Random propagation in complex systems : nonlinear matrix recursions and epidemic spread

This dissertation studies long-term behavior of random Riccati recursions and mathematical epidemic model. Riccati recursions are derived from Kalman filtering. The error covariance matrix of Kalman filtering satisfies Riccati recursions. Convergence condition of time-invariant Riccati recursions are well-studied by researchers. We focus on time-varying case, and assume that regressor matrix is random and identical and independently distributed according to given distribution whose probability distribution function is continuous, supported on whole space, and decaying faster than any polynomial. We study the geometric convergence of the probability distribution. We also study the global dynamics of the epidemic spread over complex networks for various models. For instance, in the discrete-time Markov chain model, each node is either healthy or infected at any given time. In this setting, the number of the state increases exponentially as the size of the network increases. The Markov chain has a unique stationary distribution where all the nodes are healthy with probability 1. Since the probability distribution of Markov chain defined on finite state converges to the stationary distribution, this Markov chain model concludes that epidemic disease dies out after long enough time. To analyze the Markov chain model, we study nonlinear epidemic model whose state at any given time is the vector obtained from the marginal probability of infection of each node in the network at that time. Convergence to the origin in the epidemic map implies the extinction of epidemics. The nonlinear model is upper-bounded by linearizing the model at the origin. As a result, the origin is the globally stable unique fixed point of the nonlinear model if the linear upper bound is stable. The nonlinear model has a second fixed point when the linear upper bound is unstable. We work on stability analysis of the second fixed point for both discrete-time and continuous-time models. Returning back to the Markov chain model, we claim that the stability of linear upper bound for nonlinear model is strongly related with the extinction time of the Markov chain. We show that stable linear upper bound is sufficient condition of fast extinction and the probability of survival is bounded by nonlinear epidemic map.

Robust Sliding Control of SEIR Epidemic Models

This paper is aimed at designing a robust vaccination strategy capable of eradicating an infectious disease from a population regardless of the potential uncertainty in the parameters defining the disease. For this purpose, a control theoretic approach based on a sliding-mode control law is used. Initially, the controller is designed assuming certain knowledge of an upper-bound of the uncertainty signal. Afterwards, this condition is removed while an adaptive sliding control system is designed. The closed-loop properties are proved mathematically in the nonadaptive and adaptive cases. Furthermore, the usual sign function appearing in the sliding-mode control is substituted by the saturation function in order to prevent chattering. In addition, the properties achieved by the closed-loop system under this variation are also stated and proved analytically. The closed-loop system is able to attain the control objective regardless of the parametric uncertainties of the model and the lack of a priori knowledge on the system.

Stability analysis and observer design for discrete-time SEIR epidemic models

This paper applies Micken's discretization method to obtain a discrete-time SEIR epidemic model. The positivity of the model along with the existence and stability of equilibrium points is discussed for the discrete-time case. Afterwards, the design of a state observer for this discrete-time SEIR epidemic model is tackled. The analysis of the model along with the observer design is faced in an implicit way instead of obtaining first an explicit formulation of the system which is the novelty of the presented approach. Moreover, some sufficient conditions to ensure the asymptotic stability of the observer are provided in terms of a matrix inequality that can be cast in the form of a LMI. The feasibility of the matrix inequality is proved, while some simulation examples show the operation and usefulness of the observer.

On the Stability and Equilibrium Points of Multistaged SI (n) R Epidemic Models

This paper relies on the concept of next generation matrix defined ad hoc for a new proposed extended SEIR model referred to as SI(n)R-model to study its stability. The model includes n successive stages of infectious subpopulations, each one acting at the exposed subpopulation of the next infectious stage in a cascade global disposal where each infectious population acts as the exposed subpopulation of the next infectious stage. The model also has internal delays which characterize the time intervals of the coupling of the susceptible dynamics with the infectious populations of the various cascade infectious stages. Since the susceptible subpopulation is common, and then unique, to all the infectious stages, its coupled dynamic action on each of those stages is modeled with an increasing delay as the infectious stage index increases from 1 to n. The physical interpretation of the model is that the dynamics of the disease exhibits different stages in which the infectivity and the mortality rates vary as the individual numbers go through the process of recovery, each stage with a characteristic average time.

Molecular epidemiology of the heterosexual HIV-1 transmission in Kunming, Yunnan Province of China suggests origin from the local IDU epidemic

Molecular epidemiological investigation was conducted among injecting drug users (IDUs) (n = 11) and heterosexuals (n = 15) in Kunming, Yunnan Province of China. HIV-1 genotypes were determined based on the nucleotide sequences of 2.6-kb gag-RT region. The distribution of genotypes among IDUs was as follows: CRF07_BC (5/11) and CRF08_BC (5/11); subtype B' (1/11). Similarly, a majority of Kunming heterosexuals (14/15) were infected with CRF07_BC (4/15), CRF08_BC (6/15), or subtype B' (4/15), known to predominate among IDUs in China. This contrasts with trends in the coastal regions of China and surrounding southeastern Asian countries, where CRF01_AE predominates among heterosexuals. The heterosexual HIV-1 epidemic in Kunming thus appears to derive from the local IDU epidemic. Of note, subtype B' was the most prevalent strain among heterosexuals before 1997, while CRF07_BC and CRF08_BC became predominant in 2002, indicating a transition of HIV-1 genotype distribution between the early and the more recent samples from Kunming heterosexuals.

Adult neural stem cells expressing IL-10 confer potent immunomodulation and remyelination in experimental autoimmune encephalitis

Adult neural stem cells (aNSCs) derived from the subventricular zone of the brain show therapeutic effects in EAE, an animal model of the chronic inflammatory neurodegenerative disease MS; however, the beneficial effects are modest. One critical weakness of aNSC therapy may be an insufficient antiinflammatory effect. Here, we demonstrate that i.v. or i.c.v. injection of aNSCs engineered to secrete IL-10 (IL-10–aNSCs), a potent immunoregulatory cytokine, induced more profound functional and pathological recovery from ongoing EAE than that with control aNSCs. IL-10–aNSCs exhibited enhanced antiinflammatory effects in the periphery and inflammatory foci in the CNS compared with control aNSCs, more effectively reducing myelin damage, a hallmark of MS. When compared with mice treated with control aNSCs, those treated with IL-10–aNSCs demonstrated differentiation of transplanted cells into greater numbers of oligodendrocytes and neurons but fewer astrocytes, thus enhancing exogenous remyelination and neuron/axonal growth. Finally, IL-10–aNSCs converted a hostile environment to one supportive of neurons/oligodendrocytes, thereby promoting endogenous remyelination. Thus, aNSCs engineered to express IL-10 show enhanced ability to induce immune suppression, remyelination, and neuronal repair and may represent a novel approach that can substantially improve the efficacy of neural stem cell–based therapy in EAE/MS.

Transcriptional upregulation of SOCS 1 and suppressors of cytokine signaling 3 mRNA in the absence of suppressors of cytokine signaling 2 mRNA after infection with West Nile virus or tick-borne encephalitis virus.

Suppressors of cytokine signaling (SOCS) proteins are a family of proteins that are able to act in a classic negative feedback loop to regulate cytokine signal transduction. The regulation of the immune response by SOCS proteins may contribute to persistent infection or even a fatal outcome. In this study, we have investigated the induction of SOCS 1-3 after peripheral infection with West Nile virus (WNV) or tick-borne encephalitis virus (TBEV) in the murine model. We have shown that the cytokine response after infection of mice with WNV or TBEV induces an upregulation in the brain of mRNA transcripts for SOCS 1 and SOCS 3, but not SOCS 2. We hypothesize that SOCS proteins may play a role in limiting cytokine responses in the brain as a neuroprotective mechanism, which may actually enhance the ability of neuroinvasive viruses such as WNV and TBEV to spread and cause disease.

Overcoming the Scalability Challenges of Epidemic Simulations on Blue Waters

Modeling dynamical systems represents an important application class covering a wide range of disciplines including but not limited to biology, chemistry, finance, national security, and health care. Such applications typically involve large-scale, irregular graph processing, which makes them difficult to scale due to the evolutionary nature of their workload, irregular communication and load imbalance. EpiSimdemics is such an application simulating epidemic diffusion in extremely large and realistic social contact networks. It implements a graph-based system that captures dynamics among co-evolving entities. This paper presents an implementation of EpiSimdemics in Charm++ that enables future research by social, biological and computational scientists at unprecedented data and system scales. We present new methods for application-specific processing of graph data and demonstrate the effectiveness of these methods on a Cray XE6, specifically NCSA's Blue Waters system.

Transmission Potential of Rift Valley Fever virus over the course of the 2010 epidemic in South Africa

A Rift Valley fever (RVF) epidemic affecting animals on domestic livestock farms was reported in South Africa during January-August 2010. The first cases occurred after heavy rainfall, and the virus subsequently spread countrywide. To determine the possible effect of environmental conditions and vaccination on RVF virus transmissibility, we estimated the effective reproduction number (R) for the virus over the course of the epidemic by extending the Wallinga and Teunis algorithm with spatial information. Re reached its highest value in mid-February and fell below unity around mid-March, when vaccination coverage was 7.5%-45.7% and vector-suitable environmental conditions were maintained. The epidemic fade-out likely resulted first from the immunization of animals following natural infection or vaccination. The decline in vector-suitable environmental conditions from April onwards and further vaccination helped maintain R below unity. Increased availability of vaccine use data would enable evaluation of the effect of RVF vaccination campaigns.

The worldwide epidemic of diabetic retinopathy

Diabetic retinopathy (DR), a major microvascular complication of diabetes, has a significant impact on the world′s health systems. Globally, the number of people with DR will grow from 126.6 million in 2010 to 191.0 million by 2030, and we estimate that the number with vision-threatening diabetic retinopathy (VTDR) will increase from 37.3 million to 56.3 million, if prompt action is not taken. Despite growing evidence documenting the effectiveness of routine DR screening and early treatment, DR frequently leads to poor visual functioning and represents the leading cause of blindness in working-age populations. DR has been neglected in health-care research and planning in many low-income countries, where access to trained eye-care professionals and tertiary eye-care services may be inadequate. Demand for, as well as, supply of services may be a problem. Rates of compliance with diabetes medications and annual eye examinations may be low, the reasons for which are multifactorial. Innovative and comprehensive approaches are needed to reduce the risk of vision loss by prompt diagnosis and early treatment of VTDR.