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Mathematical models provide the essential basis of rational research and development strategies in malaria, informing the choice of which technologies to target, which deployment strategies to consider, and which populations to focus on. The Internet and remote sensing technologies also enable assembly of ever more relevant field data. Together with supercomputing technology, this has made available timely descriptions of the geography of malaria transmission and disease across the world and made it possible for policy and planning to be informed by detailed simulations of the potential impact of intervention programs. These information technology advances do not replace the basic understanding of the dynamics of malaria transmission that should be embedded in the thinking of anyone planning malaria interventions. The appropriate use of modeling may determine whether we are living in an era of hubris or indeed in an age of eradication., (Copyright © 2017 Cold Spring Harbor Laboratory Press; all rights reserved.)

Vector control interventions have resulted in considerable reductions in malaria morbidity and mortality. When universal coverage cannot be achieved for financial or logistical reasons, the spatial arrangement of vector control is potentially important for optimizing benefits. This study investigated the effect of spatial clustering of vector control interventions on reducing the population of biting mosquitoes. A discrete-space continuous-time mathematical model of mosquito population dynamics and dispersal was extended to incorporate vector control interventions of insecticide treated bednets (ITNs), Indoor residual Spraying (IRS), and larviciding. Simulations were run at varying levels of coverage and degree of spatial clustering. At medium to high coverage levels of each of the interventions or in combination was more effective to spatially spread these interventions than to cluster them. Suggesting that when financial resources are limited, unclustered distribution of these interventions is more effective. Although it is often stated that locally high coverage is needed to achieve a community effect of ITNs or IRS, our results suggest that if the coverage of ITNs or IRS are insufficient to achieve universal coverage, and there is no targeting of high risk areas, the overall effects on mosquito densities are much greater if they are distributed in an unclustered way, rather than clustered in specific localities. Also, given that interventions are often delivered preferentially to accessible areas, and are therefore clustered, our model results show this may be inefficient. This study provides evidence that the effectiveness of an intervention can be highly dependent on its spatial distribution. Vector control plans should consider the spatial arrangement of any intervention package to ensure effectiveness is maximized.

Eliminating malaria from highly endemic settings will require unprecedented levels of vector control. To suppress mosquito populations, vector control products targeting their blood hosts must attain high biological coverage of all available sources, rather than merely high demographic coverage of a targeted resource subset, such as humans while asleep indoors. Beyond defining biological coverage in a measurable way, the proportion of blood meals obtained from humans and the proportion of bites upon unprotected humans occurring indoors also suggest optimal target product profiles for delivering insecticides to humans or livestock. For vectors that feed only occasionally upon humans, preferred animal hosts may be optimal targets for mosquito-toxic insecticides, and vapour-phase insecticides optimized to maximize repellency, rather than toxicity, may be ideal for directly protecting people against indoor and outdoor exposure. However, for vectors that primarily feed upon people, repellent vapour-phase insecticides may be inferior to toxic ones and may undermine the impact of contact insecticides applied to human sleeping spaces, houses or clothing if combined in the same time and place. These concepts are also applicable to other mosquito-borne anthroponoses so that diverse target species could be simultaneously controlled with integrated vector management programmes. Measurements of these two crucial mosquito behavioural parameters should now be integrated into programmatically funded, longitudinal, national-scale entomological monitoring systems to inform selection of available technologies and investment in developing new ones.

Background: The effectiveness of long-lasting, insecticidal nets (LLINs) in preventing malaria is threatened by the changing biting behaviour of mosquitoes, from nocturnal and endophagic to crepuscular and exophagic, and by their increasing resistance to insecticides., Methods: Using epidemiological stochastic simulation models, we studied the impact of a mass LLIN distribution on Plasmodium falciparum malaria. Specifically, we looked at impact in terms of episodes prevented during the effective life of the batch and in terms of net health benefits (NHB) expressed in disability adjusted life years (DALYs) averted, depending on biting behaviour, resistance (as measured in experimental hut studies), and on pre-intervention transmission levels., Results: Results were very sensitive to assumptions about the probabilistic nature of host searching behaviour. With a shift towards crepuscular biting, under the assumption that individual mosquitoes repeat their behaviour each gonotrophic cycle, LLIN effectiveness was far less than when individual mosquitoes were assumed to vary their behaviour between gonotrophic cycles. LLIN effectiveness was equally sensitive to variations in host-searching behaviour (if repeated) and to variations in resistance. LLIN effectiveness was most sensitive to pre-intervention transmission level, with LLINs being least effective at both very low and very high transmission levels, and most effective at around four infectious bites per adult per year. A single LLIN distribution round remained cost effective, except in transmission settings with a pre-intervention inoculation rate of over 128 bites per year and with resistant mosquitoes that displayed a high proportion (over 40%) of determined crepuscular host searching, where some model variants showed negative NHB., Conclusions: Shifts towards crepuscular host searching behaviour can be as important in reducing LLIN effectiveness and cost effectiveness as resistance to pyrethroids. As resistance to insecticides is likely to slow down the development of behavioural resistance and vice versa, the two types of resistance are unlikely to occur within the same mosquito population. LLINs are likely cost effective interventions against malaria, even in areas with strong resistance to pyrethroids or where a large proportion of host-mosquito contact occurs during times when LLIN users are not under their nets.

Mosquito dispersal is a key behavioural factor that affects the persistence and resurgence of several vector-borne diseases. Spatial heterogeneity of mosquito resources, such as hosts and breeding sites, affects mosquito dispersal behaviour and consequently affects mosquito population structures, human exposure to vectors, and the ability to control disease transmission. In this paper, we develop and simulate a discrete-space continuous-time mathematical model to investigate the impact of dispersal and heterogeneous distribution of resources on the distribution and dynamics of mosquito populations. We build an ordinary differential equation model of the mosquito life cycle and replicate it across a hexagonal grid (multi-patch system) that represents two-dimensional space. We use the model to estimate mosquito dispersal distances and to evaluate the effect of spatial repellents as a vector control strategy. We find evidence of association between heterogeneity, dispersal, spatial distribution of resources, and mosquito population dynamics. Random distribution of repellents reduces the distance moved by mosquitoes, offering a promising strategy for disease control., (Copyright © 2012 Elsevier Inc. All rights reserved.)

Background: The 'overall insecticidal effect' is a key measure used to evaluate public health pesticides for indoor use in experimental hut trials. It depends on the proportion of mosquitoes that are killed out of those that enter the treated hut, intrinsic mortality in the control hut, and the ratio of mosquitoes entering the treatment hut to those entering the control hut. This paper critically examines the way the effect is defined, and discusses how it can be used to infer effectiveness of intervention programmes., Findings: The overall insecticidal effect, as defined by the World Health Organization in 2006, can be negative when deterrence from entering the treated hut is high, even if all mosquitoes that enter are killed, wrongly suggesting that the insecticide enhances mosquito survival. Also in the absence of deterrence, even if the insecticide kills all mosquitoes in the treatment hut, the insecticidal effect is less than 100%, unless intrinsic mortality is nil. A proposed alternative definition for the measurement of the overall insecticidal effect has the desirable range of 0 to 1 (100%), provided mortality among non-repelled mosquitoes in the treated hut is less than the corresponding mortality in the control hut. This definition can be built upon to formulate the coverage-dependent insecticidal effectiveness of an intervention programme. Coverage-dependent population protection against feeding can be formulated similarly., Conclusions: This paper shows that the 2006 recommended quantity for measuring the overall insecticidal effect is problematic, and proposes an alternative quantity with more desirable properties.

We describe and analyze a periodically-forced difference equation model for malaria in mosquitoes that captures the effects of seasonality and allows the mosquitoes to feed on a heterogeneous population of hosts. We numerically show the existence of a unique globally asymptotically stable periodic orbit and calculate periodic orbits of field-measurable quantities that measure malaria transmission. We integrate this model with an individual-based stochastic simulation model for malaria in humans to compare the effects of insecticide-treated nets (ITNs) and indoor residual spraying (IRS) in reducing malaria transmission, prevalence, and incidence. We show that ITNs are more effective than IRS in reducing transmission and prevalence though IRS would achieve its maximal effects within 2 years while ITNs would need two mass distribution campaigns over several years to do so. Furthermore, the combination of both interventions is more effective than either intervention alone. However, although these interventions reduce transmission and prevalence, they can lead to increased clinical malaria; and all three malaria indicators return to preintervention levels within 3 years after the interventions are withdrawn.

A quantitative framework is used to explore the potential applications and probable effects of sexual stage or mosquito stage transmission blocking vaccines (TBVs) against malaria. The combination of TBVs with biocides or other malaria vaccines will increase chances of interrupting transmission, whereas the value of TBVs for morbidity control will be limited. Vaccine combination will also protect against selection of insensitive parasites. Simulations indicate that TBVs will reduce risks of reestablishment of transmission when vector control is withdrawn. Simple mathematical analysis shows that efficacy and coverage are equally important, implying that a vaccine that requires a small number of doses (ideally one) is preferable to one that is difficult to deliver, even if this entails accepting a lower efficacy., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

Background: Traps baited with synthetic human odors have been proposed as suitable technologies for controlling malaria and other mosquito-borne diseases. We investigated the potential benefits of such traps for preventing malaria transmission in Africa and the essential characteristics that they should possess so as to be effective., Methods and Principal Findings: An existing mathematical model was reformulated to distinguish availability of hosts for attack by mosquitoes from availability of blood per se. This adaptation allowed the effects of pseudo-hosts such as odor-baited mosquito traps, which do not yield blood but which can nonetheless be attacked by the mosquitoes, to be simulated considering communities consisting of users and non-users of insecticide-treated nets (ITNs), currently the primary malaria prevention method. We determined that malaria transmission declines as trap coverage (proportion of total availability of all hosts and pseudo hosts that traps constitute) increases. If the traps are more attractive than humans and are located in areas where mosquitoes are most abundant, 20-130 traps per 1000 people would be sufficient to match the impact of 50% community-wide ITN coverage. If such traps are used to complement ITNs, malaria transmission can be reduced by 99% or more in most scenarios representative of Africa. However, to match cost-effectiveness of ITNs, the traps delivery, operation and maintenance would have to cost a maximum of US$4.25 to 27.61 per unit per year., Conclusions and Significance: Odor-baited mosquito traps might potentially be effective and affordable tools for malaria control in Africa, particularly if they are used to complement, rather than replace, existing methods. We recommend that developers should focus on super-attractive baits and cheaper traps to enhance cost-effectiveness, and that the most appropriate way to deploy such technologies is through vertical delivery mechanisms.

We describe and develop a difference equation model for the dynamics of malaria in a mosquito population feeding on, infecting and getting infected from a heterogeneous population of hosts. Using the force of infection from different classes of humans to mosquitoes as parameters, we evaluate a number of entomological parameters, indicating malaria transmission levels, which can be compared to field data. By assigning different types of vector control interventions to different classes of humans and by evaluating the corresponding levels of malaria transmission, we can compare the effectiveness of these interventions. We show a numerical example of the effects of increasing coverage of insecticide-treated bed nets in a human population where the predominant malaria vector is Anopheles gambiae.