Minimization of the experimental workload for the prediction of pollutants propagation in rivers. Mathematical modelling and knowledge re-use

The present thesis in focused on the minimization of experimental efforts for the prediction of pollutant propagation in rivers by mathematical modelling and knowledge re-use. Mathematical modelling is based on the well known advection-dispersion equation, while the knowledge re-use approach employs the methods of case based reasoning, graphical analysis and text mining. The thesis contribution to the pollutant transport research field consists of: (1) analytical and numerical models for pollutant transport prediction; (2) two novel techniques which enable the use of variable parameters along rivers in analytical models; (3) models for the estimation of pollutant transport characteristic parameters (velocity, dispersion coefficient and nutrient transformation rates) as functions of water flow, channel characteristics and/or seasonality; (4) the graphical analysis method to be used for the identification of pollution sources along rivers; (5) a case based reasoning tool for the identification of crucial information related to the pollutant transport modelling; (6) and the application of a software tool for the reuse of information during pollutants transport modelling research. These support tools are applicable in the water quality research field and in practice as well, as they can be involved in multiple activities. The models are capable of predicting pollutant propagation along rivers in case of both ordinary pollution and accidents. They can also be applied for other similar rivers in modelling of pollutant transport in rivers with low availability of experimental data concerning concentration. This is because models for parameter estimation developed in the present thesis enable the calculation of transport characteristic parameters as functions of river hydraulic parameters and/or seasonality. The similarity between rivers is assessed using case based reasoning tools, and additional necessary information can be identified by using the software for the information reuse. Such systems represent support for users and open up possibilities for new modelling methods, monitoring facilities and for better river water quality management tools. They are useful also for the estimation of environmental impact of possible technological changes and can be applied in the pre-design stage or/and in the practical use of processes as well.

Teaching mathematics and programming : new approaches with empirical evaluation

Programming and mathematics are core areas of computer science (CS) and consequently also important parts of CS education. Introductory instruction in these two topics is, however, not without problems. Studies show that CS students find programming difficult to learn and that teaching mathematical topics to CS novices is challenging. One reason for the latter is the disconnection between mathematics and programming found in many CS curricula, which results in students not seeing the relevance of the subject for their studies. In addition, reports indicate that students' mathematical capability and maturity levels are dropping. The challenges faced when teaching mathematics and programming at CS departments can also be traced back to gaps in students' prior education. In Finland the high school curriculum does not include CS as a subject; instead, focus is on learning to use the computer and its applications as tools. Similarly, many of the mathematics courses emphasize application of formulas, while logic, formalisms and proofs, which are important in CS, are avoided. Consequently, high school graduates are not well prepared for studies in CS. Motivated by these challenges, the goal of the present work is to describe new approaches to teaching mathematics and programming aimed at addressing these issues: Structured derivations is a logic-based approach to teaching mathematics, where formalisms and justifications are made explicit. The aim is to help students become better at communicating their reasoning using mathematical language and logical notation at the same time as they become more confident with formalisms. The Python programming language was originally designed with education in mind, and has a simple syntax compared to many other popular languages. The aim of using it in instruction is to address algorithms and their implementation in a way that allows focus to be put on learning algorithmic thinking and programming instead of on learning a complex syntax. Invariant based programming is a diagrammatic approach to developing programs that are correct by construction. The approach is based on elementary propositional and predicate logic, and makes explicit the underlying mathematical foundations of programming. The aim is also to show how mathematics in general, and logic in particular, can be used to create better programs.

Some advances in mathematical models for preference relations

Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly. The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model. The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency. The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations. The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.

Automation Concept for Electrically Excited LV Synchronous Motor: Implementation into AC500 Programmable Logic Environment

This bachelor’s thesis is a part of the research project realized in the summer 2011 in Lappeenranta University of Technology. The goal of the project was to develop an automation concept for controlling the electrically excited synchronous motor. Thesis concentrates on the implementation of the automation concept into the ABB’s AC500 programmable logic enviroment. The automation program was developed as a state machine with the ABB’s PS501 Control Builder software. For controlling the automation program is developed a fieldbus control and with CodeSys Visualization Tool a local control with control panel. The fieldbus control is done to correspond the ABB drives communication profile and the local control is implemented with a function block which feeds right control words into the statemachine. A field current control of the synchronous motor is realized as a method presented in doctoral thesis of Olli Pyrhönen (Pyrhönen 1998). The Method combines stator flux and torque based openloop control and power factor based feedback control.

Mathematical modeling of laboratory scale three-phase fixed bed reactors

Detta arbete fokuserar på modellering av katalytiska gas-vätskereaktioner som genomförs i kontinuerliga packade bäddar. Katalyserade gas-vätskereaktioner hör till de mest typiska reaktionerna i kemisk industri; därför behandlas här packade bäddreaktorer som ett av de populäraste alternativen, då kontinuerlig drift eftersträvas. Tack vare en stor katalysatormängd per volym har de en kompakt struktur, separering av katalysatorn behövs inte och genom en professionell design kan den mest fördelaktiga strömningsbilden upprätthållas i reaktorn. Packade bäddreaktorer är attraktiva p.g.a. lägre investerings- och driftskostnader. Även om packade bäddar används intensivt i industri, är det mycket utmanande att modellera. Detta beror på att tre faser samexisterar och systemets geometri är komplicerad. Existensen av flera reaktioner gör den matematiska modelleringen även mera krävande. Många förenklingar blir därmed nödvändiga. Modellerna involverar typiskt flera parametrar som skall justeras på basis av experimentella data. I detta arbete studerades fem olika reaktionssystem. Systemen hade studerats experimentellt i vårt laboratorium med målet att nå en hög produktivitet och selektivitet genom ett optimalt val av katalysatorer och driftsbetingelser. Hydrering av citral, dekarboxylering av fettsyror, direkt syntes av väteperoxid samt hydrering av sockermonomererna glukos och arabinos användes som exempelsystem. Även om dessa system hade mycket gemensamt, hade de också unika egenskaper och krävde därför en skräddarsydd matematisk behandling. Citralhydrering var ett system med en dominerande huvudreaktion som producerar citronellal och citronellol som huvudprodukter. Produkterna används som en citrondoftande komponent i parfymer, tvålar och tvättmedel samt som plattform-kemikalier. Dekarboxylering av stearinsyra var ett specialfall, för vilket en reaktionsväg för produktion av långkedjade kolväten utgående från fettsyror söktes. En synnerligen hög produktselektivitet var karakteristisk för detta system. Även processuppskalning modellerades för dekarboxylerings-reaktionen. Direkt syntes av väteperoxid hade som målsättning att framta en förenklad process att producera väteperoxid genom att låta upplöst väte och syre reagera direkt i ett lämpligt lösningsmedel på en aktiv fast katalysator. I detta system förekommer tre bireaktioner, vilka ger vatten som oönskad produkt. Alla dessa tre reaktioner modellerades matematiskt med hjälp av dynamiska massbalanser. Målet med hydrering av glukos och arabinos är att framställa produkter med en hög förädlingsgrad, nämligen sockeralkoholer, genom katalytisk hydrering. För dessa två system löstes ämnesmängd- och energibalanserna simultant för att evaluera effekter inne i porösa katalysatorpartiklar. Impulsbalanser som bestämmer strömningsbetingelser inne i en kemisk reaktor, ersattes i alla modelleringsstudier med semi-empiriska korrelationsuttryck för vätskans volymandel och tryckförlust och med axiell dispersionsmodell för beskrivning av omblandningseffekter. Genom att justera modellens parametrar kunde reaktorns beteende beskrivas väl. Alla experiment var genomförda i laboratorieskala. En stor mängd av kopplade effekter samexisterade: reaktionskinetik inklusive adsorption, katalysatordeaktivering, mass- och värmeöverföring samt strömningsrelaterade effekter. En del av dessa effekter kunde studeras separat (t.ex. dispersionseffekter och bireaktioner). Inverkan av vissa fenomen kunde ibland minimeras genom en noggrann planering av experimenten. På detta sätt kunde förenklingar i modellerna bättre motiveras. Alla system som studerades var industriellt relevanta. Utveckling av nya, förenklade produktionsteknologier för existerande kemiska komponenter eller nya komponenter är ett gigantiskt uppdrag. Studierna som presenterades här fokuserade på en av den teknisk-vetenskapliga utfärdens första etapper.

Mathematical modeling of level of anaesthesia from EEG measurements

Problem of modeling of anaesthesia depth level is studied in this Master Thesis. It applies analysis of EEG signals with nonlinear dynamics theory and further classification of obtained values. The main stages of this study are the following: data preprocessing; calculation of optimal embedding parameters for phase space reconstruction; obtaining reconstructed phase portraits of each EEG signal; formation of the feature set to characterise obtained phase portraits; classification of four different anaesthesia levels basing on previously estimated features. Classification was performed with: Linear and quadratic Discriminant Analysis, k Nearest Neighbours method and online clustering. In addition, this work provides overview of existing approaches to anaesthesia depth monitoring, description of basic concepts of nonlinear dynamics theory used in this Master Thesis and comparative analysis of several different classification methods.

Power semiconductor nonlinearities in active du/dt output filtering

This doctoral thesis introduces an improved control principle for active du/dt output filtering in variable-speed AC drives, together with performance comparisons with previous filtering methods. The effects of power semiconductor nonlinearities on the output filtering performance are investigated. The nonlinearities include the timing deviation and the voltage pulse waveform distortion in the variable-speed AC drive output bridge. Active du/dt output filtering (ADUDT) is a method to mitigate motor overvoltages in variable-speed AC drives with long motor cables. It is a quite recent addition to the du/dt reduction methods available. This thesis improves on the existing control method for the filter, and concentrates on the lowvoltage (below 1 kV AC) two-level voltage-source inverter implementation of the method. The ADUDT uses narrow voltage pulses having a duration in the order of a microsecond from an IGBT (insulated gate bipolar transistor) inverter to control the output voltage of a tuned LC filter circuit. The filter output voltage has thus increased slope transition times at the rising and falling edges, with an opportunity of no overshoot. The effect of the longer slope transition times is a reduction in the du/dt of the voltage fed to the motor cable. Lower du/dt values result in a reduction in the overvoltage effects on the motor terminals. Compared with traditional output filtering methods to accomplish this task, the active du/dt filtering provides lower inductance values and a smaller physical size of the filter itself. The filter circuit weight can also be reduced. However, the power semiconductor nonlinearities skew the filter control pulse pattern, resulting in control deviation. This deviation introduces unwanted overshoot and resonance in the filter. The controlmethod proposed in this thesis is able to directly compensate for the dead time-induced zero-current clamping (ZCC) effect in the pulse pattern. It gives more flexibility to the pattern structure, which could help in the timing deviation compensation design. Previous studies have shown that when a motor load current flows in the filter circuit and the inverter, the phase leg blanking times distort the voltage pulse sequence fed to the filter input. These blanking times are caused by excessively large dead time values between the IGBT control pulses. Moreover, the various switching timing distortions, present in realworld electronics when operating with a microsecond timescale, bring additional skew to the control. Left uncompensated, this results in distortion of the filter input voltage and a filter self-induced overvoltage in the form of an overshoot. This overshoot adds to the voltage appearing at the motor terminals, thus increasing the transient voltage amplitude at the motor. This doctoral thesis investigates the magnitude of such timing deviation effects. If the motor load current is left uncompensated in the control, the filter output voltage can overshoot up to double the input voltage amplitude. IGBT nonlinearities were observed to cause a smaller overshoot, in the order of 30%. This thesis introduces an improved ADUDT control method that is able to compensate for phase leg blanking times, giving flexibility to the pulse pattern structure and dead times. The control method is still sensitive to timing deviations, and their effect is investigated. A simple approach of using a fixed delay compensation value was tried in the test setup measurements. The ADUDT method with the new control algorithm was found to work in an actual motor drive application. Judging by the simulation results, with the delay compensation, the method should ultimately enable an output voltage performance and a du/dt reduction that are free from residual overshoot effects. The proposed control algorithm is not strictly required for successful ADUDT operation: It is possible to precalculate the pulse patterns by iteration and then for instance store them into a look-up table inside the control electronics. Rather, the newly developed control method is a mathematical tool for solving the ADUDT control pulses. It does not contain the timing deviation compensation (from the logic-level command to the phase leg output voltage), and as such is not able to remove the timing deviation effects that cause error and overshoot in the filter. When the timing deviation compensation has to be tuned-in in the control pattern, the precalculated iteration method could prove simpler and equally good (or even better) compared with the mathematical solution with a separate timing compensation module. One of the key findings in this thesis is the conclusion that the correctness of the pulse pattern structure, in the sense of ZCC and predicted pulse timings, cannot be separated from the timing deviations. The usefulness of the correctly calculated pattern is reduced by the voltage edge timing errors. The doctoral thesis provides an introductory background chapter on variable-speed AC drives and the problem of motor overvoltages and takes a look at traditional solutions for overvoltage mitigation. Previous results related to the active du/dt filtering are discussed. The basic operation principle and design of the filter have been studied previously. The effect of load current in the filter and the basic idea of compensation have been presented in the past. However, there was no direct way of including the dead time in the control (except for solving the pulse pattern manually by iteration), and the magnitude of nonlinearity effects had not been investigated. The enhanced control principle with the dead time handling capability and a case study of the test setup timing deviations are the main contributions of this doctoral thesis. The simulation and experimental setup results show that the proposed control method can be used in an actual drive. Loss measurements and a comparison of active du/dt output filtering with traditional output filtering methods are also presented in the work. Two different ADUDT filter designs are included, with ferrite core and air core inductors. Other filters included in the tests were a passive du/dtfilter and a passive sine filter. The loss measurements incorporated a silicon carbide diode-equipped IGBT module, and the results show lower losses with these new device technologies. The new control principle was measured in a 43 A load current motor drive system and was able to bring the filter output peak voltage from 980 V (the previous control principle) down to 680 V in a 540 V average DC link voltage variable-speed drive. A 200 m motor cable was used, and the filter losses for the active du/dt methods were 111W–126 W versus 184 W for the passive du/dt. In terms of inverter and filter losses, the active du/dt filtering method had a 1.82-fold increase in losses compared with an all-passive traditional du/dt output filter. The filter mass with the active du/dt method was 17% (2.4 kg, air-core inductors) compared with 14 kg of the passive du/dt method filter. Silicon carbide freewheeling diodes were found to reduce the inverter losses in the active du/dt filtering by 18% compared with the same IGBT module with silicon diodes. For a 200 m cable length, the average peak voltage at the motor terminals was 1050 V with no filter, 960 V for the all-passive du/dt filter, and 700 V for the active du/dt filtering applying the new control principle.

Linguistic models for decision support

Linguistic modelling is a rather new branch of mathematics that is still undergoing rapid development. It is closely related to fuzzy set theory and fuzzy logic, but knowledge and experience from other fields of mathematics, as well as other fields of science including linguistics and behavioral sciences, is also necessary to build appropriate mathematical models. This topic has received considerable attention as it provides tools for mathematical representation of the most common means of human communication - natural language. Adding a natural language level to mathematical models can provide an interface between the mathematical representation of the modelled system and the user of the model - one that is sufficiently easy to use and understand, but yet conveys all the information necessary to avoid misinterpretations. It is, however, not a trivial task and the link between the linguistic and computational level of such models has to be established and maintained properly during the whole modelling process. In this thesis, we focus on the relationship between the linguistic and the mathematical level of decision support models. We discuss several important issues concerning the mathematical representation of meaning of linguistic expressions, their transformation into the language of mathematics and the retranslation of mathematical outputs back into natural language. In the first part of the thesis, our view of the linguistic modelling for decision support is presented and the main guidelines for building linguistic models for real-life decision support that are the basis of our modeling methodology are outlined. From the theoretical point of view, the issues of representation of meaning of linguistic terms, computations with these representations and the retranslation process back into the linguistic level (linguistic approximation) are studied in this part of the thesis. We focus on the reasonability of operations with the meanings of linguistic terms, the correspondence of the linguistic and mathematical level of the models and on proper presentation of appropriate outputs. We also discuss several issues concerning the ethical aspects of decision support - particularly the loss of meaning due to the transformation of mathematical outputs into natural language and the issue or responsibility for the final decisions. In the second part several case studies of real-life problems are presented. These provide background and necessary context and motivation for the mathematical results and models presented in this part. A linguistic decision support model for disaster management is presented here – formulated as a fuzzy linear programming problem and a heuristic solution to it is proposed. Uncertainty of outputs, expert knowledge concerning disaster response practice and the necessity of obtaining outputs that are easy to interpret (and available in very short time) are reflected in the design of the model. Saaty’s analytic hierarchy process (AHP) is considered in two case studies - first in the context of the evaluation of works of art, where a weak consistency condition is introduced and an adaptation of AHP for large matrices of preference intensities is presented. The second AHP case-study deals with the fuzzified version of AHP and its use for evaluation purposes – particularly the integration of peer-review into the evaluation of R&D outputs is considered. In the context of HR management, we present a fuzzy rule based evaluation model (academic faculty evaluation is considered) constructed to provide outputs that do not require linguistic approximation and are easily transformed into graphical information. This is achieved by designing a specific form of fuzzy inference. Finally the last case study is from the area of humanities - psychological diagnostics is considered and a linguistic fuzzy model for the interpretation of outputs of multidimensional questionnaires is suggested. The issue of the quality of data in mathematical classification models is also studied here. A modification of the receiver operating characteristics (ROC) method is presented to reflect variable quality of data instances in the validation set during classifier performance assessment. Twelve publications on which the author participated are appended as a third part of this thesis. These summarize the mathematical results and provide a closer insight into the issues of the practicalapplications that are considered in the second part of the thesis.

Spontaneous Focusing on Numerosity in the Development of Early Mathematical Skills

The aim of the present set of longitudinal studies was to explore 3-7-year-old children.s Spontaneous FOcusing on Numerosity (SFON) and its relation to early mathematical development. The specific goals were to capture in method and theory the distinct process by which children focus on numerosity as a part of their activities involving exact number recognition, and individual differences in this process that may be informative in the development of more complex number skills. Over the course of conducting the five studies, fifteen novel tasks were progressively developed for the SFON assessments. In the tasks, confounding effects of insufficient number recognition, verbal comprehension, other procedural skills as well as working memory capacity were aimed to be controlled. Furthermore, how children.s individual differences in SFON are related to their development of number sequence, subitizing-based enumeration, object counting and basic arithmetic skills was explored. The effect of social interaction on SFON was tested. Study I captured the first phase of the 3-year longitudinal study with 39 children. It was investigated whether there were differences in 3-year-old children.s tendency to focus on numerosity, and whether these differences were related to the children.s development of cardinality recognition skills from the age of 3 to 4 years. It was found that the two groups of children formed on the basis of their amount of SFON tendency at the age of 3 years differed in their development of recognising and producing small numbers. The children whose SFON tendency was very predominant developed faster in cardinality related skills from the age of 3 to 4 years than the children whose SFON tendency was not as predominant. Thus, children.s development in cardinality recognition skills is related to their SFON tendency. Studies II and III were conducted to investigate, firstly, children.s individual differences in SFON, and, secondly, whether children.s SFON is related to their counting development. Altogether nine tasks were designed for the assessments of spontaneous and guided focusing on numerosity. The longitudinal data of 39 children in Study II from the age of 3.5 to 6 years showed individual differences in SFON at the ages of 4, 5 and 6 years, as well as stability in children.s SFON across tasks used at different ages. The counting skills were assessed at the ages of 3.5, 5 and 6 years. Path analyses indicated a reciprocal tendency in the relationship between SFON and counting development. In Study III, these results on the individual differences in SFON tendency, the stability of SFON across different tasks and the relationship of SFON and mathematical skills were confirmed by a larger-scale cross-sectional study of 183 on average 6.5-year-old children (range 6;0-7;0 years). The significant amount of unique variance that SFON accounted for number sequence elaboration, object counting and basic arithmetic skills stayed statistically significant (partial correlations varying from .27 to .37) when the effects of non-verbal IQ and verbal comprehension were controlled. In addition, to confirm that the SFON tasks assess SFON tendency independently from enumeration skills, guided focusing tasks were used for children who had failed in SFON tasks. It was explored whether these children were able to proceed in similar tasks to SFON tasks once they were guided to focus on number. The results showed that these children.s poor performance in the SFON tasks was not caused by their deficiency in executing the tasks but on lacking focusing on numerosity. The longitudinal Study IV of 39 children aimed at increasing the knowledge of associations between children.s long-term SFON tendency, subitizing-based enumeration and verbal counting skills. Children were tested twice at the age of 4-5 years on their SFON, and once at the age of 5 on their subitizing-based enumeration, number sequence production, as well as on their skills for counting of objects. Results showed considerable stability in SFON tendency measured at different ages, and that there is a positive direct association between SFON and number sequence production. The association between SFON and object counting skills was significantly mediated by subitizing-based enumeration. These results indicate that the associations between the child.s SFON and sub-skills of verbal counting may differ on the basis of how significant a role understanding the cardinal meanings of number words plays in learning these skills. The specific goal of Study V was to investigate whether it is possible to enhance 3-year old children.s SFON tendency, and thus start children.s deliberate practice in early mathematical skills. Participants were 3-year-old children in Finnish day care. The SFON scores and cardinality-related skills of the experimental group of 17 children were compared to the corresponding results of the 17 children in the control group. The results show an experimental effect on SFON tendency and subsequent development in cardinality-related skills during the 6-month period from pretest to delayed posttest in the children with some initial SFON tendency in the experimental group. Social interaction has an effect on children.s SFON tendency. The results of the five studies assert that within a child.s existing mathematical competence, it is possible to distinguish a separate process, which refers to the child.s tendency to spontaneously focus on numerosity. Moreover, there are significant individual differences in children.s SFON at the age of 3-7 years. Moderate stability was found in this tendency across different tasks assessed both at the same and at different ages. Furthermore, SFON tendency is related to the development of early mathematical skills. Educational implications of the findings emphasise, first, the importance of regarding focusing on numerosity as a separate, essential process in the assessments of young children.s mathematical skills. Second, the substantial individual differences in SFON tendency during the childhood years suggest that uncovering and modeling this kind of mathematically meaningful perceiving of the surroundings and tasks could be an efficient tool for promoting young children.s mathematical development, and thus prevent later failures in learning mathematical skills. It is proposed to consider focusing on numerosity as one potential sub-process of activities involving exact number recognition in future studies.

Mathematical modeling and optimal control of malaria

Malaria continues to infect millions and kill hundreds of thousands of people worldwide each year, despite over a century of research and attempts to control and eliminate this infectious disease. Challenges such as the development and spread of drug resistant malaria parasites, insecticide resistance to mosquitoes, climate change, the presence of individuals with subpatent malaria infections which normally are asymptomatic and behavioral plasticity in the mosquito hinder the prospects of malaria control and elimination. In this thesis, mathematical models of malaria transmission and control that address the role of drug resistance, immunity, iron supplementation and anemia, immigration and visitation, and the presence of asymptomatic carriers in malaria transmission are developed. A within-host mathematical model of severe Plasmodium falciparum malaria is also developed. First, a deterministic mathematical model for transmission of antimalarial drug resistance parasites with superinfection is developed and analyzed. The possibility of increase in the risk of superinfection due to iron supplementation and fortification in malaria endemic areas is discussed. The model results calls upon stakeholders to weigh the pros and cons of iron supplementation to individuals living in malaria endemic regions. Second, a deterministic model of transmission of drug resistant malaria parasites, including the inflow of infective immigrants, is presented and analyzed. The optimal control theory is applied to this model to study the impact of various malaria and vector control strategies, such as screening of immigrants, treatment of drug-sensitive infections, treatment of drug-resistant infections, and the use of insecticide-treated bed nets and indoor spraying of mosquitoes. The results of the model emphasize the importance of using a combination of all four controls tools for effective malaria intervention. Next, a two-age-class mathematical model for malaria transmission with asymptomatic carriers is developed and analyzed. In development of this model, four possible control measures are analyzed: the use of long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic, and screening and treatment of asymptomatic individuals. The numerical results show that a disease-free equilibrium can be attained if all four control measures are used. A common pitfall for most epidemiological models is the absence of real data; model-based conclusions have to be drawn based on uncertain parameter values. In this thesis, an approach to study the robustness of optimal control solutions under such parameter uncertainty is presented. Numerical analysis of the optimal control problem in the presence of parameter uncertainty demonstrate the robustness of the optimal control approach that: when a comprehensive control strategy is used the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the design of cost-effective strategies for disease control with multiple interventions, even under considerable uncertainty of model parameters. Finally, a separate work modeling the within-host Plasmodium falciparum infection in humans is presented. The developed model allows re-infection of already-infected red blood cells. The model hypothesizes that in severe malaria due to parasite quest for survival and rapid multiplication, the Plasmodium falciparum can be absorbed in the already-infected red blood cells which accelerates the rupture rate and consequently cause anemia. Analysis of the model and parameter identifiability using Markov chain Monte Carlo methods is presented.