Modeling Dengue Transmission and Vaccination

Dengue is one of the most rapidly spreading mosquito-borne viral diseases in the world and inflicts significant health, economic and social burdens on populations. In this dissertation, I studied different aspects of modeling of dengue and vector-borne diseases in general. Among various dengue models that have appeared in literature, some explicitly model the mosquito population, while others model them implicitly. In spite of extensive use of both modeling approaches, little guidance exists for which type of model should be preferred. I developed a Bayesian approach that uses a Markov chain Monte Carlo (MCMC) method to fit disease models to epidemiological data and used it to explore how well these models explain observed incidence and to find good estimates for the epidemiological parameters for dengue. I fitted dengue hemorrhagic fever data from Thailand to both type of models and found using Akaike Information Criterion that explicitly incorporating the mosquito population may not be necessary in modeling dengue transmission. On comparing my estimates of the basic reproduction number, R0, with other estimates in literature, I found a wide variability in R0 estimates among studies. This variability in R0 estimate for dengue transmission is not well understood. By fitting a simple dengue model to dengue incidence for varying R0 values, I found a logarithmic type relationship between population immunity levels and R0, which may be a reason for the variability in R0 estimates. The result also highlighted the importance of finding better estimates of population immunity level to help more accurately estimate R0 and other epidemiological parameters for dengue. Driven by the seasonality in mosquito abundance and complex dynamics of denuge, introducing a vaccine may induce a transient period immediately after vaccine introduction where prevalence can spike higher than in the pre-vaccine period. These transient spikes could lead to doubts about the vaccination program among the public and decision makers, possibly impeding the vaccination program. Using simple dengue-transmission models, I found that large transient spikes in prevalence are robust phenomena that occur when vaccine efficacy and vaccine coverage is not either both very high or both very low. Despite the presence of these spikes, vaccination always reduced total number of infections in the 15 years after vaccine introduction. Therefore, policy makers should prepare for spikes in prevalence after vaccine introduction to mitigate the burden of these spikes and to accurately measure the effectiveness of the vaccine program

Output Consensus Control for Heterogeneous Multi-Agent Systems

We study distributed output feedback control of a heterogeneous multi-agent system (MAS), consisting of N different continuous-time linear dynamical systems. For achieving output consensus, a virtual reference model is assumed to generate the desired trajectory for which the MAS is required to track and synchronize. A full information (FI) protocol is assumed for consensus control. This protocol includes information exchange with the feed-forward signals. In this dissertation we study two different kinds of consensus problems. First, we study the consensus control over the topology involving time delays and prove that consensus is independent of delay lengths. Second, we study the consensus under communication constraints. In contrast to the existing work, the reference trajectory is transmitted to only one or a few agents and no local reference models are employed in the feedback controllers thereby eliminating synchronization of the local reference models. Both significantly lower the communication overhead. In addition, our study is focused on the case when the available output measurements contain only relative information from the neighboring agents and reference signal. Conditions are derived for the existence of distributed output feedback control protocols, and solutions are proposed to synthesize the stabilizing and consensus control protocol over a given connected digraph. It is shown that the H-inf loop shaping and LQG/LTR techniques from robust control can be directly applied to design the consensus output feedback control protocol. The results in this dissertation complement the existing ones, and are illustrated by a numerical example. The MAS approach developed in this dissertation is then applied to the development of autonomous aircraft traffic control system. The development of such systems have already started to replace the current clearance-based operations to trajectory based operations. Such systems will help to reduce human errors, increase efficiency, provide safe flight path, and improve the performance of the future flight

Consensusability of discrete-time multi-agent systems

The study of multi-agent systems (MAS) focuses on systems in which many intelligent agents interact within an environment. The agents are considered to be autonomous entities. MAS can be used to solve problems that are difficult or impossible for an individual agent to solve. The main feature which is achieved when developing MAS, if they work, is flexibility, since MAS can be added to, modified and reconstructed, without the need for detailed rewriting of the application. MAS can manifest self-organization as well as self-steering related complex behaviors even when the individual strategies of all their agents are simple. The goal of MAS research is to find methods that allow us to build complex systems composed of autonomous agents who, while operating on local knowledge and possessing only limited abilities, are nonetheless capable of enacting the desired global behaviors. We want to know how to take a description of what a system of agents should do and break it down into individual agent behaviors. This thesis investigates the problem when discrete-time MAS are consensusable under undirected graph. A discussion is provided to show how the problem differs from continuous time system. Then a consensusability condition is derived in terms of the Mahler measure of the agent system for single input single out systems (SISO) and result shows that there is an improved consensusability by a power of two. An algorithm is proposed for distributed consensus feedback control law when the consensusability holds. Also the case of output feedback is considered in which the consensusability problem becomes more complicated. To solve this we decompose the problem into two parts i.e. state feedback and state estimation. Simulation results demonstrate the effectiveness of the established results

Strain-induced electronic phase transition and strong enhancement of thermopower of TiS2

Using first principles density functional theory calculations, we show a semimetal to semiconducting electronic phase transition for bulk TiS 2 by applying uniform biaxial tensile strain. This electronic phase transition is triggered by charge transfer from Ti to S, which eventually reduces the overlap between Ti-(d) and S-(p) orbitals. The electronic transport calculations show a large anisotropy in electrical conductivity and thermopower, which is due to the difference in the effective masses along the in-plane and out of plane directions. Strain induced opening of band gap together with changes in dispersion of bands lead to three-fold enhancement in thermopower for both p- and n-type TiS2 . We further demonstrate that the uniform tensile strain, which enhances the thermoelectric performance, can be achieved by doping TiS2 with larger iso-electronic elements such as Zr or Hf at Ti sites.Comment: 8 pages, 6 figure

Effect of strain on electronic and thermoelectric properties of few layers to bulk MoS2_{2}

The sensitive dependence of electronic and thermoelectric properties of MoS$_2$ on the applied strain opens up a variety of applications in the emerging area of straintronics. Using first principles based density functional theory calculations, we show that the band gap of few layers of MoS$_2$ can be tuned by applying i) normal compressive (NC), ii) biaxial compressive (BC), and iii) biaxial tensile (BT) strain. A reversible semiconductor to metal transition (S-M transition) is observed under all three types of strain. In the case of NC strain, the threshold strain at which S-M transition occurs increases with increasing number of layers and becomes maximum for the bulk. On the other hand, the threshold strain for S-M transition in both BC and BT strain decreases with the increase in number of layers. The difference in the mechanisms for the S-M transition is explained for different types of applied strain. Furthermore, the effect of strain type and number of layers on the transport properties are also studied using Botzmann transport theory. We optimize the transport properties as a function of number of layers and applied strain. 3L- and 2L-MoS$_2$ emerge as the most efficient thermoelectric material under NC and BT strain, respectively. The calculated thermopower is large and comparable to some of the best thermoelectric materials. A comparison between the feasibility of these three types of strain is also discussed.Comment: 18 pages, 7 figure

Benford's distribution in extrasolar world: Do the exoplanets follow Benford's distribution?

In many real life situations, it is observed that the first digits (i.e., $1,2,\ldots,9$) of a numerical data-set, which is expressed using decimal system, do not follow a random distribution. Instead, smaller numbers are favoured by nature in accordance with a logarithmic distribution law, which is referred to as Benford's law. The existence and applicability of this empirical law have been extensively studied by physicists, accountants, computer scientists, mathematicians, statisticians, etc., and it has been observed that a large number of data-sets related to diverse problems follow this distribution. However, applicability of Benford's law has been hardly tested for extrasolar objects. Motivated by this fact, this paper investigates the existence of Benford's distribution in the extrasolar world using Kepler data for exoplanets. The investigation has revealed the presence of Benford's distribution in various physical properties of these exoplanets. Further, Benford goodness parameters are computed to provide a quantitative measure of coincidence of real data with the ideal values obtained from Benford's distribution. The quantitative analysis and the plots have revealed that several physical parameters associated with the exoplanets (e.g., mass, volume, density, orbital semi-major axis, orbital period, and radial velocity) nicely follow Benford's distribution, whereas some physical parameters (e.g., total proper motion, stellar age and stellar distance) moderately follow the distribution, and some others (e.g., longitude, radius, and effective temperature) do not follow Benford's distribution. Further, some specific comments have been made on the possible generalizations of the obtained result, its potential applications in analyzing data-set of candidate exoplanets, and how interested readers can perform similar investigations on other interesting data-sets.Comment: 7 pages, 3 figures and one potrai