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.

Homogeneous Assays for Simplified Screening of HLA-conferred Genetic Disease Risk

The increasing incidence of type 1 diabetes has led researchers on a quest to find the reason behind this phenomenon. The rate of increase is too great to be caused simply by changes in the genetic component, and many environmental factors are under investigation for their possible contribution. These studies require, however, the participation of those individuals most likely to develop the disease, and the approach chosen by many is to screen vast populations to find persons with increased genetic risk factors. The participating individuals are then followed for signs of disease development, and their exposure to suspected environmental factors is studied. The main purpose of this study was to find a suitable tool for easy and inexpensive screening of certain genetic risk markers for type 1 diabetes. The method should be applicable to using whole blood dried on sample collection cards as sample material, since the shipping and storage of samples in this format is preferred. However, the screening of vast sample libraries of extracted genomic DNA should also be possible, if such a need should arise, for example, when studying the effect of newly discovered genetic risk markers. The method developed in this study is based on homogeneous assay chemistry and an asymmetrical polymerase chain reaction (PCR). The generated singlestranded PCR product is probed by lanthanide-labelled, LNA (locked nucleic acid)-spiked, short oligonucleotides with exact complementary sequences. In the case of a perfect match, the probe is hybridised to the product. However, if even a single nucleotide difference occurs, the probe is bound instead of the PCR product to a complementary quencher-oligonucleotide labelled with a dabcyl-moiety, causing the signal of the lanthanide label to be quenched. The method was applied to the screening of the well-known type 1 diabetes risk alleles of the HLA-DQB1 gene. The method was shown to be suitable as an initial screening step including thousands of samples in the scheme used in the TEDDY (The Environmental Determinants of Diabetes in the Young) study to identify those individuals at increased genetic risk. The method was further developed into dry-reagent form to allow an even simpler approach to screening. The reagents needed in the assay were in dry format in the reaction vessel, and performing the assay required only the addition of the sample and, if necessary, water to rehydrate the reagents. This allows the assay to be successfully executed even by a person with minimal laboratory experience.