Cost-effective Control Strategies Research Articles

Mixed Integer Linear Programming Models for Selecting Ground-Level Ozone Control Strategies

The traditional strategy for ground-level ozone control is to apply emission reductions across the board throughout certain time periods and locations. In this paper, we study various mixed integer linear programming (MILP) models that seek to select targeted control strategies for the Dallas Fort-Worth (DFW) region to reduce emissions, in order to achieve the State Implementation Plan (SIP) requirements with minimum cost. Statistics and optimization methods are used to determine a potential set of cost-effective control strategies for reducing ozone. These targeted control strategies are specified for different types of emission sources in various time periods and locations. Three MILP models, a static model, a sequential model, and a dynamic model, are studied in this research. These different MILP models allow decision makers to study how the targeted control strategies change under different circumstances. Meanwhile, two types of auxiliary variables are considered as supplemental control strategies in the optimization if the current set of control strategies is unable to reduce ozone to comply with the 8-h ozone standard. Results from the different models can provide decision makers with information concerning how the effectiveness of the control strategies varies with daily emission patterns and meteorology.

Optimal control of a two-strain tuberculosis-HIV/AIDS co-infection model

Tuberculosis is a bacterial disease caused by Mycobacterium tuberculosis (TB). The risk for TB infection greatly increases with HIV infection; TB disease occurs in 7-10% of patients with HIV infection each year, increasing the potential for transmission of drug-resistant Mycobacterium tuberculosis strains. In this paper a deterministic model is presented and studied for the transmission of TB-HIV/AIDS co-infection. Optimal control theory is then applied to investigate optimal strategies for controlling the spread of the disease using treatment of infected individuals with TB as the system control variables. Various combination strategies were examined so as to investigate the impact of the controls on the spread of the disease. And incremental cost-effectiveness ratio (ICER) was used to investigate the cost effectiveness of all the control strategies. Our results show that the implementation of the combination strategy involving the prevention of treatment failure in drug-sensitive TB infectious individuals and the treatment of individuals with drug-resistant TB is the most cost-effective control strategy. Similar results were obtained with different objective functionals involving the minimization of the number of individuals with drug-sensitive TB-only and drug-resistant TB-only with the efforts involved in applying the control.

Dynamics of the Force of Infection: Insights from Echinococcus multilocularis Infection in Foxes

Characterizing the force of infection (FOI) is an essential part of planning cost effective control strategies for zoonotic diseases. Echinococcus multilocularis is the causative agent of alveolar echinococcosis in humans, a serious disease with a high fatality rate and an increasing global spread. Red foxes are high prevalence hosts of E. multilocularis. Through a mathematical modelling approach, using field data collected from in and around the city of Zurich, Switzerland, we find compelling evidence that the FOI is periodic with highly variable amplitude, and, while this amplitude is similar across habitat types, the mean FOI differs markedly between urban and periurban habitats suggesting a considerable risk differential. The FOI, during an annual cycle, ranges from (0.1,0.8) insults (95% CI) in urban habitat in the summer to (9.4, 9.7) (95% CI) in periurban (rural) habitat in winter. Such large temporal and spatial variations in FOI suggest that control strategies are optimal when tailored to local FOI dynamics.

Cost estimate of multi-pollutant abatement from the power sector in the Yangtze River Delta region of China

Coal-fired power plants in China have emitted multiple pollutants including sulfur dioxide, nitrogen oxides and fine particulates, contributing to serious environmental impairments and human health issues. To meet ambient air quality standards, the installation of effective pollution control technologies are required and consequently, the cost of installing or retrofitting control technologies is an important economic and political concern. A multi-pollutant control cost model, CoST CE, is developed to calculate the cost of multi-pollutant control strategies in the Yangtze River Delta region (YRD) of China, adopting an LP algorithm to optimize the sorting of control technology costs and quickly obtain a solution. The output shows that total costs will increase along with emission abatement. Meanwhile, the slope becomes steeper as greater emission reductions are pursued, due to the need to install highly effective, but expensive, technologies like SCR and FF. Moreover, it is evident that the cost curve shapes, maximum abatement potential and total cost for the three provinces in the YRD region are quite different due to differences in power plant type and technologies, current emission levels and existing pollution controls. The results from this study can aid policy makers to develop cost-effective control strategies for the power sector.

Reduction in dengue cases observed during mass control of Aedes (Stegomyia) in street catch basins in an endemic urban area in Colombia

Dengue incidence continues to increase globally and, in the absence of an efficacious vaccine, prevention strategies are limited to vector control. It has been suggested that targeting the most productive breeding sites instead of all water-holding containers could be a cost-effective vector control strategy. We sought to identify and continuously control the most productive Aedes (Stegomyia) breeding site in an endemic urban area in Colombia and followed the subsequent incidence of dengue. In the urban area of Guadalajara de Buga, southwestern Colombia, potential breeding sites inside and outside houses were first characterized, and local personnel trained to assess their productivity based on the pupae/person index. Simultaneously, training and monitoring were implemented to improve the dengue case surveillance system. Entomological data and insecticide resistance studies were used to define the targeted intervention. Then, a quasi-experimental design was used to assess the efficacy of the intervention in terms of the positivity index of the targeted and non- targeted breeding sites, and the impact on dengue cases. Street catch basins (storm drains) were the potential breeding site most frequently found containing Aedes immature stages in the baseline (58.3% of 108). Due to the high resistance to temephos (0% mortality after 24h), the intervention consisted of monthly application of pyriproxyfen in all the street catch basins (n=4800). A significant decrease in catch basins positivity for Aedes larvae was observed after each monthly treatment (p<0.001). Over the intervention period, a reduction in the dengue incidence in Buga was observed (rate ratio 0.19, 95% CI 0.12–0.30, p<0.0001) after adjusting for autocorrelation and controlling with a neighboring town, Palmira, This study highlights the importance of street catch basins as Aedes breeding sites and suggests that their targeted control could help to decrease dengue transmission in such areas.

On the role of HIV/AIDS support groups on combating new infections

AimSince its emergence in the 1980s, the human immunodeficiency virus (HIV), the causative agent of the acquired immune deficiency syndrome (AIDS), remain a major challenge to the global health and human development. We explore the role of optimal HIV counseling and support groups on combating new infections. BackgroundThe stigma surrounding HIV/AIDS makes life more difficult for people living with HIV/AIDS and their families. People living with HIV/AIDS needs a lot of emotional, spiritual, psychological, social, physical and clinical support. During voluntary HIV testing and counseling detected individuals are encouraged to become a member of an HIV/AIDS support group where they will receive useful information on how to live positively. MethodsMathematical model have become invaluable management for epidemiologists, both shedding light on mechanisms underlying observed dynamics as well as making quantitative predictions on the effectiveness of different control measures. Here, we propose a deterministic HIV model that incorporates HIV counseling and support groups. After qualitative analysis the model is extended to incorporate optimal control theory. The objective function minimizes the population of infectious individuals unaware of their HIV status and infectious individuals aware of their HIV status but are reluctant to completely desist from risk sexual activities. The optimal control is characterized and solved numerically for several cases. ResultsQualitative analysis of the proposed model show that voluntary HIV testing and HIV/AIDS support groups have a positive impact on effective control or elimination of the disease. It is shown that in the presence of time dependent HIV testing and support groups more reduction of new infections is achieved. For instance, if more effort and resource are availed on voluntary HIV testing than on support groups, then after a period of twenty years then the population of individuals unaware of their HIV status will decrease by more than fifty percent. ConclusionWith regard to voluntary HIV counseling and support groups results in this study provide a frame work for designing cost-effective strategies for effective control of HIV in the absence of HIV therapy.

Cost-benefit Analysis of Epidemics Spreading on Clustered Random Networks

We study, control of infectious disease epidemics spreading on random networks with different levels of clustering. We use Gleeson's et al., Phys. Rev. E80, 036107 (2009) algorithm to create clustered networks in which a proportion of individuals is located in fully-connected cliques of certain size. A SIR model is extended to include delayed and imperfect detection of infectious individuals. We also include a combination of responsive (palliative) and preventive (vaccination) treatments and design cost-effective disease control strategies. Cost-benefit analysis is used in combination with epidemiological simulations to identify an optimal radius for a treatment centred upon the symptomatic individual. Three general control strategies occur depending on the relative cost of treatment and prevention. Network topology and, in particular, clustering also affects the applicability of the control strategy. The average path length appears to be more important; the range for the control strategy is wider with the length, but the optimal radius of control also extends. As the proportion of individuals in cliques and therefore the coefficient of clustering is higher, the range of the costs for which control scenario is optimal is greater. This results have important consequences for designing disease control strategies that also satisfy economic optimality criteria.

An Optimal Cost Effectiveness Study on Zimbabwe Cholera Seasonal Data from 2008–2011

Incidence of cholera outbreak is a serious issue in underdeveloped and developing countries. In Zimbabwe, after the massive outbreak in 2008–09, cholera cases and deaths are reported every year from some provinces. Substantial number of reported cholera cases in some provinces during and after the epidemic in 2008–09 indicates a plausible presence of seasonality in cholera incidence in those regions. We formulate a compartmental mathematical model with periodic slow-fast transmission rate to study such recurrent occurrences and fitted the model to cumulative cholera cases and deaths for different provinces of Zimbabwe from the beginning of cholera outbreak in 2008–09 to June 2011. Daily and weekly reported cholera incidence data were collected from Zimbabwe epidemiological bulletin, Zimbabwe Daily cholera updates and Office for the Coordination of Humanitarian Affairs Zimbabwe (OCHA, Zimbabwe). For each province, the basic reproduction number () in periodic environment is estimated. To the best of our knowledge, this is probably a pioneering attempt to estimate in periodic environment using real-life data set of cholera epidemic for Zimbabwe. Our estimates of agree with the previous estimate for some provinces but differ significantly for Bulawayo, Mashonaland West, Manicaland, Matabeleland South and Matabeleland North. Seasonal trend in cholera incidence is observed in Harare, Mashonaland West, Mashonaland East, Manicaland and Matabeleland South. Our result suggests that, slow transmission is a dominating factor for cholera transmission in most of these provinces. Our model projects cholera cases and cholera deaths during the end of the epidemic in 2008–09 to January 1, 2012. We also determine an optimal cost-effective control strategy among the four government undertaken interventions namely promoting hand-hygiene & clean water distribution, vaccination, treatment and sanitation for each province.

Vector Control of Four Switch Three-Phase Inverter Fed Synchronous Reluctance Motor Drive Including Saturation and Iron Losses Effects Based Maximum Torque Control

This paper presents a cost-effective vector control strategy for four switch three phase (FSTP) inverter fed a synchronous reluctance motor with conventional rotor (SynRM) drive. The reduction of the number of power switches from six to four improves the cost-effectiveness, volume-compactness and reliability of the three phase inverters. In this paper, a simulation model of the drive system is developed and analyzed in order to verify the effectiveness of the approach. The application of vector control to a SynRM at maximum torque control (MTC) operation is presented with emphasis on the effects of saturation and iron losses are briefly considered. A PI controller is used to process the speed error. Two independent hysteresis current controllers with a suitable hysteresis band are utilized for inverter switches signals. A simplified steady-state d-q model including saturation and iron losses is presented. Simulation results show that the drive system provides a fast speed response and good disturbance rejection capability. DOI: http://dx.doi.org/10.11591/telkomnika.v11i11.3366

Crouching Tiger, Hidden Trouble: Urban Sources of Aedes albopictus (Diptera: Culicidae) Refractory to Source-Reduction

Our ultimate objective is to design cost-effective control strategies for Aedes albopictus, the Asian tiger mosquito, an important urban nuisance and disease vector that expanded worldwide during the last 40 years. We conducted mosquito larval surveys from May through October 2009 in the City of Trenton, New Jersey, USA, while performing intensive monthly source-reduction campaigns that involved removing, emptying, or treating all accessible containers with larvicides and pupicides. We examined patterns of occurrence of Ae. albopictus and Culex pipiens, another urban mosquito, among different container types by comparing observed and expected number of positive containers of each type. Expected use was based on the relative frequency of each container type in the environment. Aedes albopictus larvae and pupae were found significantly more often than expected in medium volumes of water in buckets and plant saucers but were rarely collected in small volumes of water found in trash items such as discarded cups and cans. They were also absent from large volumes of water such as in abandoned swimming pools and catch basins, although we consistently collected Cx. pipiens from those habitats. The frequency of Ae. albopictus in tires indicated rapid and extensive use of these ubiquitous urban containers. Standard larval-based indices did not correlate with adult catches in BG-Sentinel traps, but when based only on Ae. albopictus key containers (buckets, plant saucers, equipment with pockets of water, and tires) they did. Although we found that only 1.2% of the 20,039 water-holding containers examined contained immature Ae. albopictus (5.3% if only key containers were counted), adult populations were still above nuisance action thresholds six times during the 2009 mosquito season. We conclude that in urban New Jersey, effective source reduction for Ae. albopictus control will require scrupulous and repeated cleaning or treatment of everyday use containers and extensive homeowner collaboration.

The effect of insecticide-treated bed nets on the incidence and prevalence of malaria in children in an area of unstable seasonal transmission in western Myanmar

BackgroundInsecticide-treated bed nets (ITN) reduce malaria morbidity and mortality consistently in Africa, but their benefits have been less consistent in Asia. This study’s objective was to evaluate the malaria protective efficacy of village-wide usage of ITN in Western Myanmar and estimate the cost-effectiveness of ITN compared with extending early diagnosis and treatment services.MethodsA cluster-randomized controlled trial was conducted in Rakhine State to assess the efficacy of ITNs in preventing malaria and anaemia in children and their secondary effects on nutrition and development. The data were aggregated for each village to obtain cluster-level infection rates. In total 8,175 children under 10 years of age were followed up for 10 months, which included the main malaria transmission period. The incidence and prevalence of Plasmodium falciparum and Plasmodium vivax infections, and the biting behaviour of Anopheles mosquitoes in the area were studied concurrently. The trial data along with costs for current recommended treatment practices were modelled to estimate the cost-effectiveness of ITNs compared with, or in addition to extending the coverage of early diagnosis and treatment services.ResultsIn aggregate, malaria infections, spleen rates, haemoglobin concentrations, and weight for height, did not differ significantly during the study period between villages with and without ITNs, with a weighted mean difference of −2.6 P. falciparum episodes per 1,000 weeks at risk (95% Confidence Interval −7 to 1.8). In areas with a higher incidence of malaria there was some evidence ITN protective efficacy. The economic analysis indicated that, despite the uncertainty and variability in their protective efficacy in the different study sites, ITN could still be cost-effective, but not if they displaced funding for early diagnosis and effective treatment which is substantially more cost-effective.ConclusionIn Western Myanmar deployment of ITNs did not provide consistent protection against malaria in children living in malaria endemic villages. Early diagnosis and effective treatment is a more cost effective malaria control strategy than deployment of ITNs in this area where the main vector bites early in the evening, often before people are protected by an ITN.

Vector control of FSTP inverter fed synchronous reluctance reluctance motor based maximum torque control

This paper presents a cost-effective vector control strategy for four switch three phase (FSTP) inverter fed a

Standardized extract of Piper ovatum (Piperaceae) to control Aedes aegypti larvae (Diptera: Culicidae)

Dengue fever as well as its severe complications is a vector-borne disease transmitted mainly by Aedes aegypti. As mosquito control is practically the only method available to control such disease, alternative and cost-effective pest control strategies need to be explored. Thus, this study proposed the production and standardization of Piper ovatum extract and evaluate the larvicidal activity against A. aegypti. The results showed that the main piperine derivative extracts from leaves, stems and roots was the piperlonguminine. Root extract was used to produce a standardized extract of P. ovatum called SEPO that showed LC50 and LC99 of 2.1 and 4.1ppm, respectively. The piperlonguminine concentration was 13.6%; the maximum activity was observed after 4.2h; residual activity lasted 20 days, and the stability of the LC99 solution lasted more than 120 days. In addition, no changes in female oviposition behavior were observed. Our findings demonstrated that the P. ovatum roots were a good source for producing a standardized extract with piperlonguminine. The extract known as SEPO showed high larvicidal activity against A. aegypti, good stability, residual activity for more than 15 days, and did not change the female oviposition activity. The standardized extract seemed to be a good candidate to produce insecticides against A. aegypti.

Integration of Epidemiological Evidence in a Decision Support Model for the Control of Campylobacter in Poultry Production

The control of human Campylobacteriosis is a priority in public health agendas all over the world. Poultry is considered a significant risk factor for human infections with Campylobacter and risk assessment models indicate that the successful implementation of Campylobacter control strategies in poultry will translate on a reduction of human Campylobacteriosis cases. Efficient control strategies implemented during primary production will reduce the risk of Campylobacter introduction in chicken houses and/or decrease Campylobacter concentration in infected chickens and their products. Consequently, poultry producers need to make difficult decisions under conditions of uncertainty regarding the implementation of Campylobacter control strategies. This manuscript presents the development of probabilistic graphical models to support decision making in order to control Campylobacter in poultry. The decision support systems are constructed as probabilistic graphical models (PGMs) which integrate knowledge and use Bayesian methods to deal with uncertainty. This paper presents a specific model designed to integrate epidemiological knowledge from the United Kingdom (UK model) in order to assist poultry managers in specific decisions related to vaccination of commercial broilers for the control of Campylobacter. Epidemiological considerations and other crucial aspects including challenges associated with the quantitative part of the models are discussed in this manuscript. The outcome of the PGMs will depend on the qualitative and quantitative data included in the models. Results from the UK model and sensitivity analyses indicated that the financial variables (cost/reward functions) and the effectiveness of the control strategies considered in the UK model were driving the results. In fact, there were no or only small financial gains when using a hypothetical vaccine B (able to decrease Campylobacter numbers from two to six logs in 20% of the chickens with a cost of 0.025 £/chicken) and reward system 1 (based on similar gross profits in relation to Campylobacter levels) under the specific assumptions considered in the UK model. In contrast, significant reductions in expected Campylobacter numbers and substantial associated expected financial gains were obtained from this model when considering the reward system 2 (based on quite different gross profits in relation to Campylobacter levels) and the use of a hypothetical cost-effective vaccine C (able to reduce the level of Campylobacter from two to six logs in 90% of the chickens with a cost of 0.03 £/chicken). The flexibility of probabilistic graphical models allows for the inclusion of more than one Campylobacter vaccination strategy and more than one reward system and consequently, diverse potential solutions for the control of Campylobacter may be considered. Cost-effective Campylobacter control strategies that can significantly reduce the probability of Campylobacter introduction into a flock and/or the numbers of Campylobacter in already infected chickens, and translate to an attractive cost-reward balance will be preferred by poultry producers.

Neural network model for the prediction of PM10 daily concentrations in two sites in the Western Mediterranean

An artificial neural network (ANN) was developed and tested to forecast PM10 daily concentration in two contrasted environments in NE Spain, a regional background site (Montseny), and an urban background site (Barcelona-CSIC), which was highly influenced by vehicular emissions. In order to predict 24-h average PM10 concentrations, the artificial neural network previously developed by Caselli et al. (2009) was improved by using hourly PM concentrations and deterministic factors such as a Saharan dust alert. In particular, the model input data for prediction were the hourly PM10 concentrations 1-day in advance, local meteorological data and information about air masses origin. The forecasted performance indexes for both sites were calculated and they showed better results for the regional background site in Montseny (R2=0.86, SI=0.75) than for urban site in Barcelona (R2=0.73, SI=0.58), influenced by local and sometimes unexpected sources. Moreover, a sensitivity analysis conducted to understand the importance of the different variables included among the input data, showed that local meteorology and air masses origin are key factors in the model forecasts. This result explains the reason for the improvement of ANN's forecasting performance at the Montseny site with respect to the Barcelona site. Moreover, the artificial neural network developed in this work could prove useful to predict PM10 concentrations, especially, at regional background sites such as those on the Mediterranean Basin which are primarily affected by long-range transports. Hence, the artificial neural network presented here could be a powerful tool for obtaining real time information on air quality status and could aid stakeholders in their development of cost-effective control strategies.

Spatial distribution of leprosy in areas of risk in Vitoria, State of Espirito Santo, Brazil, 2005 to 2009

Leprosy remains a relevant public health issue in Brazil. The objective of this study was to analyze the spatial distribution of new cases of leprosy and to detect areas with higher risks of disease in the City of Vitória. The study was ecologically based on the spatial distribution of leprosy in the City of Vitória, State of Espírito Santo between 2005 and 2009. The data sources used came from the available records of the State Health Secretary of Espírito Santo. A global and local empirical Bayesian method was used in the spatial analysis to produce a leprosy risk estimation, and the fluctuation effect was smoothed from the detection coefficients. The study used thematic maps to illustrate that leprosy is distributed heterogeneously between the neighborhoods and that it is possible to identify areas with high risk of disease. The Pearson correlation coefficient of 0.926 (p = 0.001) for the Local Method indicated highly correlated coefficients. The Moran index was calculated to evaluate correlations between the incidences of adjoining districts. We identified the spatial contexts in which there were the highest incidence rates of leprosy in Vitória during the studied period. The results contribute to the knowledge of the spatial distribution of leprosy in the City of Vitória, which can help establish more cost-effective control strategies because they indicate specific regions and priority planning activities that can interfere with the transmission chain.

Oral toxicity of Photorhabdus luminescens and Xenorhabdus nematophila (Enterobacteriaceae) against Aedes aegypti (Diptera: Culicidae)

Dengue fever is an important vector-borne disease, mainly transmitted by Aedes aegypti. To date, there are no vaccines or effective drugs available against this arboviral disease. As mosquito control is practically the only method available to control dengue fever, alternative and cost-effective pest control strategies need to be explored. The gram-negative enteric bacteria Xenorhabdus and Photorhabdus are symbiotically associated with nematode parasites, which themselves are highly pathogenic for insect larvae. Here, we evaluate the oral toxicity of these entomopathogenic bacteria in A. aegypti larvae. The susceptibility of larvae (third late or fourth early instars) was assessed by exposing them to suspensions containing Photorhabdus luminescens or Xenorhabdus nematophila, respectively. Two diet treatments were tested with larvae fed on pet food and unfed larvae. After 24 h, larvae began to die when exposed to the bacteria. Exposure to P. luminescens killed 73% of the fed and 83% of the unfed larvae, respectively. In comparison, X. nematophila was less pathogenic, killing 52% of the larvae in the fed and 42% in the unfed treatment. Remarkably, cannibalism was observed in all bioassays after exposing larvae to either of the bacterial species. To our knowledge, this is the first report demonstrating the efficiency of these entomopathogenic bacteria for oral A. aegypti killing. Our results provide a promising basis for using these bacteria as bioinsecticides for mosquito control in the future.

Nosocomial infections in neonatal intensive care units: Cost-effective control strategies in resource-limited countries

Background: Nosocomial infections or hospital-acquired infectionsconstitute a global health problem. They lead to significant morbidity and mortality in both developed and resource-limited countries. The neonatal intensive care unit (NICU) is a suitable environment for disseminating these infections; underscoring the need for preventive intervention measures.Objectives: This review aims to highlight the global burden of nosocomialinfections in neonatal intensive care units (NICUs), to discuss their epidemiology and clinical spectrum, as well as the costeffective control strategies in resource-limited settings.Sources: Sources of information were from Google searches andPubMed- linked articles using the key words- nosocomial infections,neonatal intensive care unit, control. Related articles from hard copiesof medical literature and journals were also gathered.Results: Although paucity of data exists on the incidence of nosocomialinfections in NICUs in developing countries, reports from developedcountries indicate a range of 6% to 25%. Much higher figures were noted in some developing countries. Several risk factors for nosocomial infections were identified but varied in different NICUs surveyed. Effective control strategies have been recommended but hand washing or hand hygiene appears universally applicable in both developed and resource-limitedcountries. Economic analyses of these strategies in developed countrieshave established their costeffectiveness while the adaptability of hand hygiene program to resource-limited settings has been demonstrated in a World Health Organization pilot study in sub- Saharan Africa.Conclusion: Hand washing or hand hygiene by health-care personnelremains the most important evidence-based and cost-effective controlstrategy for the spread of nosocomial infections in NICUs in resource-limited countries.Key words: nosocomial infections; neonatal intensive care unit;control.

Synergies in integrated malaria control

Synergies in integrated malaria control

Optimal control strategies and cost-effectiveness analysis of a malaria model

The aim of this paper is to investigate the effectiveness and cost-effectiveness of three malaria preventive measures (use of treated bednets, spray of insecticides and a possible treatment of infective humans that blocks transmission to mosquitoes). For this, we consider a mathematical model for the transmission dynamics of the disease that includes these measures. We first consider the constant control parameters’ case, we calculate the basic reproduction number and investigate the existence and stability of equilibria; the model is found to exhibit backward bifurcation. We then assess the relative impact of each of the constant control parameters measures by calculating the sensitivity index of the basic reproductive number to the model's parameters. In the time-dependent constant control case, we use Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. We also calculate the Infection Averted Ratio (IAR) and the Incremental Cost-Effectiveness Ratio (ICER) to investigate the cost-effectiveness of all possible combinations of the three control measures. One of our findings is that the most cost-effective strategy for malaria control, is the combination of the spray of insecticides and treatment of infective individuals. This strategy requires a 100% effort in both treatment (for 20 days) and spray of insecticides (for 57 days). In practice, this will be extremely difficult, if not impossible to achieve. The second most cost-effective strategy which consists of a 100% use of treated bednets and 87% treatment of infective individuals for 42 and 100 days, respectively, is sustainable and therefore preferable.