A large-scale stochastic spatiotemporal model for Aedes albopictus-borne chikungunya epidemiology.

Chikungunya is a viral disease transmitted to humans primarily via the bites of infected Aedes mosquitoes. The virus caused a major epidemic in the Indian Ocean in 2004, affecting millions of inhabitants, while cases have also been observed in Europe since 2007. We developed a stochastic spatiotemporal model of Aedes albopictus-borne chikungunya transmission based on our recently developed environmentally-driven vector population dynamics model. We designed an integrated modelling framework incorporating large-scale gridded climate datasets to investigate disease outbreaks on Reunion Island and in Italy. We performed Bayesian parameter inference on the surveillance data, and investigated the validity and applicability of the underlying biological assumptions. The model successfully represents the outbreak and measures of containment in Italy, suggesting wider applicability in Europe. In its current configuration, the model implies two different viral strains, thus two different outbreaks, for the two-stage Reunion Island epidemic. Characterisation of the posterior distributions indicates a possible relationship between the second larger outbreak on Reunion Island and the Italian outbreak. The model suggests that vector control measures, with different modes of operation, are most effective when applied in combination: adult vector intervention has a high impact but is short-lived, larval intervention has a low impact but is long-lasting, and quarantining infected territories, if applied strictly, is effective in preventing large epidemics. We present a novel approach in analysing chikungunya outbreaks globally using a single environmentally-driven mathematical model. Our study represents a significant step towards developing a globally applicable Ae. albopictus-borne chikungunya transmission model, and introduces a guideline for extending such models to other vector-borne diseases.

Correction: Structural Perturbations to Population Skeletons: Transient Dynamics, Coexistence of Attractors and the Rarity of Chaos.

[This corrects the article DOI: 10.1371/journal.pone.0024200.].

Large-Scale Modelling of the Environmentally-Driven Population Dynamics of Temperate Aedes albopictus (Skuse).

The Asian tiger mosquito, Aedes albopictus, is a highly invasive vector species. It is a proven vector of dengue and chikungunya viruses, with the potential to host a further 24 arboviruses. It has recently expanded its geographical range, threatening many countries in the Middle East, Mediterranean, Europe and North America. Here, we investigate the theoretical limitations of its range expansion by developing an environmentally-driven mathematical model of its population dynamics. We focus on the temperate strain of Ae. albopictus and compile a comprehensive literature-based database of physiological parameters. As a novel approach, we link its population dynamics to globally-available environmental datasets by performing inference on all parameters. We adopt a Bayesian approach using experimental data as prior knowledge and the surveillance dataset of Emilia-Romagna, Italy, as evidence. The model accounts for temperature, precipitation, human population density and photoperiod as the main environmental drivers, and, in addition, incorporates the mechanism of diapause and a simple breeding site model. The model demonstrates high predictive skill over the reference region and beyond, confirming most of the current reports of vector presence in Europe. One of the main hypotheses derived from the model is the survival of Ae. albopictus populations through harsh winter conditions. The model, constrained by the environmental datasets, requires that either diapausing eggs or adult vectors have increased cold resistance. The model also suggests that temperature and photoperiod control diapause initiation and termination differentially. We demonstrate that it is possible to account for unobserved properties and constraints, such as differences between laboratory and field conditions, to derive reliable inferences on the environmental dependence of Ae. albopictus populations.

Larval and adult environmental temperatures influence the adult reproductive traits of Anopheles gambiae s.s.

BACKGROUND: Anopheles mosquito life-history parameters and population dynamics strongly influence malaria transmission, and environmental factors, particularly temperature, strongly affect these parameters. There are currently some studies on how temperature affects Anopheles gambiae s.s. survival but very few exist examining other life-history traits. We investigate here the effect of temperature on population dynamics parameters. METHODS: Anopheles gambiae s.s. immatures were reared individually at 23 ± 1 °C, 27 ± 1 °C, 31 ± 1 °C, and 35 ± 1 °C, and adults were held at their larval temperature or at one of the other temperatures. Larvae were checked every 24 h for development to the next stage and measured for size; wing length was measured as a proxy for adult size. Females were blood fed three times, and the number of females feeding and laying eggs was counted. The numbers of eggs and percentage of eggs hatched were recorded. RESULTS: Increasing temperatures during the larval stages resulted in significantly smaller larvae (p = 0.005) and smaller adults (p < 0.001). Adult temperature had no effect on the time to egg laying, and the larval temperature of adults only affected the incubation period of the first egg batch. Temperature influenced the time to hatching of eggs, as well as the time to development at every stage. The number of eggs laid was highest when adults were kept at 27 °C, and lowest at 31 °C, and higher adult temperatures decreased the proportion of eggs hatching after the second and third blood meal. Higher adult temperatures significantly decreased the probability of blood feeding, but the larval temperature of adults had no influence on the probability of taking a blood meal. Differences were observed between the first, second, and third blood meal in the times to egg laying and hatching, number of eggs laid, and probabilities of feeding and laying eggs. CONCLUSIONS: Our study shows that environmental temperature during the larval stages as well as during the adult stages affects Anopheles life-history parameters. Data on how temperature and other climatic factors affect vector life-history parameters are necessary to parameterise more reliably models predicting how global warming may influence malaria transmission.

Modelling Anopheles gambiae s.s. Population Dynamics with Temperature- and Age-Dependent Survival.

Climate change and global warming are emerging as important threats to human health, particularly through the potential increase in vector- and water-borne diseases. Environmental variables are known to affect substantially the population dynamics and abundance of the poikilothermic vectors of disease, but the exact extent of this sensitivity is not well established. Focusing on malaria and its main vector in Africa, Anopheles gambiae sensu stricto, we present a set of novel mathematical models of climate-driven mosquito population dynamics motivated by experimental data suggesting that in An. gambiae, mortality is temperature and age dependent. We compared the performance of these models to that of a "standard" model ignoring age dependence. We used a longitudinal dataset of vector abundance over 36 months in sub-Saharan Africa for comparison between models that incorporate age dependence and one that does not, and observe that age-dependent models consistently fitted the data better than the reference model. This highlights that including age dependence in the vector component of mosquito-borne disease models may be important to predict more reliably disease transmission dynamics. Further data and studies are needed to enable improved fitting, leading to more accurate and informative model predictions for the An. gambiae malaria vector as well as for other disease vectors.

Climate, environmental and socio-economic change: weighing up the balance in vector-borne disease transmission.

Arguably one of the most important effects of climate change is the potential impact on human health. While this is likely to take many forms, the implications for future transmission of vector-borne diseases (VBDs), given their ongoing contribution to global disease burden, are both extremely important and highly uncertain. In part, this is owing not only to data limitations and methodological challenges when integrating climate-driven VBD models and climate change projections, but also, perhaps most crucially, to the multitude of epidemiological, ecological and socio-economic factors that drive VBD transmission, and this complexity has generated considerable debate over the past 10-15 years. In this review, we seek to elucidate current knowledge around this topic, identify key themes and uncertainties, evaluate ongoing challenges and open research questions and, crucially, offer some solutions for the field. Although many of these challenges are ubiquitous across multiple VBDs, more specific issues also arise in different vector-pathogen systems.

Climate influences on the cost-effectiveness of vector-based interventions against malaria in elimination scenarios.

Despite the dependence of mosquito population dynamics on environmental conditions, the associated impact of climate and climate change on present and future malaria remains an area of ongoing debate and uncertainty. Here, we develop a novel integration of mosquito, transmission and economic modelling to assess whether the cost-effectiveness of indoor residual spraying (IRS) and long-lasting insecticidal nets (LLINs) against Plasmodium falciparum transmission by Anopheles gambiae s.s. mosquitoes depends on climatic conditions in low endemicity scenarios. We find that although temperature and rainfall affect the cost-effectiveness of IRS and/or LLIN scale-up, whether this is sufficient to influence policy depends on local endemicity, existing interventions, host immune response to infection and the emergence rate of insecticide resistance. For the scenarios considered, IRS is found to be more cost-effective than LLINs for the same level of scale-up, and both are more cost-effective at lower mean precipitation and higher variability in precipitation and temperature. We also find that the dependence of peak transmission on mean temperature translates into optimal temperatures for vector-based intervention cost-effectiveness. Further cost-effectiveness analysis that accounts for country-specific epidemiological and environmental heterogeneities is required to assess optimal intervention scale-up for elimination and better understand future transmission trends under climate change.

The impact of climate change on the geographical distribution of two vectors of Chagas disease: implications for the force of infection.

Chagas disease, caused by the parasite Trypanosoma cruzi, is the most important vector-borne disease in Latin America. The vectors are insects belonging to the Triatominae (Hemiptera, Reduviidae), and are widely distributed in the Americas. Here, we assess the implications of climatic projections for 2050 on the geographical footprint of two of the main Chagas disease vectors: Rhodnius prolixus (tropical species) and Triatoma infestans (temperate species). We estimated the epidemiological implications of current to future transitions in the climatic niche in terms of changes in the force of infection (FOI) on the rural population of two countries: Venezuela (tropical) and Argentina (temperate). The climatic projections for 2050 showed heterogeneous impact on the climatic niches of both vector species, with a decreasing trend of suitability of areas that are currently at high-to-moderate transmission risk. Consequently, climatic projections affected differently the FOI for Chagas disease in Venezuela and Argentina. Despite the heterogeneous results, our main conclusions point out a decreasing trend in the number of new cases of Tr. cruzi human infections per year between current and future conditions using a climatic niche approach.

Temperature during larval development and adult maintenance influences the survival of Anopheles gambiae s.s.

BACKGROUND: Malaria transmission depends on vector life-history parameters and population dynamics, and particularly on the survival of adult Anopheles mosquitoes. These dynamics are sensitive to climatic and environmental factors, and temperature is a particularly important driver. Data currently exist on the influence of constant and fluctuating adult environmental temperature on adult Anopheles gambiae s.s. survival and on the effect of larval environmental temperature on larval survival, but none on how larval temperature affects adult life-history parameters. METHODS: Mosquito larvae and pupae were reared individually at different temperatures (23 ± 1°C, 27 ± 1°C, 31 ± 1°C, and 35 ± 1°C), 75 ± 5% relative humidity. Upon emergence into imagoes, individual adult females were either left at their larval temperature or placed at a different temperature within the range above. Survival was monitored every 24 hours and data were analysed using non-parametric and parametric methods. The Gompertz distribution fitted the survivorship data better than the gamma, Weibull, and exponential distributions overall and was adopted to describe mosquito mortality rates. RESULTS: Increasing environmental temperature during the larval stages decreased larval survival (p < 0.001). Increases of 4°C (from 23°C to 27°C, 27°C to 31°C, and 31°C to 35°C), 8°C (27°C to 35°C) and 12°C (23°C to 35°C) statistically significantly increased larval mortality (p < 0.001). Higher environmental temperature during the adult stages significantly lowered adult survival overall (p < 0.001), with increases of 4°C and 8°C significantly influencing survival (p < 0.001). Increasing the larval environment temperature also significantly increased adult mortality overall (p < 0.001): a 4°C increase (23°C to 27°C) did not significantly affect adult survival (p > 0.05), but an 8°C increase did (p < 0.05). The effect of a 4°C increase in larval temperature from 27°C to 31°C depended on the adult environmental temperature. The data also suggest that differences between the temperatures of the larval and adult environments affects adult mosquito survival. CONCLUSIONS: Environmental temperature affects Anopheles survival directly during the juvenile and adult stages, and indirectly, since temperature during larval development significantly influences adult survival. These results will help to parameterise more reliable mathematical models investigating the potential impact of temperature and global warming on malaria transmission.

The role of environmental variables on Aedes albopictus biology and chikungunya epidemiology.

Aedes albopictus is a vector of dengue and chikungunya viruses in the field, along with around 24 additional arboviruses under laboratory conditions. As an invasive mosquito species, Ae. albopictus has been expanding in geographical range over the past 20 years, although the poleward extent of mosquito populations is limited by winter temperatures. Nonetheless, population densities depend on environmental conditions and since global climate change projections indicate increasing temperatures and altered patterns of rainfall, geographic distributions of previously tropical mosquito species may change. Although mathematical models can provide explanatory insight into observed patterns of disease prevalence in terms of epidemiological and entomological processes, understanding how environmental variables affect transmission is possible only with reliable model parameterisation, which, in turn, is obtained only through a thorough understanding of the relationship between mosquito biology and environmental variables. Thus, in order to assess the impact of climate change on mosquito population distribution and regions threatened by vector-borne disease, a detailed understanding (through a synthesis of current knowledge) of the relationship between climate, mosquito biology, and disease transmission is required, but this process has not yet been undertaken for Ae. albopictus. In this review, the impact of temperature, rainfall, and relative humidity on Ae. albopictus development and survival are considered. Existing Ae. albopictus populations across Europe are mapped with current climatic conditions, considering whether estimates of climatic cutoffs for Ae. albopictus are accurate, and suggesting that environmental thresholds must be calibrated according to the scale and resolution of climate model outputs and mosquito presence data.

Modelling co-infection with malaria and lymphatic filariasis.

Malaria and lymphatic filariasis (LF) continue to cause a considerable public health burden globally and are co-endemic in many regions of sub-Saharan Africa. These infections are transmitted by the same mosquito species which raises important questions about optimal vector control strategies in co-endemic regions, as well as the effect of the presence of each infection on endemicity of the other; there is currently little consensus on the latter. The need for comprehensive modelling studies to address such questions is therefore significant, yet very few have been undertaken to date despite the recognised explanatory power of reliable dynamic mathematical models. Here, we develop a malaria-LF co-infection modelling framework that accounts for two key interactions between these infections, namely the increase in vector mortality as LF mosquito prevalence increases and the antagonistic Th1/Th2 immune response that occurs in co-infected hosts. We consider the crucial interplay between these interactions on the resulting endemic prevalence when introducing each infection in regions where the other is already endemic (e.g. due to regional environmental change), and the associated timescale for such changes, as well as effects on the basic reproduction number R0 of each disease. We also highlight potential perverse effects of vector controls on human infection prevalence in co-endemic regions, noting that understanding such effects is critical in designing optimal integrated control programmes. Hence, as well as highlighting where better data are required to more reliably address such questions, we provide an important framework that will form the basis of future scenario analysis tools used to plan and inform policy decisions on intervention measures in different transmission settings.

Modeling the role of environmental variables on the population dynamics of the malaria vector Anopheles gambiae sensu stricto.

BACKGROUND: The impact of weather and climate on malaria transmission has attracted considerable attention in recent years, yet uncertainties around future disease trends under climate change remain. Mathematical models provide powerful tools for addressing such questions and understanding the implications for interventions and eradication strategies, but these require realistic modeling of the vector population dynamics and its response to environmental variables. METHODS: Published and unpublished field and experimental data are used to develop new formulations for modeling the relationships between key aspects of vector ecology and environmental variables. These relationships are integrated within a validated deterministic model of Anopheles gambiae s.s. population dynamics to provide a valuable tool for understanding vector response to biotic and abiotic variables. RESULTS: A novel, parsimonious framework for assessing the effects of rainfall, cloudiness, wind speed, desiccation, temperature, relative humidity and density-dependence on vector abundance is developed, allowing ease of construction, analysis, and integration into malaria transmission models. Model validation shows good agreement with longitudinal vector abundance data from Tanzania, suggesting that recent malaria reductions in certain areas of Africa could be due to changing environmental conditions affecting vector populations. CONCLUSIONS: Mathematical models provide a powerful, explanatory means of understanding the role of environmental variables on mosquito populations and hence for predicting future malaria transmission under global change. The framework developed provides a valuable advance in this respect, but also highlights key research gaps that need to be resolved if we are to better understand future malaria risk in vulnerable communities.

Structural perturbations to population skeletons: transient dynamics, coexistence of attractors and the rarity of chaos.

BACKGROUND: Simple models of insect populations with non-overlapping generations have been instrumental in understanding the mechanisms behind population cycles, including wild (chaotic) fluctuations. The presence of deterministic chaos in natural populations, however, has never been unequivocally accepted. Recently, it has been proposed that the application of chaos control theory can be useful in unravelling the complexity observed in real population data. This approach is based on structural perturbations to simple population models (population skeletons). The mechanism behind such perturbations to control chaotic dynamics thus far is model dependent and constant (in size and direction) through time. In addition, the outcome of such structurally perturbed models is [almost] always equilibrium type, which fails to commensurate with the patterns observed in population data. METHODOLOGY/PRINCIPAL FINDINGS: We present a proportional feedback mechanism that is independent of model formulation and capable of perturbing population skeletons in an evolutionary way, as opposed to requiring constant feedbacks. We observe the same repertoire of patterns, from equilibrium states to non-chaotic aperiodic oscillations to chaotic behaviour, across different population models, in agreement with observations in real population data. Model outputs also indicate the existence of multiple attractors in some parameter regimes and this coexistence is found to depend on initial population densities or the duration of transient dynamics. Our results suggest that such a feedback mechanism may enable a better understanding of the regulatory processes in natural populations.

Outbreak properties of epidemic models: the roles of temporal forcing and stochasticity on pathogen invasion dynamics.

Despite temporally forced transmission driving many infectious diseases, analytical insight into its role when combined with stochastic disease processes and non-linear transmission has received little attention. During disease outbreaks, however, the absence of saturation effects early on in well-mixed populations mean that epidemic models may be linearised and we can calculate outbreak properties, including the effects of temporal forcing on fade-out, disease emergence and system dynamics, via analysis of the associated master equations. The approach is illustrated for the unforced and forced SIR and SEIR epidemic models. We demonstrate that in unforced models, initial conditions (and any uncertainty therein) play a stronger role in driving outbreak properties than the basic reproduction number R0, while the same properties are highly sensitive to small amplitude temporal forcing, particularly when R0 is small. Although illustrated for the SIR and SEIR models, the master equation framework may be applied to more realistic models, although analytical intractability scales rapidly with increasing system dimensionality. One application of these methods is obtaining a better understanding of the rate at which vector-borne and waterborne infectious diseases invade new regions given variability in environmental drivers, a particularly important question when addressing potential shifts in the global distribution and intensity of infectious diseases under climate change.

Modelling climate change and malaria transmission.

The impact of climate change on human health has received increasing attention in recent years, with potential impacts due to vector-borne diseases only now beginning to be understood. As the most severe vector-borne disease, with one million deaths globally in 2006, malaria is thought most likely to be affected by changes in climate variables due to the sensitivity of its transmission dynamics to environmental conditions. While considerable research has been carried out using statistical models to better assess the relationship between changes in environmental variables and malaria incidence, less progress has been made on developing process-based climate-driven mathematical models with greater explanatory power. Here, we develop a simple model of malaria transmission linked to climate which permits useful insights into the sensitivity of disease transmission to changes in rainfall and temperature variables. Both the impact of changes in the mean values of these key external variables and importantly temporal variation in these values are explored. We show that the development and analysis of such dynamic climate-driven transmission models will be crucial to understanding the rate at which P. falciparum and P. vivax may either infect, expand into or go extinct in populations as local environmental conditions change. Malaria becomes endemic in a population when the basic reproduction number R0 is greater than unity and we identify an optimum climate-driven transmission window for the disease, thus providing a useful indicator for determing how transmission risk may change as climate changes. Overall, our results indicate that considerable work is required to better understand ways in which global malaria incidence and distribution may alter with climate change. In particular, we show that the roles of seasonality, stochasticity and variability in environmental variables, as well as ultimately anthropogenic effects, require further study. The work presented here offers a theoretical framework upon which this future research may be developed.

Space and contact networks: capturing the locality of disease transmission.

While an arbitrary level of complexity may be included in simulations of spatial epidemics, computational intensity and analytical intractability mean that such models often lack transparency into the determinants of epidemiological dynamics. Although numerous approaches attempt to resolve this complexity-tractability trade-off, moment closure methods arguably offer the most promising and robust frameworks for capturing the role of the locality of contact processes on global disease dynamics. While a close analogy may be made between full stochastic spatial transmission models and dynamic network models, we consider here the special case where the dynamics of the network topology change on time-scales much longer than the epidemiological processes imposed on them; in such cases, the use of static network models are justified. We show that in such cases, static network models may provide excellent approximations to the underlying spatial contact process through an appropriate choice of the effective neighbourhood size. We also demonstrate the robustness of this mapping by examining the equivalence of deterministic approximations to the full spatial and network models derived under third-order moment closure assumptions. For systems where deviation from homogeneous mixing is limited, we show that pair equations developed for network models are at least as good an approximation to the underlying stochastic spatial model as more complex spatial moment equations, with both classes of approximation becoming less accurate only for highly localized kernels.