AIDS-related Kaposis sarcoma pathogenesis

Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, KenyaKaposis sarcoma (KS), the most common tumor associated with human immunodeficiency virus- I (HIV-I) and human herpesvirus-8 (HHV-8) (also referred to as Kaposis associated herpesvirus (KSHV) infection, develops in approximately 20 percent of patients infected with HIV-I. The lesions of this multicentric vascular neoplasm are purplish patches, plaques, or nodules. Although highly active antiretroviral therapy (HAART) can prolong the time to treatment failure in patients with KS, nearly every patient with AIDS-related (or epidemic) KS eventually develops disseminated disease. Progression usually occurs in an orderly fashion from new localized or widespread mucocutaneous lesions to more numerous lesions and generalized skin disease with involvement of lyrnph nodes, gastrointestinal tract (GIT), lungs and other organs. Studies have shown that KS cells themselves are not infected with HIV-I; therefore, it is widely accepted than HIV-I does not play a direct oncogenic role in AIDS-KS. However, the precise role of HIV-I in AIDS-KS is still not completely understood, and there is considerable debate over whether HIVI plays a passive role (through the induction of immunosuppression) or a more direct role in the pathogenesis of this disease. We formulate a mathematical model to study the dynamics of HIVI related KS pathogenesis. In this model, it is assumed that HIV-I infects only the CD4 + T cells and HHV-8 infects the B- cells, which largely remain latently infected and only become reactivated after exposure to inflammatory cytokines and other growth factors secreted from HIV-I infected cells. The Infection free and Infection persistent equilibria have been found and their stability established. It is found that the disease can exist even if both sub-group reproduction numbers, relating to HIV-I and HHV-8, are less than unity.Botswana International University of Science and Technology Palapye, Botswana

Effect of innate and adaptive immune mechanisms on treatment regimens in an AIDS-related Kaposi's Sarcoma model

Kaposi Sarcoma (KS) is the most common AIDS-defining cancer, even as HIV-positive people live longer. Like other herpesviruses, human herpesvirus-8 (HHV-8) establishes a lifelong infection of the host that in association with HIV infection may develop at any time during the illness. With the increasing global incidence of KS, there is an urgent need of designing optimal therapeutic strategies for HHV-8-related infections. Here we formulate two models with innate and adaptive immune mechanisms, relevant for non-AIDS KS (NAKS) and AIDS-KS, where the initial condition of the second model is given by the equilibrium state of the first one. For the model with innate mechanism (MIM), we define an infectivity resistance threshold that will determine whether the primary HHV-8 infection of B-cells will progress to secondary infection of progenitor cells, a concept relevant for viral carriers in the asymptomatic phase. The optimal control strategy has been employed to obtain treatment efficacy in case of a combined antiretroviral therapy (cART). For the MIM we have shown that KS therapy alone is capable of reducing the HHV-8 load. In the model with adaptive mechanism (MAM), we show that if cART is administered at optimal levels, that is, 0.48 for protease inhibitors, 0.79 for reverse transcriptase inhibitors and 0.25 for KS therapy, both HIV-1 and HHV-8 can be reduced. The predictions of these mathematical models have the potential to offer more effective therapeutic interventions in the treatment of NAKS and AIDS-KS

Optimal multi-dimensional stochastic harvesting with density-dependent prices

We prove a verification theorem for a class of singular control problems which model optimal harvesting with density-dependent prices or optimal dividend policy with capital-dependent utilities. The result is applied to solve explicitly some examples of such optimal harvesting/optimal dividend problems. In particular, we show that if the unit price decreases with population density, then the optimal harvesting policy may not exist in the ordinary sense, but can be expressed as a “chattering policy”, i.e. the limit as Δ x and Δ t go to 0 of taking out a sequence of small quantities of size Δ x within small time periods of size Δ t.</p

A mathematical model of contact tracing during the 2014-2016 west African ebola outbreak

The 2014-2016 West African outbreak of Ebola Virus Disease (EVD) was the largest and most deadly to date. Contact tracing, following up those who may have been infected through contact with an infected individual to prevent secondary spread, plays a vital role in controlling such outbreaks. Our aim in this work was to mechanistically represent the contact tracing process to illustrate potential areas of improvement in managing contact tracing efforts. We also explored the role contact tracing played in eventually ending the outbreak. We present a system of ordinary differential equations to model contact tracing in Sierra Leonne during the outbreak. Using data on cumulative cases and deaths we estimate most of the parameters in our model. We include the novel features of counting the total number of people being traced and tying this directly to the number of tracers doing this work. Our work highlights the importance of incorporatingchanging behavior into one’s model as needed when indicated by the data and reported trends. Our results show that a larger contact tracing program would have reduced the death toll of the outbreak. Counting the total number of people being traced and including changes in behavior in our model led to better understanding of disease management

The Atacama Cosmology Telescope: Two-Season ACTPol Spectra and Parameters

We present the temperature and polarization angular power spectra measured by the Atacama Cosmology Telescope Polarimeter (ACTPol). We analyze night-time data collected during 2013-14 using two detector arrays at 149 GHz, from 548 deg$^2$ of sky on the celestial equator. We use these spectra, and the spectra measured with the MBAC camera on ACT from 2008-10, in combination with Planck and WMAP data to estimate cosmological parameters from the temperature, polarization, and temperature-polarization cross-correlations. We find the new ACTPol data to be consistent with the LCDM model. The ACTPol temperature-polarization cross-spectrum now provides stronger constraints on multiple parameters than the ACTPol temperature spectrum, including the baryon density, the acoustic peak angular scale, and the derived Hubble constant. Adding the new data to planck temperature data tightens the limits on damping tail parameters, for example reducing the joint uncertainty on the number of neutrino species and the primordial helium fraction by 20%.Comment: 23 pages, 25 figure

The Simons Observatory: Beam characterization for the Small Aperture Telescopes

We use time-domain simulations of Jupiter observations to test and develop a beam reconstruction pipeline for the Simons Observatory Small Aperture Telescopes. The method relies on a map maker that estimates and subtracts correlated atmospheric noise and a beam fitting code designed to compensate for the bias caused by the map maker. We test our reconstruction performance for four different frequency bands against various algorithmic parameters, atmospheric conditions and input beams. We additionally show the reconstruction quality as function of the number of available observations and investigate how different calibration strategies affect the beam uncertainty. For all of the cases considered, we find good agreement between the fitted results and the input beam model within a ~1.5% error for a multipole range l = 30 - 700.Comment: 22 pages, 21 figures, to be submitted to Ap

In situ Performance of the Low Frequency Arrayfor Advanced ACTPol

The Advanced Atacama Cosmology Telescope Polarimeter (AdvACT) \cite{thornton} is an upgrade for the Atacama Cosmology Telescope using Transition Edge Sensor (TES) detector arrays to measure cosmic microwave background (CMB) temperature and polarization anisotropies in multiple frequencies. The low frequency (LF) array was deployed early 2020. It consists of 292 TES bolometers observing in two bands centered at 27 GHz and 39 GHz. At these frequencies, it is sensitive to synchrotron radiation from our galaxy as well as to the CMB, and complements the AdvACT arrays operating at 90, 150 and 230 GHz. We present the initial LF array on-site characterization, including the time constant, optical efficiency and array sensitivity

Evidence of lensing of the cosmic microwave background by dark matter halos

We present evidence of the gravitational lensing of the cosmic microwave background by 1013 solar mass dark matter halos. Lensing convergence maps from the Atacama Cosmology Telescope Polarimeter (ACTPol) are stacked at the positions of around 12 000 optically selected CMASS galaxies from the SDSS-III/BOSS survey. The mean lensing signal is consistent with simulated dark matter halo profiles and is favored over a null signal at 3.2σ significance. This result demonstrates the potential of microwave background lensing to probe the dark matter distribution in galaxy group and galaxy cluster halos

The Simons Observatory microwave SQUID multiplexing detector module design

Advances in cosmic microwave background (CMB) science depend on increasing the number of sensitive detectors observing the sky. New instruments deploy large arrays of superconducting transition-edge sensor (TES) bolometers tiled densely into ever larger focal planes. High multiplexing factors reduce the thermal loading on the cryogenic receivers and simplify their design. We present the design of focal-plane modules with an order of magnitude higher multiplexing factor than has previously been achieved with TES bolometers. We focus on the novel cold readout component, which employs microwave SQUID multiplexing ($\mu$mux). Simons Observatory will use 49 modules containing 60,000 bolometers to make exquisitely sensitive measurements of the CMB. We validate the focal-plane module design, presenting measurements of the readout component with and without a prototype detector array of 1728 polarization-sensitive bolometers coupled to feedhorns. The readout component achieves a $95\%$ yield and a 910 multiplexing factor. The median white noise of each readout channel is 65 $\mathrm{pA/\sqrt{Hz}}$. This impacts the projected SO mapping speed by $< 8\%$, which is less than is assumed in the sensitivity projections. The results validate the full functionality of the module. We discuss the measured performance in the context of SO science requirements, which are exceeded.Comment: Accepted to The Astrophysical Journa

The atacama cosmology telescope: lensing of CMB temperature and polarization derived from cosmic infrared background cross-correlation

We present a measurement of the gravitational lensing of the Cosmic Microwave Background (CMB) temperature and polarization fields obtained by cross-correlating the reconstructed convergence signal from the first season of Atacama Cosmology Telescope Polarimeter data at 146 GHz with Cosmic Infrared Background (CIB) fluctuations measured using the Planck satellite. Using an effective overlap area of 92.7 square degrees, we detect gravitational lensing of the CMB polarization by large-scale structure at a statistical significance of $4.5\sigma$. Combining both CMB temperature and polarization data gives a lensing detection at $9.1\sigma$ significance. A B-mode polarization lensing signal is present with a significance of $3.2\sigma$. We also present the first measurement of CMB lensing–CIB correlation at small scales corresponding to $l\gt 2000$. Null tests and systematic checks show that our results are not significantly biased by astrophysical or instrumental systematic effects, including Galactic dust. Fitting our measurements to the best-fit lensing-CIB cross-power spectrum measured in Planck data, scaled by an amplitude A, gives $A={1.02}_{-0.08}^{+0.12}$(stat.) ± 0.06(syst.), consistent with the Planck results