Faculty Works, Department of MathematicsResearch articles, presentations, and other scholarshiphttp://hdl.handle.net/10919/242852019-05-24T15:07:41Z2019-05-24T15:07:41ZA note on best approximation and invertibility of operators on uniformly convex Banach spacesHolub, James R.http://hdl.handle.net/10919/895742019-05-21T07:07:06Z1991-01-01T00:00:00ZHolub, James R.
1991-01-01T00:00:00ZIt is shown that if X is a uniformly convex Banach space and S a bounded linear operator onX for which ?I-S?=1, then S is invertible if and only if ?I-12S? <1. From this it follows thatif S is invertible on X then either (i) dist(I,[S])<1, or (ii) 0 is the unique best approximation toI from [S], a natural (partial) converse to the well-known sufficient condition for invertibility thatdist(I,[S])<1.Editorial: Integrative Computational Systems Biology Approaches in Immunology and MedicineKaderali, LarsTheis, FabianGanusov, Vitaly V.Ciupe, Stanca M.Mehr, RamitRibeiro, Ruy M.Hernandez-Vargas, Esteban A.http://hdl.handle.net/10919/884332019-03-14T07:06:36Z2019-01-23T00:00:00ZKaderali, Lars; Theis, Fabian; Ganusov, Vitaly V.; Ciupe, Stanca M.; Mehr, Ramit; Ribeiro, Ruy M.; Hernandez-Vargas, Esteban A.
2019-01-23T00:00:00ZDisrupting Mosquito Reproduction and Parasite Development for Malaria ControlChilds, Lauren M.Cai, Francisco Y.Kakani, Evdoxia G.Mitchell, Sara N.Paton, DougGabrieli, PaoloBuckee, Caroline O.Catteruccia, Flaminiahttp://hdl.handle.net/10919/862162018-12-05T08:06:57Z2016-12-15T00:00:00ZChilds, Lauren M.; Cai, Francisco Y.; Kakani, Evdoxia G.; Mitchell, Sara N.; Paton, Doug; Gabrieli, Paolo; Buckee, Caroline O.; Catteruccia, Flaminia
2016-12-15T00:00:00ZThe control of mosquito populations with insecticide treated bed nets and indoor residual sprays remains the cornerstone of malaria reduction and elimination programs. In light of widespread insecticide resistance in mosquitoes, however, alternative strategies for reducing transmission by the mosquito vector are urgently needed, including the identification of safe compounds that affect vectorial capacity via mechanisms that differ from fast-acting insecticides. Here, we show that compounds targeting steroid hormone signaling disrupt multiple biological processes that are key to the ability of mosquitoes to transmit malaria. When an agonist of the steroid hormone 20-hydroxyecdysone (20E) is applied to Anopheles gambiae females, which are the dominant malaria mosquito vector in Sub Saharan Africa, it substantially shortens lifespan, prevents insemination and egg production, and significantly blocks Plasmodium falciparum development, three components that are crucial to malaria transmission. Modeling the impact of these effects on Anopheles population dynamics and Plasmodium transmission predicts that disrupting steroid hormone signaling using 20E agonists would affect malaria transmission to a similar extent as insecticides. Manipulating 20E pathways therefore provides a powerful new approach to tackle malaria transmission by the mosquito vector, particularly in areas affected by the spread of insecticide resistance.Antibody Responses during Hepatitis B Viral InfectionCiupe, Stanca M.Ribeiro, Ruy M.Perelson, Alan S.http://hdl.handle.net/10919/859102018-11-20T08:02:00Z2014-07-01T00:00:00ZCiupe, Stanca M.; Ribeiro, Ruy M.; Perelson, Alan S.
2014-07-01T00:00:00ZHepatitis B is a DNA virus that infects liver cells and can cause both acute and chronic disease. It is believed that both viral and host factors are responsible for determining whether the infection is cleared or becomes chronic. Here we investigate the mechanism of protection by developing a mathematical model of the antibody response following hepatitis B virus (HBV) infection. We fitted the model to data from seven infected adults identified during acute infection and determined the ability of the virus to escape neutralization through overproduction of non-infectious subviral particles, which have HBs proteins on their surface, but do not contain nucleocapsid protein and viral nucleic acids. We showed that viral clearance can be achieved for high anti-HBV antibody levels, as in vaccinated individuals, when: (1) the rate of synthesis of hepatitis B subviral particles is slow; (2) the rate of synthesis of hepatitis B subviral particles is high but either anti-HBV antibody production is fast, the antibody affinity is high, or the levels of pre-existent HBV-specific antibody at the time of infection are high, as could be attained by vaccination. We further showed that viral clearance can be achieved for low equilibrium anti-HBV antibody levels, as in unvaccinated individuals, when a strong cellular immune response controls early infection.Mathematical Models of E-Antigen Mediated Immune Tolerance and Activation following Prenatal HBV InfectionCiupe, Stanca M.Hews, Sarahhttp://hdl.handle.net/10919/855352018-10-27T07:10:26Z2012-07-02T00:00:00ZCiupe, Stanca M.; Hews, Sarah
2012-07-02T00:00:00ZWe develop mathematical models for the role of hepatitis B e-antigen in creating immunological tolerance during hepatitis B virus infection and propose mechanisms for hepatitis B e-antigen clearance, subsequent emergence of a potent cellular immune response, and the effect of these on liver damage. We investigate the dynamics of virus-immune cells interactions, and derive parameter regimes that allow for viral persistence. We modify the model to account for mechanisms responsible for hepatitis B e-antigen loss, such as seroconversion and virus mutations that lead to emergence of cellular immune response to the mutant virus. Our models demonstrate that either seroconversion or mutations can induce immune activation and that instantaneous loss of e-antigen by either mechanism is associated with least liver damage and is therefore more beneficial for disease outcomes.An introduction to compartmental modeling for the budding infectious disease modelerBlackwood, Julie C.Childs, Lauren M.http://hdl.handle.net/10919/849932018-09-12T07:05:16Z2018-08-16T00:00:00ZBlackwood, Julie C.; Childs, Lauren M.
2018-08-16T00:00:00ZMathematical models are ubiquitous in the study of the transmission dynamics of infectious diseases, In particular, the classic ‘susceptible-infectious-recovered’ (SIR) paradigm provides a modeling framework that can be adapted to describe the core transmission dynamics of a range of human and wildlife diseases. These models provide an important tool for uncovering the mechanisms generating observed disease dynamics, evaluating potential control strategies, and predicting future outbreaks. With ongoing advances in computational tools as well as access to disease incidence data, the use of such models continues to increase. Here, we provide a basic introduction to disease modeling that is primarily intended for individuals who are new to developing SIR-type models. In particular, we highlight several common issues encountered when structuring and analyzing these models.Modeling the Mechanisms by Which HIV Associated Immunosuppression Influences HPV Persistence at the Oral MucosaVerma, MeghnaErwin, SamanthaAbedi, VidaHontecillas, RaquelHoops, StefanLeber, AndrewBassaganya-Riera, JosepCiupe, Stanca M.http://hdl.handle.net/10919/844612018-08-02T07:01:46Z2017-01-06T00:00:00ZVerma, Meghna; Erwin, Samantha; Abedi, Vida; Hontecillas, Raquel; Hoops, Stefan; Leber, Andrew; Bassaganya-Riera, Josep; Ciupe, Stanca M.
2017-01-06T00:00:00ZHuman immunodeficiency virus (HIV)-infected patients are at an increased risk of co-infection with human papilloma virus (HPV), and subsequent malignancies such as oral cancer. To determine the role of HIV-associated immune suppression on HPV persistence and pathogenesis, and to investigate the mechanisms underlying the modulation of HPV infection and oral cancer by HIV, we developed a mathematical model of HIV/HPV co-infection. Our model captures known immunological and molecular features such as impaired HPV-specific effector T helper 1 (Th1) cell responses, and enhanced HPV infection due to HIV. We used the model to determine HPV prognosis in the presence of HIV infection, and identified conditions under which HIV infection alters HPV persistence in the oral mucosa system. The model predicts that conditions leading to HPV persistence during HIV/HPV co-infection are the permissive immune environment created by HIV and molecular interactions between the two viruses. The model also determines when HPV infection continues to persist in the short run in a co-infected patient undergoing antiretroviral therapy. Lastly, the model predicts that, under efficacious antiretroviral treatment, HPV infections will decrease in the long run due to the restoration of CD4+ T cell numbers and protective immune responses.A Bistable Switch in Virus Dynamics Can Explain the Differences in Disease Outcome Following SIV Infections in Rhesus MacaquesCiupe, Stanca M.Miller, Christopher J.Forde, Jonathan E.http://hdl.handle.net/10919/843122019-04-01T19:05:52Z2018-06-06T00:00:00ZCiupe, Stanca M.; Miller, Christopher J.; Forde, Jonathan E.
2018-06-06T00:00:00ZExperimental studies have shown that the size and infectious-stage of viral inoculum influence disease outcomes in rhesus macaques infected with simian immunodeficiency virus. The possible contribution to disease outcome of antibody developed after transmission and/or present in the inoculum in free or bound form is not understood. In this study, we develop a mathematical model of virus-antibody immune complex formation and use it to predict their role in transmission and protection. The model exhibits a bistable switch between clearance and persistence states. We fitted it to temporal virus data and estimated the parameter values for free virus infectivity rate and antibody carrying capacity for which the model transitions between virus clearance and persistence when the initial conditions (in particular the ratio of immune complexes to free virus) vary. We used these results to quantify the minimum virus amount in the inoculum needed to establish persistent infections in the presence and absence of protective antibodies.Existence Theorems on Solvability of Constrained Inclusion Problems and ApplicationsAsfaw, Teffera M.Asfaw, Teffera M.http://hdl.handle.net/10919/839662019-04-01T19:05:51Z2018-07-12T00:00:00ZAsfaw, Teffera M.; Asfaw, Teffera M.
2018-07-12T00:00:00ZLet 𝑋 be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space 𝑋∗. Let𝑇 : 𝑋 ⊇ 𝐷(𝑇) → 2𝑋∗ be a maximal monotone operator and 𝐶 : 𝑋 ⊇ 𝐷(𝐶) → 𝑋∗ be bounded and continuous with 𝐷(𝑇) ⊆ 𝐷(𝐶). The paper provides new existence theorems concerning solvability of inclusion problems involving operators of the type 𝑇 + 𝐶 provided that 𝐶 is compact or 𝑇 is of compact resolvents underweak boundary condition. The Nagumo degree mapping and homotopy invariance results are employed.The paper presents existence results under the weakest coercivity condition on 𝑇+𝐶. The operator 𝐶 is neither required to be defined everywhere nor required to be pseudomonotone type.The results are applied to prove existence of solution for nonlinear variational inequality problems.Randomized Approach to Nonlinear Inversion Combining Simultaneous Random and Optimized Sources and DetectorsSariaydin Aslan, Sde Sturler, EKilmer, MEhttp://hdl.handle.net/10919/819352018-11-12T18:06:29ZSariaydin Aslan, S; de Sturler, E; Kilmer, ME
In partial differential equations-based inverse problems with many measurements, we have to solve many large linear system for each evaluation of the objective function. In the nonlinear case, each evaluation of the Jacobian requires solving an additional set of systems. This leads to a tremendous computational cost, which is by far the dominant cost for these problems. Several authors have proposed to drastically reduce the number of system solves by exploiting stochastic techniques [Haber et al., SIAM Optim., 22:739-757] and posing the problem as a stochastic optimization problem [Shapiro et al., Lectures on Stochastic Programming, SIAM, 2009]. In this approach, the objective function is estimated using only a few random linear combinations of the sources, referred to as simultaneous random sources. For the Jacobian, we show that a similar approach can be used to reduce the number of additional adjoint solves for the detectors. While others have reported good solution quality at a greatly reduced computational cost using these randomized approaches, for our problem of interest, diffuse optical tomography, the approach often does not lead to sufficiently accurate solutions. Therefore, we replace a few random simultaneous sources and detectors by simultaneous sources and detectors that are optimized to maximize the Frobenius norm of the sampled Jacobian after solving to a modest tolerance. This choice is inspired by (1) the regularized model problem solves in the TREGS nonlinear least squares solver [de Sturler and Kilmer, SIAM Sci. Comput., 33:3057-3086] used for minimization in our method and (2) the fact that these optimized directions correspond to the most informative data components. Our approach leads to solutions of the same quality as obtained using all sources and detectors but at a greatly reduced computational cost.