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.

Early Life Intestinal Microbiota in Health and in Atopic Eczema

Decrease in microbial contacts in affluent societies is considered to lie behind the rise in allergic and other chronic inflammatory diseases during the last decades. Indeed, deviations in the intestinal microbiota composition and diversity have been associated with several diseases, such as atopic eczema. However, there is no consensus yet on what would constitute a beneficial or harmful microbiota. The aim of this thesis was to study the microbiota development in healthy infants and to characterize intestinal microbiota signatures associated with disease status and severity in infants with atopic eczema. The methodological aim was to compare and optimize methods for DNA extraction from fecal samples to be used in high-throughput microbiota analyses. It was confirmed that the most critical step in successful microbial DNA extraction from fecal samples is the mechanical cell lysis procedure. Based on this finding, an efficient semi-automated extraction process was developed that can be scaled for use in high-throughput platforms such as phylogenetic microarray used in this series of studies. By analyzing a longitudinal motherchild cohort for 3 years it was observed that the microbiota development is a gradual process, where some bacterial groups reach the degree of adult-type pattern earlier than others. During the breast-feeding period, the microbiota appeared to be relatively simple, while major diversification was found to start during the weaning process. By the age of 3 years, the child’s microbiota composition started to resemble that of an adult, but the bacterial diversity has still not reached the full diversity, indicating that the microbiota maturation extends beyond this age. In addition, at three years of age, the child’s microbiota was more similar to mother’s microbiota than to microbiota of nonrelated women.In infants with atopic eczema, a high total microbiota diversity and abundance of butyrate-producing bacteria was found to correlate with mild symptoms at 6 months. At 18 months, infants with mild eczema had significantly higher microbiota diversity and aberrant microbiota composition when compared to healthy controls at the same age. In conclusion, the comprehensive phylogenetic microarray analysis of early life microbiota shows the synergetic effect of vertical transmission and shared environment on the intestinal microbiota development. By the age of three years, the compositional development of intestinal microbiota is close to adult level, but the microbiota diversification continues beyond this age. In addition, specific microbiota signatures are associated with the existence and severity of atopic eczema and intestinal microbiota seems to have a role in alleviating the symptoms of this disease.

Borrelia burgdorferi evades the effects of ceftriaxone treatment in a mouse model of Lyme borreliosis

Borrelia burgdorferi infektoitujen hiirten antibioottihoidon jälkeinen oireilu Lymen borrelioosi on puutiaisten välittämä monimuotoinen infektiotauti, jonka tunnetuin oire on ns. vaeltava ihottuma eli erythema migrans. Muita tavallisia ilmentymiä ovat erityisesti nivel- ja hermosto-oireet sekä harvemmin sydän- ja silmäoireet. Suurin osa potilaista paranee täysin terveeksi antibioottihoidon avulla, mutta jopa 10 % borrelioosiin sairastuneista oireilee suositusten mukaisesta hoidosta huolimatta. Pitkittyneen oireilun on ajateltu johtuvan mm. infektion laukaisemasta autoimmuunitaudista tai kroonisesta infektiosta, mutta teorioiden tueksi ei ole kyetty esittämään kiistattomia todisteita. Onkin todennäköistä, että antibioottihoidon jälkeisen oireilun takana on useampia mekanismeja eikä yksi teoria selitä kaikkien potilaiden oireilua. Tässä väitöskirjatyössä on tutkittu hoidonjälkeistä borrelioosia hiirimallin avulla. Varhaisvaiheessa (2 viikkoa infektoinnin jälkeen) annettu antibiootti vähensi hiirten nivelturvotusta ja esti B. burgdorferi – bakteerin kasvun kudoksista otetuista näytteissä. Hoidettu¬jen hiirten B. burgdorferi -spesifiset IgG-luokan vasta-aineet pysyivät kuitenkin koholla ja osasta kudosnäytteistä löytyi B. burgdorferi:n DNA:ta PCR-tutkimuksen avulla. Mikäli hiiret hoidettiin myöhäisessä vaiheessa (yli 18 viikkoa infektoinnista) tulokset olivat muuten samanlaiset, mutta keftriaksoni ei vaikuttanut nivelturvotukseen. Näin hiirissä oli aikaansaatu tilanne, joka on hyvin samankaltainen ihmisen hoitoresistentin borrelia-artriitin kanssa: oireet jatkuvat, mutta taudinaiheuttajaa ei saada esiin. Inflammaatiota vaimentavaa anti-TNF-alphaa on käytetty nivelreuman hoidossa menestyksekkäästi huonosti muuhun hoitoon reagoivilla potilailla ja siitä syystä sen ajateltiin voivan vaikuttaa suotuisasti myös B. burgdorferi -infektoitujen hiirten hoidonjälkeiseen nivelturvotukseen. Sillä ei kuitenkaan ollut vaikutusta nivelturvotukseen, mutta yllättäen hoidon jälkeen osa hiirten kudosnäytteistä osoittautui viljelypositiivisiksi. On siis ilmeistä, että hiirimallissamme osa B. burgdorferi spirokeetoista pystyy välttämään keftriaksonihoidon vaikutuksen joko hakeutumalla elimistössä kudokseen, jossa antibiootin pitoisuus ei nouse riittävän korkeaksi, tai ne kykenevät muuntautumaan metabolisesti inaktiiviin tilaan eikä mikrobilääke yhdessä immuunipuolustuksen kanssa onnistu tappamaan niitä. Jatkotutkimuksissa selvitimme B. burgdorferi - spirokeetan mahdollista piilopaikkaa tutkimalla antibioottihoidon jälkeen useita eri kudoksia PCR-menetelmällä. Tulosten perusteella spirokeetta näyttää suosivan nivelkudosta tai soluja, joita esiintyy nivelessä runsaasti. On kuitenkin edelleen epäselvää, missä muodossa B. burgdorferi –spirokeetat säilyvät kudoksessa antibioottihoidon jälkeen.