Products of Compartmental Models in Epidemiology.

We show that many structured epidemic models may be described using a straightforward product structure in this paper. Such products, derived from products of directed graphs, may represent useful refinements including geographic and demographic structure, age structure, gender, risk groups, or immunity status. Extension to multistrain dynamics, that is, pathogen heterogeneity, is also shown to be feasible in this framework. Systematic use of such products may aid in model development and exploration, can yield insight, and could form the basis of a systematic approach to numerical structural sensitivity analysis

Prevention and control of Zika fever as a mosquito-borne and sexually transmitted disease

The ongoing Zika virus (ZIKV) epidemic poses a major global public health emergency. It is known that ZIKV is spread by \textit{Aedes} mosquitoes, recent studies show that ZIKV can also be transmitted via sexual contact and cases of sexually transmitted ZIKV have been confirmed in the U.S., France, and Italy. How sexual transmission affects the spread and control of ZIKV infection is not well-understood. We presented a mathematical model to investigate the impact of mosquito-borne and sexual transmission on spread and control of ZIKV and used the model to fit the ZIKV data in Brazil, Colombia, and El Salvador. Based on the estimated parameter values, we calculated the median and confidence interval of the basic reproduction number R0=2.055 (95% CI: 0.523-6.300), in which the distribution of the percentage of contribution by sexual transmission is 3.044 (95% CI: 0.123-45.73). Our study indicates that R0 is most sensitive to the biting rate and mortality rate of mosquitoes while sexual transmission increases the risk of infection and epidemic size and prolongs the outbreak. In order to prevent and control the transmission of ZIKV, it must be treated as not only a mosquito-borne disease but also a sexually transmitted disease

The effect of treatment on pathogen virulence.

The optimal virulence of a pathogen is determined by a trade-off between maximizing the rate of transmission and maximizing the duration of infectivity. Treatment measures such as curative therapy and case isolation exert selective pressure by reducing the duration of infectivity, reducing the value of duration-increasing strategies to the pathogen and favoring pathogen strategies that maximize the rate of transmission. We extend the trade-off models of previous authors, and represents the reproduction number of the pathogen as a function of the transmissibility, host contact rate, disease-induced mortality, recovery rate, and treatment rate, each of which may be influenced by the virulence. We find that when virulence is subject to a transmissibility-mortality trade-off, treatment can lead to an increase in optimal virulence, but that in other scenarios (such as the activity-recovery trade-off) treatment decreases the optimal virulence. Paradoxically, when levels of treatment rise with pathogen virulence, increasing control efforts may raise predicted levels of optimal virulence. Thus we show that conflict can arise between the epidemiological benefits of treatment and the evolutionary risks of heightened virulence

Agreement of Anterior Segment Parameters Obtained From Swept-Source Fourier-Domain and Time-Domain Anterior Segment Optical Coherence Tomography.

PurposeTo assess the interdevice agreement between swept-source Fourier-domain and time-domain anterior segment optical coherence tomography (AS-OCT).MethodsFifty-three eyes from 41 subjects underwent CASIA2 and Visante OCT imaging. One hundred eighty-degree axis images were measured with the built-in two-dimensional analysis software for the swept-source Fourier-domain AS-OCT (CASIA2) and a customized program for the time-domain AS-OCT (Visante OCT). In both devices, we examined the angle opening distance (AOD), trabecular iris space area (TISA), angle recess area (ARA), anterior chamber depth (ACD), anterior chamber width (ACW), and lens vault (LV). Bland-Altman plots and intraclass correlation (ICC) were performed. Orthogonal linear regression assessed any proportional bias.ResultsICC showed strong correlation for LV (0.925) and ACD (0.992) and moderate agreement for ACW (0.801). ICC suggested good agreement for all angle parameters (0.771-0.878) except temporal AOD500 (0.743) and ARA750 (nasal 0.481; temporal 0.481). There was a proportional bias in nasal ARA750 (slope 2.44, 95% confidence interval [CI]: 1.95-3.18), temporal ARA750 (slope 2.57, 95% CI: 2.04-3.40), and nasal TISA500 (slope 1.30, 95% CI: 1.12-1.54). Bland-Altman plots demonstrated in all measured parameters a minimal mean difference between the two devices (-0.089 to 0.063); however, evidence of constant bias was found in nasal AOD250, nasal AOD500, nasal AOD750, nasal ARA750, temporal AOD500, temporal AOD750, temporal ARA750, and ACD. Among the parameters with constant biases, CASIA2 tends to give the larger numbers.ConclusionsBoth devices had generally good agreement. However, there were proportional and constant biases in most angle parameters. Thus, it is not recommended that values be used interchangeably

Hamiltonian analysis of subcritical stochastic epidemic dynamics

We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models, and may lead to techniques for analysis of these models beyond the quasistationary distribution. For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations but not identical. For a birth-death process without depletion of susceptibles, the approximation is exact. Dynamics on the phase plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics

Identifying a sufficient core group for trachoma transmission.

BackgroundIn many infectious diseases, a core group of individuals plays a disproportionate role in transmission. If these individuals were effectively prevented from transmitting infection, for example with a perfect vaccine, then the disease would disappear in the remainder of the community. No vaccine has yet proven effective against the ocular strains of chlamydia that cause trachoma. However, repeated treatment with oral azithromycin may be able to prevent individuals from effectively transmitting trachoma.Methodology/principal findingsHere we assess several methods for identifying a core group for trachoma, assuming varying degrees of knowledge about the transmission process. We determine the minimal core group from a completely specified model, fitted to results from a large Ethiopian trial. We compare this benchmark to a core group that could actually be identified from information available to trachoma programs. For example, determined from the rate of return of infection in a community after mass treatments, or from the equilibrium prevalence of infection.Conclusions/significanceSufficient groups are relatively easy for programs to identify, but will likely be larger than the theoretical minimum

Relationship Between Foveal Cone Structure and Visual Acuity Measured With Adaptive Optics Scanning Laser Ophthalmoscopy in Retinal Degeneration.

PurposeTo evaluate foveal function in patients with inherited retinal degenerations (IRD) by measuring visual acuity (VA) after correction of higher-order aberrations.MethodsAdaptive optics scanning laser ophthalmoscopy (AOSLO) was used to image cones in 4 healthy subjects and 15 patients with IRD. The 840-nm scanning laser delivered an "E" optotype to measure AOSLO-mediated VA (AOSLO-VA). Cone spacing was measured at the preferred retinal locus by two independent graders and the percentage of cones below the average density of 47 age-similar healthy subjects was computed. Cone spacing was correlated with best-corrected VA measured with the Early Treatment of Diabetic Retinopathy Study protocol (ETDRS-VA), AOSLO-VA, and foveal sensitivity.ResultsETDRS-VA significantly correlated with AOSLO-VA (ρ = 0.79, 95% confidence interval [CI] 0.5-0.9). Cone spacing correlated with AOSLO-VA (ρ = 0.54, 95% CI 0.02-0.7), and negatively correlated with ETDRS letters read (ρ = -0.64, 95% CI -0.8 to -0.2). AOSLO-VA remained ≥20/20 until cones decreased to 40.2% (CI 31.1-45.5) below normal. Similarly, ETDRS-VA remained ≥20/20 until cones were 42.0% (95% CI 36.5-46.1) below normal. Cone spacing z scores negatively correlated with foveal sensitivity (ρ = -0.79, 95% CI -0.9 to -0.4) and foveal sensitivity was ≥35 dB until cones were 43.1% (95% CI 39.3-46.6) below average.ConclusionsVA and foveal cone spacing were weakly correlated until cones were reduced by 40% to 43% below normal. The relationship suggests that VA is an insensitive measure of foveal cone survival; cone spacing may be a more sensitive measure of cone loss

Loss of Foveal Cone Structure Precedes Loss of Visual Acuity in Patients With Rod-Cone Degeneration.

PurposeTo assess the relationship between cone spacing and visual acuity in eyes with rod-cone degeneration (RCD) followed longitudinally.MethodsHigh-resolution images of the retina were obtained using adaptive optics scanning laser ophthalmoscopy from 13 eyes of nine RCD patients and 13 eyes of eight healthy subjects at two sessions separated by 10 or more months (mean 765 days, range 311-1935 days). Cone spacing Z-score measured as close as possible (average <0.25°) to the preferred retinal locus was compared with visual acuity (letters read on the Early Treatment of Diabetic Retinopathy Study [ETDRS] chart and logMAR) and foveal sensitivity.ResultsCone spacing was significantly correlated with ETDRS letters read (ρ = -0.47, 95%CI -0.67 to -0.24), logMAR (ρ = 0.46, 95%CI 0.24 to 0.66), and foveal sensitivity (ρ = -0.30, 95%CI -0.52 to -0.018). There was a small but significant increase in mean cone spacing Z-score during follow-up of +0.97 (95%CI 0.57 to 1.4) in RCD patients, but not in healthy eyes, and there was no significant change in any measure of visual acuity.ConclusionsCone spacing was correlated with visual acuity and foveal sensitivity. In RCD patients, cone spacing increased during follow-up, while visual acuity did not change significantly. Cone spacing Z-score may be a more sensitive measure of cone loss at the fovea than visual acuity in patients with RCD