Biomathematics of Chlamydia

Chlamydia trachomatis (C. trachomatis) related sexually transmitted infections are a major global public health concern. C. trachomatis afflict millions of men, women, and children worldwide and frequently result in serious medical diseases. In this thesis, mathematical modeling is applied in order to comprehend the dynamics of Chlamydia pathogens within host, their interactions with the immune systems, behavior in the presence of other pathogens, transmission dynamics in a human population, and the efficacy of control measures. The thesis begins with a brief introduction of the bacteria Chlamydia in Chapter 1. In Chapter 2, we give a brief detail of the mathematical modeling of infectious diseases, and its specific application to study the pathogen. In Chapter 3, a linear delay differential compartmental model is developed, and its special application is shown for a laboratory experiment conducted to study the intracellular development cycle of Chlamydia. The delay accounts for the time spent by bacteria in their various forms and for the time taken to go through the replication cycle. The mathematical model tracks the number of Chlamydia infected cells at each stage of the cell division cycle. Moreover, the formula for the final size of each compartment is derived. With initial conditions taken from the experiment, the model is fitted to results from the laboratory data. This simple linear model is capable of reflecting the outcomes of the laboratory experiment. In Chapter 4, at a population level, a novel mathematical model is introduced to study the dynamics of the co-infection between C. trachomatis, and herpes simplex virus (HSV). The concept of the model is based on the observation that in an individual simultaneously infected with both pathogens, the presence of HSV will make the Chlamydia persistent. In its persistent phase, Chlamydia is not replicating and is non-infectious. Important threshold parameters are obtained for the persistence of both infections. We prove global stability results for the disease-free and the boundary equilibria by applying the theory of asymptotically autonomous systems. Further, the model is calibrated to disease parameters to determine the population prevalence of both diseases and compare it with epidemiological findings. In Chapter 5, a compartmental maturity structured model is developed to investigate an optimal control problem for the treatment of chronic Chlamydia infection. The model takes into account the interaction of the pathogens with the immune system and its effects on the formation of persistent Chlamydia particles. As the system takes the form of a mixed ODE-PDE system, the results of the conventional form of Pontryagin’s maximal principle for ordinary differential equations are not suitable. For our purpose, we construct an optimal control problem for a general maturity compartmental model, and hence it consists of ordinary and partial differential equations, moreover, the boundary conditions are also nonlinear. For a fixed control, we verify the existence, uniqueness, and boundedness of the solutions. The system is numerically simulated for a variety of cost functions in order to calculate the optimal treatment for curing Chlamyida infection. We believe that since our findings were validated for a general model with maturity structure, they may be applied to any specific compartmental model that is compatible with the established system

Modeling and Optimal Control Applied to a Vector Borne Disease

A model with six mutually-exclusive compartments related to Dengue disease is presented. In this model there are three vector control tools: insecticides (larvicide and adulticide) and mechanical control. The problem is studied using an Optimal Control (OC) approach. The human data for the model is based on the Cape Verde Dengue outbreak. Some control measures are simulated and their consequences analyzed

Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection

A human respiratory syncytial virus surveillance system was implemented in Florida in 1999, to support clinical decision-making for prophylaxis of premature newborns. Recently, a local periodic SEIRS mathematical model was proposed in [Stat. Optim. Inf. Comput. 6 (2018), no.1, 139--149] to describe real data collected by Florida's system. In contrast, here we propose a non-local fractional (non-integer) order model. A fractional optimal control problem is then formulated and solved, having treatment as the control. Finally, a cost-effectiveness analysis is carried out to evaluate the cost and the effectiveness of proposed control measures during the intervention period, showing the superiority of obtained results with respect to previous ones.Comment: This is a preprint of a paper whose final and definite form is with 'Chaos, Solitons & Fractals', available from [http://www.elsevier.com/locate/issn/09600779]. Submitted 23-July-2018; Revised 14-Oct-2018; Accepted 15-Oct-2018. arXiv admin note: substantial text overlap with arXiv:1801.0963

Optimal treatment allocations in space and time for on-line control of an emerging infectious disease

A key component in controlling the spread of an epidemic is deciding where, whenand to whom to apply an intervention.We develop a framework for using data to informthese decisionsin realtime.We formalize a treatment allocation strategy as a sequence of functions, oneper treatment period, that map up-to-date information on the spread of an infectious diseaseto a subset of locations where treatment should be allocated. An optimal allocation strategyoptimizes some cumulative outcome, e.g. the number of uninfected locations, the geographicfootprint of the disease or the cost of the epidemic. Estimation of an optimal allocation strategyfor an emerging infectious disease is challenging because spatial proximity induces interferencebetween locations, the number of possible allocations is exponential in the number oflocations, and because disease dynamics and intervention effectiveness are unknown at outbreak.We derive a Bayesian on-line estimator of the optimal allocation strategy that combinessimulation–optimization with Thompson sampling.The estimator proposed performs favourablyin simulation experiments. This work is motivated by and illustrated using data on the spread ofwhite nose syndrome, which is a highly fatal infectious disease devastating bat populations inNorth America

Efficient regularized isotonic regression with application to gene--gene interaction search

Isotonic regression is a nonparametric approach for fitting monotonic models to data that has been widely studied from both theoretical and practical perspectives. However, this approach encounters computational and statistical overfitting issues in higher dimensions. To address both concerns, we present an algorithm, which we term Isotonic Recursive Partitioning (IRP), for isotonic regression based on recursively partitioning the covariate space through solution of progressively smaller "best cut" subproblems. This creates a regularized sequence of isotonic models of increasing model complexity that converges to the global isotonic regression solution. The models along the sequence are often more accurate than the unregularized isotonic regression model because of the complexity control they offer. We quantify this complexity control through estimation of degrees of freedom along the path. Success of the regularized models in prediction and IRPs favorable computational properties are demonstrated through a series of simulated and real data experiments. We discuss application of IRP to the problem of searching for gene--gene interactions and epistasis, and demonstrate it on data from genome-wide association studies of three common diseases.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS504 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org