surveillance of DENV prevalence in Ae. aegypti and detecting their natural foci in the dry season provide an early warning signal of dengue outbreak.     

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.     

Virulence and community dynamics of fungal species with vertical and horizontal transmission on a plant with multiple infections

The virulence evolution of multiple infections of parasites from the same species has been modeled widely in evolution theory. However, experimental studies on this topic remain scarce, particularly regarding multiple infections by different parasite species. Here, we characterized the virulence and community dynamics of fungal pathogens on the invasive plant Ageratina adenophora to verify the predictions made by the model. We observed that A. adenophora was highly susceptible to diverse foliar pathogens with mixed vertical and horizontal transmission within leaf spots. The transmission mode mainly determined the pathogen community structure at the leaf spot level. Over time, the pathogen community within a leaf spot showed decreased Shannon diversity; moreover, the vertically transmitted pathogens exhibited decreased virulence to the host A. adenophora, but the horizontally transmitted pathogens exhibited increased virulence to the host. Our results demonstrate that the predictions of classical models for the virulence evolution of multiple infections are still valid in a complex realistic environment and highlight the impact of transmission mode on disease epidemics of foliar fungal pathogens. We also propose that seedborne fungi play an important role in structuring the foliar pathogen community from multiple infections within a leaf spot.