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Optimal release strategies for mosquito population replacement
... Since H is constant we can remove R H from the system of differential equations and compute it as (1) can be used for modeling, a priori, any vector-borne disease without other means of transmission and for which reinfection cannot occur. ...
... The infected compartments in our case are those in which there are individuals carrying the dengue virus. For model (1) these are E H ,I H ,E M and I M . ...
... H (t) dt. Other works have studied related problems in the case of Wolbachia[38], or problems involving only the mosquito population[2,3,1,4] considering controls in L ∞ (0, T ). ...
This paper is devoted to the study of optimal release strategies to control vector-borne diseases, such as dengue, Zika, chikungunya and malaria. Two techniques are considered: the sterile insect one (SIT), which consists in releasing sterilized males among wild vectors in order to perturb their reproduction, and the Wolbachia one (presently used mainly for mosquitoes), which consists in releasing vectors, that are infected with a bacterium limiting their vector capacity, in order to replace the wild population by one with reduced vector capacity. In each case, the time dynamics of the vector population is modeled by a system of ordinary differential equations in which the releases are represented by linear combinations of Dirac measures with positive coefficients determining their intensity. We introduce optimal control problems that we solve numerically using ad-hoc algorithms, based on writing first-order optimality conditions characterizing the best combination of Dirac measures. We then discuss the results obtained, focusing in particular on the complexity and efficiency of optimal controls and comparing the strategies obtained. Mathematical modeling can help testing a great number of scenarios that are potentially interesting in future interventions (even those that are orthogonal to the present strategies) but that would be hard, costly or even impossible to test in the field in present conditions.
In the fight against vector-borne arboviruses, an important strategy of control of epidemic consists in controlling the population of the vector, Aedes mosquitoes in this case. Among possible actions, two techniques consist either in releasing sterile mosquitoes to reduce the size of the population (Sterile Insect Technique) or in replacing the wild population by one carrying a bacteria, called Wolbachia, blocking the transmission of viruses from insects to humans. This article addresses the issue of optimizing the dissemination protocol for each of these strategies, in order to get as close as possible to these objectives. Starting from a mathematical model describing population dynamics, we study the control problem and introduce the cost function standing for population replacement and sterile insect technique. Then, we establish some properties of the optimal control and illustrate them with numerical simulations.
Experiments and field trials have shown that the intracellular bacterium Wolbachia may be introduced into populations of the mosquito Aedes aegypti, the primary vector for dengue fever. In the absence of Wolbachia, a mosquito acquiring the dengue virus from an infected human enters an exposed (infected but not infectious) period before becoming infectious itself. A Wolbachia-infected mosquito that acquires dengue (i) may have a reduced lifespan, so that it is less likely to survive the exposed period and become infectious, and (ii) may have a reduced ability to transmit dengue, even if it has survived the exposed period. Wolbachia introduction has therefore been suggested as a potential dengue control measure. We set up a mathematical model for the system to investigate this suggestion and to evaluate the desirable properties of the Wolbachia strain to be introduced. We show that Wolbachia has excellent potential for dengue control in areas where R 0 is not too large. However, if R 0 is large, Wolbachia strains that reduce but do not eliminate dengue transmission have little effect on endemic steady states or epidemic sizes. Unless control measures to reduce R 0 by reducing mosquito populations are also put in place, it may be worth the extra effort in such cases to introduce Wolbachia strains that eliminate dengue transmission completely.
Dengue is a growing problem both in its geographical spread and in its intensity, and yet current global distribution remains highly uncertain. Challenges in diagnosis and diagnostic methods as well as highly variable national health systems mean no single data source can reliably estimate the distribution of this disease. As such, there is a lack of agreement on national dengue status among international health organisations. Here we bring together all available information on dengue occurrence using a novel approach to produce an evidence consensus map of the disease range that highlights nations with an uncertain dengue status.
A baseline methodology was used to assess a range of evidence for each country. In regions where dengue status was uncertain, additional evidence types were included to either clarify dengue status or confirm that it is unknown at this time. An algorithm was developed that assesses evidence quality and consistency, giving each country an evidence consensus score. Using this approach, we were able to generate a contemporary global map of national-level dengue status that assigns a relative measure of certainty and identifies gaps in the available evidence.
The map produced here provides a list of 128 countries for which there is good evidence of dengue occurrence, including 36 countries that have previously been classified as dengue-free by the World Health Organization and/or the US Centers for Disease Control. It also identifies disease surveillance needs, which we list in full. The disease extents and limits determined here using evidence consensus, marks the beginning of a five-year study to advance the mapping of dengue virus transmission and disease risk. Completion of this first step has allowed us to produce a preliminary estimate of population at risk with an upper bound of 3.97 billion people. This figure will be refined in future work.
Genetic manipulations of insect populations for pest control have been advocated for some time, but there are few cases where manipulated individuals have been released in the field and no cases where they have successfully invaded target populations. Population transformation using the intracellular bacterium Wolbachia is particularly attractive because this maternally-inherited agent provides a powerful mechanism to invade natural populations through cytoplasmic incompatibility. When Wolbachia are introduced into mosquitoes, they interfere with pathogen transmission and influence key life history traits such as lifespan. Here we describe how the wMel Wolbachia infection, introduced into the dengue vector Aedes aegypti from Drosophila melanogaster, successfully invaded two natural A. aegypti populations in Australia, reaching near-fixation in a few months following releases of wMel-infected A. aegypti adults. Models with plausible parameter values indicate that Wolbachia-infected mosquitoes suffered relatively small fitness costs, leading to an unstable equilibrium frequency <30% that must be exceeded for invasion. These findings demonstrate that Wolbachia-based strategies can be deployed as a practical approach to dengue suppression with potential for area-wide implementation.
Dengue fever is the most important mosquito-borne viral disease of humans with more than 50 million cases estimated annually in more than 100 countries. Disturbingly, the geographic range of dengue is currently expanding and the severity of outbreaks is increasing. Control options for dengue are very limited and currently focus on reducing population abundance of the major mosquito vector, Aedes aegypti. These strategies are failing to reduce dengue incidence in tropical communities and there is an urgent need for effective alternatives. It has been proposed that endosymbiotic bacterial Wolbachia infections of insects might be used in novel strategies for dengue control. For example, the wMelPop-CLA Wolbachia strain reduces the lifespan of adult A. aegypti mosquitoes in stably transinfected lines. This life-shortening phenotype was predicted to reduce the potential for dengue transmission. The recent discovery that several Wolbachia infections, including wMelPop-CLA, can also directly influence the susceptibility of insects to infection with a range of insect and human pathogens has markedly changed the potential for Wolbachia infections to control human diseases. Here we describe the successful transinfection of A. aegypti with the avirulent wMel strain of Wolbachia, which induces the reproductive phenotype cytoplasmic incompatibility with minimal apparent fitness costs and high maternal transmission, providing optimal phenotypic effects for invasion. Under semi-field conditions, the wMel strain increased from an initial starting frequency of 0.65 to near fixation within a few generations, invading A. aegypti populations at an accelerated rate relative to trials with the wMelPop-CLA strain. We also show that wMel and wMelPop-CLA strains block transmission of dengue serotype 2 (DENV-2) in A. aegypti, forming the basis of a practical approach to dengue suppression.
Wolbachia are maternally inherited intracellular bacterial symbionts that are estimated to infect more than 60% of all insect species. While Wolbachia is commonly found in many mosquitoes it is absent from the species that are considered to be of major importance for the transmission of human pathogens. The successful introduction of a life-shortening strain of Wolbachia into the dengue vector Aedes aegypti that halves adult lifespan has recently been reported. Here we show that this same Wolbachia infection also directly inhibits the ability of a range of pathogens to infect this mosquito species. The effect is Wolbachia strain specific and relates to Wolbachia priming of the mosquito innate immune system and potentially competition for limiting cellular resources required for pathogen replication. We suggest that this Wolbachia-mediated pathogen interference may work synergistically with the life-shortening strategy proposed previously to provide a powerful approach for the control of insect transmitted diseases.
The mosquito Aedes aegypti was recently transinfected with a life-shortening strain of the endosymbiont Wolbachia pipientis (wMelPop) as the first step in developing a biocontrol strategy for dengue virus transmission. In addition to life-shortening, the wMelPop-infected mosquitoes also exhibit increased daytime activity and metabolic rates. Here we sought to quantify the blood-feeding behaviour of Wolbachia-infected females as an indicator of any virulence or energetic drain associated with Wolbachia infection.
In a series of blood-feeding trials in response to humans, we have shown that Wolbachia-infected mosquitoes do not differ in their response time to humans, but that as they age they obtain fewer and smaller blood meals than Wolbachia-uninfected controls. Lastly, we observed a behavioural characteristic in the Wolbachia infected mosquitoes best described as a "bendy" proboscis that may explain the decreased biting success.
Taken together the evidence suggests that wMelPop infection may be causing tissue damage in a manner that intensifies with mosquito age and that leads to reduced blood-feeding success. These behavioural changes require further investigation with respect to a possible physiological mechanism and their role in vectorial capacity of the insect. The selective decrease of feeding success in older mosquitoes may act synergistically with other Wolbachia-associated traits including life-shortening and viral protection in biocontrol strategies.
Effective vector control, and more specifically mosquito control, is a complex and difficult problem, as illustrated by the continuing prevalence (and spread) of mosquito-transmitted diseases. The sterile insect technique and similar methods control certain agricultural insect pest populations in a species-specific, environmentally sound, and effective manner; there is increased interest in applying this approach to vector control. Such an approach, like all others in use and development, is not a one-size-fits-all solution, and will be more appropriate in some situations than others. In addition, the proposed release of pest insects, and more so genetically modified pest insects, is bound to raise questions in the general public and the scientific community as to such a method's efficacy, safety, and sustainability. This article attempts to address these concerns and indicate where sterile-insect methods are likely to be useful for vector control.
Genetics can potentially provide new, species-specific, environmentally friendly methods for mosquito control. Genetic control strategies aim either to suppress target populations or to introduce a harm-reducing novel trait. Different approaches differ considerably in their properties, especially between self-limiting strategies, where the modification has limited persistence, and self-sustaining strategies, which are intended to persist indefinitely in the target population and may invade other populations. Several methods with different molecular biology are under development and the first field trials have been completed successfully. Expected final online publication date for the Annual Review of Entomology Volume 59 is January 07, 2014. Please see http://www.annualreviews.org/catalog/pubdates.aspx for revised estimates.
The chikungunya (CHIK) outbreak that struck La Reunion Island in 2005 was preceded by few human cases of Dengue (DEN), but which surprisingly did not lead to an epidemic as might have been expected in a non-immune population. Both arboviral diseases are transmitted to humans by two main mosquito species, Aedes aegypti and Aedes albopictus. In the absence of the former, Ae. albopictus was the only species responsible for viral transmission on La Reunion Island. This mosquito is naturally super-infected with two Wolbachia strains, wAlbA and wAlbB. While Wolbachia does not affect replication of CHIK virus (CHIKV) in Ae. albopictus, a similar effect was not observed with DEN virus (DENV).
To understand the weak vectorial status of Ae. albopictus towards DENV, we used experimental oral infections of mosquitoes from La Reunion Island to characterize the impact of Wolbachia on DENV infection. Viral loads and Wolbachia densities were measured by quantitative PCR in different organs of Ae. albopictus where DENV replication takes place after ingestion. We found that: (i) Wolbachia does not affect viral replication, (ii) Wolbachia restricts viral density in salivary glands, and (iii) Wolbachia limits transmission of DENV, as infectious viral particles were only detected in the saliva of Wolbachia-uninfected Ae. albopictus, 14 days after the infectious blood-meal.
We show that Wolbachia does not affect the replication of DENV in Ae. albopictus. However, Wolbachia is able to reduce viral infection of salivary glands and limit transmission, suggesting a role of Wolbachia in naturally restricting the transmission of DENV in Ae. albopictus from La Reunion Island. The extension of this conclusion to other Ae. albopictus populations should be investigated.
Wolbachia is one of the most common symbionts of arthropods. Its establishment requires lateral transfer to and successful transmission within novel host species. However, Wolbachia performs poorly when introduced into new host species, and models predict that Wolbachia should seldom be able to establish from low initial frequencies. Recently, various symbionts, including Wolbachia, have been shown to protect their hosts from natural enemies. Hence, Wolbachia invasion may be facilitated by the dynamic interaction between it, its host, and a natural enemy. We model such an interaction whereby Wolbachia induces either complete resistance, partial resistance, or tolerance to a host-specific pathogen and also induces the common manipulation phenotype of cytoplasmic incompatibility (CI). We show that the presence of the pathogen greatly facilitates Wolbachia invasion from rare and widens the parameter space in which "imperfect" Wolbachia strains can invade. Furthermore, positive frequency-dependent selection through CI can drive Wolbachia to very high frequencies, potentially excluding the pathogen. These results may explain a poorly understood aspect of Wolbachia biology: it is widespread, despite performing poorly after transfer to new host species. They also support the intriguing possibility that Wolbachia strains that encode both CI and natural-enemy resistance could potentially rid insects, including human disease vectors, of important pathogens.
Dengue fever and dengue haemorrhagic fever are important arthropod-borne viral diseases. Each year, there are ∼50 million dengue infections and ∼500,000 individuals are hospitalized with dengue haemorrhagic fever, mainly in Southeast Asia, the Pacific and the Americas. Illness is produced by any of the four dengue virus serotypes. A global strategy aimed at increasing the capacity for surveillance and outbreak response, changing behaviours and reducing the disease burden using integrated vector management in conjunction with early and accurate diagnosis has been advocated. Antiviral drugs and vaccines that are currently under development could also make an important contribution to dengue control in the future.
We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont Wolbachia. The continuous models are characterized by partial vertical transmission, cytoplasmic incompatibility and fitness costs associated with the infection. A particular aspect of interest is competitions between mutually incompatible strains. We further introduce an age-structured model that takes into account different fertility and mortality rates at different stages of the life cycle of the individuals. With only a few parameters, the ordinary differential equation models exhibit already interesting dynamics and can be used to predict criteria under which a strain of bacteria is able to invade a population. Interestingly, but not surprisingly, the age-structured model shows significant differences concerning the existence and stability of equilibrium solutions compared to the unstructured model.
Wolbachia are maternally inherited bacteria that induce cytoplasmic incompatibility in mosquitoes, and are able to use these patterns of sterility to spread themselves through populations. For this reason they have been proposed as a gene drive system for mosquito genetic replacement, as well as for the reduction of population size or for modulating population age structure in order to reduce disease transmission. Here, recent progress in the study of mosquito Wolbachia is reviewed. We now have much more comprehensive estimates of the parameters that can affect the spread of Wolbachia through natural populations from low starting frequencies, and for waves of spread to be maintained in the face of partial barriers to gene flow. In Aedes albopictus these dynamics are extremely favourable, with very high maternal transmission fidelity and levels of incompatibility recorded. Correspondence between measurements taken in the lab and field is much better than in the Drosophila simulans model system. Important research goals are also discussed, including Wolbachia transformation, interspecific transfer and the elucidation of the mechanisms of incompatibility and rescue; all will be aided by a wealth of new Wolbachia genome information.
Vector-borne diseases
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