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.

Moderate-term reproducibility of heart rate variability during rest and light to moderate exercise in children

Previous studies have demonstrated the high reproducibility of heart rate variability (HRV) measures in adults while little information exists concerning HRV reproducibility in children. Subsequently, the aim of the current study was to examine the moderate-term reproducibility of heart rate and frequency domain measures of HRV during rest and light to moderate exercise in children. Ten healthy children (6 males, 4 females) aged between 7 and 12 years of age volunteered for this study with HRV recordings obtained during supine rest and three treadmill walking exercise work rates (≤60% maximum heart rate), initially and then 8 weeks later. Differences (P < 0.05) between variables were examined using paired t-tests or Wilcoxon signed rank tests while reliability and reproducibility were examined by intraclass correlation coefficients (ICC), coefficients of variation (CV), and mean bias ratio and ratio limits of agreement (LOA). Heart rate and all measures of HRV at rest and exercise were unchanged after 8 weeks. Significant ICC were documented primarily during rest (0.72-0.85) while weaker relationships (-0.02-0.87) were evident during exercise. A large range of CV was identified during rest (6-33%) and exercise (3-128%) while the ratio LOA were variable and substantial (1.04-2.73). Despite similar HRV over an 8-week period, variable ICC and sizable CV and ratio LOA indicate moderate to poor reproducibility of HRV in children, particularly during light to moderate exercise. Studies examining HRV in children should include age- or maturation stage-matched control participants to address the age-related change in HRV and inadequate HRV reliability.

Influence of exercise modality on agreement between gas exchange and heart rate variability thresholds

The main purpose of this study was to investigate the level of agreement between the gas exchange threshold (GET) and heart rate variability threshold (HRVT) during maximal cardiopulmonary exercise testing (CPET) using three different exercise modalities. A further aim was to establish whether there was a 1:1 relationship between the percentage heart rate reserve (%HRR) and percentage oxygen uptake reserve (%V˙O2R) at intensities corresponding to GET and HRVT. Sixteen apparently healthy men 17 to 28 years of age performed three maximal CPETs (cycling, walking, and running). Mean heart rate and V˙O2 at GET and HRVT were 16 bpm (P<0.001) and 5.2 mL·kg-1·min-1 (P=0.001) higher in running than cycling, but no significant differences were observed between running and walking, or cycling and walking (P>0.05). There was a strong relationship between GET and HRVT, with R2 ranging from 0.69 to 0.90. A 1:1 relationship between %HRR and %V˙O2R was not observed at GET and HRVT. The %HRR was higher during cycling (GET mean difference=7%; HRVT mean difference=11%; both P<0.001), walking (GET mean difference=13%; HRVT mean difference=13%; both P<0.001), or running (GET mean difference=11%; HRVT mean difference=10%; both P<0.001). Therefore, using HRVT to prescribe aerobic exercise intensity appears to be valid. However, to assume a 1:1 relationship between %HRR and %V˙O2R at HRVT would probably result in overestimation of the energy expenditure during the bout of exercise.

Interdependence of Macroeconomics Variables, Stock Market Returns and Stock Market Volatility in Latin America

This thesis examines the interdependence of macroeconomic variables, stock market returns and stock market volatility in Latin America between 2000 and 2015. Argentina, Brazil, Chile, Colombia, Mexico and Peru were chosen as the sample markets, while inflation, interest rate, exchange rate, money supply, oil and gold were chosen as the sample macroeconomic variables. Bivariate VAR (1) model was applied to examine the mean return spillovers between the variables, whereas GARCH (1, 1) – BEKK model was applied to capture the volatility spillovers. The sample was divided into two smaller sub-periods, where the first sub-period covers from 2000 to 2007, and the second sub-period covers from 2007 to 2015. The empirical results report significant shock transmissions and volatility spillovers between inflation, interest rate, exchange rate, money supply, gold, oil and the selected markets, which suggests interdependence between the variables.

The Dutch disease and its neutralization: a Ricardian approach

The Dutch disease is a major market failure originated in the existence of cheap and abundant natural or human resources that keep overvalued the currency of a country for an undetermined period of time, thus turning non profitable the production of tradable goods using technology in the state-of-the-art. It is an obstacle to growth on the demand side, because it limits investment opportunities. The severity of the Dutch disease varies according to the extent of the Ricardian rents involved, i.e., according to the difference between two exchange rate equilibriums: the ‘current’ or market rate and the ‘industrial’ rate - the one that make viable efficient tradable industries. Its main symptoms, besides overvalued currency, are low rates of growth of the manufacturing industry, artificially high real wages, and unemployment. Its neutralization requires managing the exchange rate. The principal instrument for that is a sales or export tax on the commodities that give origin to the Dutch disease. In order to neutralize it policymakers face major political obstacles since it involves taxing exports and reducing wages. Finally, this papers argues that there is an extended concept of Dutch disease: besides having its origin in natural resources, it may arise from cheap labor provided that the ‘wage spread’ in the developing country is considerably larger than in the developed one - a condition that is usually present.

On high interest rates in Brazil

This article examines the question of why interest rates are so high in Brazil as compared to the international average. It looks at theoretical arguments based on excessive government deficits, structural lack of private savings, inflation bias, excessive investment demand and fear of floating. An informal look at the evidence does not strongly corroborate any of these arguments. Hence a wise central bank should consider "testing" the market to make sure it is not dealing with an extreme equilibrium configuration or a long standing disequilibrium.

Effects of overvaluation and exchange rate volatility over industrial investment: empirical evidence and economic policy proposals for Brazil

The present article aims to analyze the recent behavior of real exchange rate in Brazil and its effects over investment per worker in Brazilian manufacturing and extractive industry. Preliminary estimates presented in the article shows an over-valuation of 48% of real exchange rate in Brazil. The reaction between the level (and volatility) of real exchange rate and investment (per worker) in Brazil is analyzed by means of a panel data econometric model for 30 sectors of Brazilian manufacturing and extractive industry. The empirical results show that the level and volatility of real exchange rate has a strong effect over investment per worker in Brazilian industry. Finally, we conclude the article presenting a proposal for a new macroeconomic regime that aims to produce an acceleration of economic growth of Brazilian economy and, by that, a catching-up process with developed countries.

POLITICAL ENVIRONMENT AND BUSINESS DEVELOPMENT IN THE ARCTIC Strategic opportunities and threats for Finnish companies

The Arctic environment is changing constantly. There are several factors that constitute to the rate and immensity of the development. The region differs from the surrounding markets that most of the countries in the region have been used to. Therefore the purpose of the study was to understand how the political environment affects Finnish companies’ strategies and business operations. The issues analyzed were the political environment in the region, the business environment and economic development, and the opportunities and threats that the Finnish companies have in Arctic. The main theories were found from strategic management and market analysis tools. The different theories and definitions were gone through in order to understand the context of the study. This is a qualitative study that uses content analysis as its main method of analyzing the data. Therefore the data analyzed was gathered from already existing material and it was analyzed until the saturation point was found. This was done in order to minimize the risks related to using secondary data. The data collected was then categorized into themes accordingly. First the general political environment in the Arctic was studied, especially the Arctic Council and its work as the main political entity. From there the focus shifted to the business environment and the general opportunities and threats that are found from Arctic economic development. China offered another point of view to this as it represented a non-Arctic state with a keen interest on the region. Lastly the two previous objectives were combined and looked through from a Finnish perspective. Finnish companies have a great starting point to Arctic business and the operational business environment gives them the framework with which they have to operate in. As a conclusion it can be said that there are three main factors leading the Arctic economic development; the climate change, the development of technology, and the political environment. These set the framework with which the companies operating in the region must comply with. The industry that is likely to lead the development is the marine industry. Furthermore it became evident that the Finnish companies operating in the Arctic face many opportunities as well as threats which can be utilized, taken advantage of or controlled through effective strategic management. The key characteristics needed in the region are openness and understanding of the challenging environment and the ability to face and manage the arising challenges.

Determinants of bankruptcy protection duration for Canadian firms

The present thesis examines the determinants of the bankruptcy protection duration for Canadian firms. Using a sample of Canadian firms that filed for bankruptcy protection between the calendar years 1992 and 2009, we fmd that the firm age, the industry adjusted operating margin, the default spread, the industrial production growth rate or the interest rate are influential factors on determining the length of the protection period. Older firms tend to stay longer under protection from creditors. As older firms have more complicated structures and issues to settle, the risk of exiting soon the protection (the hazard rate) is small. We also find that firms that perform better than their benchmark as measured by the industry they belong to, tend to leave quickly the bankruptcy protection state. We conclude that the fate of relatively successful companies is determined faster. Moreover, we report that it takes less time to achieve a final solution to firms under bankrupt~y when the default spread is low or when the appetite for risk is high. Conversely, during periods of high default spreads and flight for quality, it takes longer time to resolve the bankruptcy issue. This last finding may suggest that troubled firms should place themselves under protection when spreads are low. However, this ignores the endogeneity issue: high default spread may cause and incidentally reflect higher bankruptcy rates in the economy. Indeed, we find that bankruptcy protection is longer during economic downturns. We explain this relation by the natural increase in default rate among firms (and individuals) during economically troubled times. Default spreads are usually larger during these harsh periods as investors become more risk averse since their wealth shrinks. Using a Log-logistic hazard model, we also fmd that firms that file under the Companies' Creditors Arrangement Act (CCAA) protection spend longer time restructuring than firms that filed under the Bankruptcy and Insolvency Act (BIA). As BIA is more statutory and less flexible, solutions can be reached faster by court orders.

Asymmetric Smiles, Leverage Effects and Structural Parameters.

In this paper, we characterize the asymmetries of the smile through multiple leverage effects in a stochastic dynamic asset pricing framework. The dependence between price movements and future volatility is introduced through a set of latent state variables. These latent variables can capture not only the volatility risk and the interest rate risk which potentially affect option prices, but also any kind of correlation risk and jump risk. The standard financial leverage effect is produced by a cross-correlation effect between the state variables which enter into the stochastic volatility process of the stock price and the stock price process itself. However, we provide a more general framework where asymmetric implied volatility curves result from any source of instantaneous correlation between the state variables and either the return on the stock or the stochastic discount factor. In order to draw the shapes of the implied volatility curves generated by a model with latent variables, we specify an equilibrium-based stochastic discount factor with time non-separable preferences. When we calibrate this model to empirically reasonable values of the parameters, we are able to reproduce the various types of implied volatility curves inferred from option market data.

Habit Formation and the Persistence of Monetary Shocks

This paper studies the persistent effects of monetary shocks on output. Previous empirical literature documents this persistence, but standard general equilibrium models with sticky prices fail to generate output responses beyond the duration of nominal contracts. This paper constructs and estimates a general equilibrium model with price rigidities, habit formation, and costly capital adjustment. The model is estimated via Maximum Likelihood using US data on output, the real money stock, and the nominal interest rate. Econometric results suggest that habit formation and adjustment costs to capital play an important role in explaining the output effects of monetary policy. In particular, impulse response analysis indicates that the model generates persistent, hump-shaped output responses to monetary shocks.

Risk Aversion, Intertemporal Substitution, and Option Pricing

This paper develops a general stochastic framework and an equilibrium asset pricing model that make clear how attitudes towards intertemporal substitution and risk matter for option pricing. In particular, we show under which statistical conditions option pricing formulas are not preference-free, in other words, when preferences are not hidden in the stock and bond prices as they are in the standard Black and Scholes (BS) or Hull and White (HW) pricing formulas. The dependence of option prices on preference parameters comes from several instantaneous causality effects such as the so-called leverage effect. We also emphasize that the most standard asset pricing models (CAPM for the stock and BS or HW preference-free option pricing) are valid under the same stochastic setting (typically the absence of leverage effect), regardless of preference parameter values. Even though we propose a general non-preference-free option pricing formula, we always keep in mind that the BS formula is dominant both as a theoretical reference model and as a tool for practitioners. Another contribution of the paper is to characterize why the BS formula is such a benchmark. We show that, as soon as we are ready to accept a basic property of option prices, namely their homogeneity of degree one with respect to the pair formed by the underlying stock price and the strike price, the necessary statistical hypotheses for homogeneity provide BS-shaped option prices in equilibrium. This BS-shaped option-pricing formula allows us to derive interesting characterizations of the volatility smile, that is, the pattern of BS implicit volatilities as a function of the option moneyness. First, the asymmetry of the smile is shown to be equivalent to a particular form of asymmetry of the equivalent martingale measure. Second, this asymmetry appears precisely when there is either a premium on an instantaneous interest rate risk or on a generalized leverage effect or both, in other words, whenever the option pricing formula is not preference-free. Therefore, the main conclusion of our analysis for practitioners should be that an asymmetric smile is indicative of the relevance of preference parameters to price options.

Non-Commitment and Savings in Dynamic Risk-Sharing Contracts

We characterize the solution to a model of consumption smoothing using financing under non-commitment and savings. We show that, under certain conditions, these two different instruments complement each other perfectly. If the rate of time preference is equal to the interest rate on savings, perfect smoothing can be achieved in finite time. We also show that, when random revenues are generated by periodic investments in capital through a concave production function, the level of smoothing achieved through financial contracts can influence the productive investment efficiency. As long as financial contracts cannot achieve perfect smoothing, productive investment will be used as a complementary smoothing device.

The Dynamic (In)efficiency of Monetary Policy by Committee

This paper develops a model where the value of the monetary policy instrument is selected by a heterogenous committee engaged in a dynamic voting game. Committee members differ in their institutional power and, in certain states of nature, they also differ in their preferred instrument value. Preference heterogeneity and concern for the future interact to generate decisions that are dynamically ineffcient and inertial around the previously-agreed instrument value. This model endogenously generates autocorrelation in the policy variable and provides an explanation for the empirical observation that the nominal interest rate under the central bank’s control is infrequently adjusted.

A Semi-Parametric Factor Model for Interest Rates.

Understanding the dynamics of interest rates and the term structure has important implications for issues as diverse as real economic activity, monetary policy, pricing of interest rate derivative securities and public debt financing. Our paper follows a longstanding tradition of using factor models of interest rates but proposes a semi-parametric procedure to model interest rates.