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.

Brain imaging studies in severe somatization

Somatization was described 4000 years ago but the pathophysiology of the, phenomenon is unknown. The aim of this investigation was to explore whether central nervous system (CNS) pathology is associated with severe somatization which was operationalized as somatization disorder (SD) and undifferentiated somatoform disorder. The study sample consisted of severely somatizing people who were included into the study after a multi-phase screening procedure in order to exclude psychiatric comorbidities and physical illnesses. Diagnosis of somatization disorder or undifferentiated sofatoform disorder were set according to Diagnostic and Statistical Manual of Mental Disorders 4th ed. (DSM-IV). The first study explored the regional cerebral metabolic rate of glucose (rCMRGlc) in severely somatizing females and found it to be reduced in several regions of the brain compared to healthy controls. The second study observed brain morphology with magnetic resonance imaging (MRI) based on the findings from the first study and showed enlarged caudate nuclei in somatizing women compared to healthy volunteers. The third study investigated temperament factors and brain metabolism, and their association with severe somatization. Low caudate and putamen metabolism, low novelty seeking as well as high harm avoidance were found to be associated with severe somatization in women, reduced caudate metabolism having the strongest association. The last study is a report of man with left-side gradient of multiple symptoms of unknown origin in the body. The examination revealed a hypermetabolic nucleus putamen on the contralateral side. All the main results reported in these four articles are original findings. The results suggest that CNS pathology is involved in the pathophysiology of severe somatization.

Survival and Quality of Life among Patients with Severe Lower Extremity Peripheral Arterial Disease

Lower extremity peripheral arterial disease (PAD) is associated with decreased functional status, diminished quality of life (QoL), amputation, myocardial infarction, stroke, and death. Nevertheless, public awareness of PAD as a morbid and mortal disease is low. The aim of this study was to assess the incidence of major lower extremity amputation due to PAD, the extent of reamputations, and survival after major lower extremity amputation (LEA) in a population based PAD patient cohort. Furthermore, the aim was to assess the functional capacity in patients with LEA, and the QoL after lower extremity revascularization and major amputation. All 210 amputees due to PAD in 1998–2002 and all 519 revascularized patients in 1998–2003 were explored. 59 amputees alive in 2004 were interviewed using a structured questionnaire of QoL. Two of each amputee age-, gender- and domicile-matched controls filled in and returned postal self-administered QoL questionnaire as well as 231 revascularized PAD patients (the amount of these patients who engaged themselves to the study), and one control person for each patient completed postal self-administered QoL questionnaire. The incidence rate of major LEA was 24.1/100 000 person-years and it was considerably high during the years studied. The one-month mortality rate was 21%, 52% at one-year, and the overall mortality rate was 80%. When comparing the one-year mortality risk of amputees, LEAs were associated with a 7.4-fold annual mortality risk compared with the reference population in Turku. Twenty-two patients (10%) had ipsilateral transversions from BK to AK amputation. Fifty patients (24%) ended up with a contralateral major LEA within two to four amputation operations. Three bilateral amputations were performed at the first major LEA operation. Of the 51 survivors returning home after their first major LEA, 36 (71%) received a prosthesis; (16/36, 44%) and were able to walk both in- and outdoors. Of the 68 patients who were discharged to institutional care, three (4%) had a prosthesis one year after LEA. Both amputees and revascularized patients had poor physical functioning and significantly more depressive symptoms than their controls. Depressive symptoms were more common in the institutionalized amputees than the home-dwelling amputees. The surviving amputees and their controls had similar life satisfaction. The amputees felt themselves satisfied and contented, whether or not they lived in long-term care or at home. PAD patients who had undergone revascularizations had poorer QoL than their controls. The revascularized patients’ responses on their perceived physical functioning gave an impression that these patients are in a declining life cycle and that revascularizations, even when successful, may not be sufficient to improve the overall function. It is possible that addressing rehabilitation issues earlier in the care may produce a more positive functional outcome. Depressive symptoms should be recognized and thoroughly considered at the same time the patients are recovering from their revascularization operation. Also primary care should develop proper follow-up, and community organizations should have exercise groups for those who are able to return home, since they very often live alone. In rehabilitation programs we should consider not only physical disability assessment but also QoL.

Early detection of severe sepsis in the emergency room in adults - Clinical utility of prognostic markers

Vaikean sepsiksen varhainen tunnistaminen päivystyspoliklinikalla – merkkiaineiden käyttökelpoisuus aikuispotilaiden arvioinnissa Päivystyspotilaan vakavan yleisinfektion eli sepsiksen varhainen tunnistaminen ja taudin vaikeusasteen arviointi on päivystävälle lääkärille tärkeä haaste. Arvioimme prospektiivisessa kohorttitutkimuksessa eri merkkiaineiden hyödyllisyyttä sepsiksen varhaisessa tunnistamisessa ja vaikeusasteen arvioinnissa. Työssä I ja III oli 539 päivystyspotilasta, joilta kliinikko päätti ottaa veriviljelyn sepsistä epäillen. Tutkimuksessa II oli 525 potilasta ja tutkimuksessa IV 537 potilasta. Tutkimuksessa I plasman C-reaktiivisen proteiinin (CRP) pitoisuuksia verrattiin plasman prokalsitoniinin (PCT) ja interleukiinin (IL-6) pitoisuuksiin. Tutkimuksessa II verrattiin plasman baktersidisen/ permeabiliteettia lisäävän proteiinin (BPI), ryhmän IIA fosfolipaasi A2:n (PLA2GIIA) ja CRP:n pitoisuuksia sekä valkosolujen määriä toisiinsa. Tutkimuksessa III arvioitiin liukoisen urokinaasi-tyyppisen plasminogeenin aktivaattorireseptorin (suPAR) ja tutkimuksessa IV pentraksiini 3:n (PTX3) määrityksen käyttökelpoisuutta. Tutkimuksessa I todettiin päivystystilanteessa mitattujen korkeiden PCT - ja IL-6 - pitoisuuksien ennustavan vaikean sepsiksen kehittymistä paremmin kuin korkean CRP:n. Tutkimuksessa II plasman PLA2GIIA vaikutti hiukan paremmalta vaikean sepsiksen ennustajalta kuin CRP tai veren valkosolutaso, mutta BPI ei ollut hyödyllinen. Tutkimuksessa III korkea plasman suPAR- pitoisuus osoittautui itsenäiseksi kuolleisuuden riskitekijäksi ja se liittyi myös vaikean sepsiksen kehittymiseen. Tutkimuksessa IV korkea PTX3 - pitoisuus toimi samaan tapaan kuin suPAR. Kokonaisuutena PCT osoittautui parhaaksi merkkiaineeksi ennustamaan elinhäiriön kehittymistä ja suPAR kuolleisuutta. PTX3 ei tarjonnut merkittävää lisäetua PCT:iin ja suPAR:iin verrattuna. CRP osoitti suhteellisen hyvin bakteeri-infektion esiintymistä, mutta ennusteellista arvoa sillä ei ollut. suPAR on kiinnostava kuolleisuuden ja elinhäiriön kehittymisen merkkiaine.