Proportionate mixing models for age-dependent infection transmission

We present explicit formulas for the transmission potential of an immunizing infection where the contact rates and the vaccination rates depend on the chronological age of an individual, and the infectivity and the recovery rate depend on the duration of an infection.     

Using approximate Bayesian computation to estimate tuberculosis transmission parameters from genotype data

Tuberculosis can be studied at the population level by genotyping strains of Mycobacterium tuberculosis isolated from patients. We use an approximate Bayesian computational method in combination with a stochastic model of tuberculosis transmission and mutation of a molecular marker to estimate the net transmission rate, the doubling time, and the reproductive value of the pathogen. This method is applied to a published data set from San Francisco of tuberculosis genotypes based on the marker IS6110. The mutation rate of this marker has previously been studied, and we use those estimates to form a prior distribution of mutation rates in the inference procedure. The posterior point estimates of the key parameters of interest for these data are as follows: net transmission rate, 0.69/year [95% credibility interval (C.I.) 0.38, 1.08]; doubling time, 1.08 years (95% C.I. 0.64, 1.82); and reproductive value 3.4 (95% C.I. 1.4, 79.7). These figures suggest a rapidly spreading epidemic, consistent with observations of the resurgence of tuberculosis in the United States in the 1980s and 1990s.     

Revisiting the basic reproductive number for malaria and its implications for malaria control

The prospects for the success of malaria control depend, in part, on the basic reproductive number for malaria, R0. Here, we estimate R0 in a novel way for 121 African populations, and thereby increase the number of R0 estimates for malaria by an order of magnitude. The estimates range from around one to more than 3,000. We also consider malaria transmission and control in finite human populations, of size H. We show that classic formulas approximate the expected number of mosquitoes that could trace infection back to one mosquito after one parasite generation, Z0(H), but they overestimate the expected number of infected humans per infected human, R0(H). Heterogeneous biting increases R0 and, as we show, Z0(H), but we also show that it sometimes reduces R0(H); those who are bitten most both infect many vectors and absorb infectious bites. The large range of R0 estimates strongly supports the long-held notion that malaria control presents variable challenges across its transmission spectrum. In populations where R0 is highest, malaria control will require multiple, integrated methods that target those who are bitten most. Therefore, strategic planning for malaria control should consider R0, the spatial scale of transmission, human population density, and heterogeneous biting.     

Monitoring the trend of the transmission rate of vertically acquired HIV infection: a simple method applied to Italian data.

The objective of this study was to develop and validate a method for estimating and monitoring over time the transmission rate of vertically acquired HIV infection at the population level. We estimated the annual number of children born to HIV-infected women in Italy in 1991-1994 by multiplying the seroprevalence rates, provided by Anonymous Unlinked HIV Serosurveys among Italian Newborns, by the annual number of births, provided by the Italian National Institute of Statistics. The number of HIV-infected children was estimated by applying a simplified back-calculation method to the incident cases of vertically acquired AIDS reported to the AIDS surveillance registry, using seven different estimates of the distribution of the incubation period identified through a literature search. The annual vertical transmission rates were estimated by dividing the estimated number of children with vertically acquired HIV infection by the estimated number of births to an HIV-infected mother. Depending on the chosen distribution of the incubation period, the estimated transmission rate for the four-year period ranges from 0.10 to 0.30. Five of the seven incubation distributions provided a rate falling within the very narrow interval 0.18-0.20. The method provided estimates of vertical transmission rates consistent with those of longitudinal studies performed in European countries. The method presented here could be useful for monitoring the impact of interventions aimed at reducing HIV vertical transmission rate.     

Estimating the magnitude and direction of altered arbovirus transmission due to viral phenotype

Vectorial capacity is a measure of the transmission potential of a vector borne pathogen within a susceptible population. Vector competence, a component of the vectorial capacity equation, is the ability of an arthropod to transmit an infectious agent following exposure to that agent. Comparisons of arbovirus strain-specific vector competence estimates have been used to support observed or hypothesized differences in transmission capability. Typically, such comparisons are made at a single time point during the extrinsic incubation period, the time in days it takes for the virus to replicate and disseminate to the salivary glands. However, vectorial capacity includes crucial parameters needed to effectively evaluate transmission capability, though often this is based on the discrete vector competence values. Utilization of the rate of change of vector competence over a range of days gives a more accurate measurement of the transmission potential. Accordingly, we investigated the rate of change in vector competence of dengue virus in Aedes aegypti mosquitoes and the resulting vectorial capacity curves. The areas under the curves represent the effective vector competence and the cumulative transmission potentials of arboviruses within a population of mosquitoes. We used the calculated area under the curve for each virus strain and the corresponding variance estimates to test for differences in cumulative transmission potentials between strains of dengue virus based on our dynamic model. To further characterize differences between dengue strains, we devised a displacement index interpreted as the capability of a newly introduced strain to displace the established, dominant circulating strain. The displacement index can be used to better understand the transmission dynamics in systems where multiple strains/serotypes circulate or even multiple arbovirus species. The use of a rate of a rate of change based model of vectorial capacity and the informative calculations of the displacement index will lead to better measurements of the differences in transmission potential of arboviruses.     

Characterization of hydrotropism: the timing of perception and signal movement from the root cap in the agravitropic pea mutant ageotropum

In this study, ageotropum pea mutant was used to determine the threshold time for perception of an osmotic stimulation in the root cap and the time requirement for transduction and transmission of the hydrotropic signal from the root cap to the elongation region. The threshold time for the perception of an osmotic stimulation was compared to current estimates of threshold times for graviperception in roots. The time required for transduction and transmission in the hydrotropic response of ageotropum was compared to the time requirement in the gravity response of Alaska pea roots. We determined that threshold time for perception of an osmotic stimulation in the root cap is very rapid, occurring in less than 2 min following the application of sorbitol to the root cap. Furthermore, a single 5 min exposure of sorbitol to the root cap fully induced a hydrotropic response. We also found that transduction and transmission of an osmotic stimulus requires 90-120 min for movement from the root cap to more basal tissues involved in differential growth leading to root curvature. The very rapid threshold time for perception of root hydrotropism is similar to those times reported for root gravitropism. However, the time required for the transduction and transmission of an osmotic stimulation from the root cap is significantly longer than the time required in gravitropism. These results suggest that there must exist some differences between root hydrotropism and gravitropism in either the rate or mechanisms of transduction and transmission of the tropistic signal from the root cap.     

High infection rates at low transmission potentials in West African onchocerciasis

Onchocerciasis has been successfully controlled for many years in endemic countries but more than 120 million people are still at risk. Factors which stabilise the persistence of the parasite in the population must be studied to minimise the future risk of re-infection. Among these factors, the relationship between the annual transmission potential and the parasite establishment rate is a main determinant which has to date not been quantified. Using entomological information and palpation data collected by the Onchocerciasis Control Programme in West Africa prior to the initiation of control activities, we derive annual transmission potential-dependent estimates of the parasite establishment rate from statistical analyses and computer simulations. Even at very low transmission intensities, the filarial parasite Onchocerca volvulus can efficiently establish in the human population, originating from an infection process which is strongly limited with respect to the annual transmission potential. Implementing the estimates into a simplified transmission model predicts that the critical annual biting rate, below which transmission is not possible, is much lower than previously assumed. We conclude that under the current strategy of mass distribution of microfilaricides without additional measures of vector control, the risk of re-infection is higher than previously assumed.     

Electricity Intensity of Internet Data Transmission: Untangling the Estimates

In order to understand the electricity use of Internet services, it is important to have accurate estimates for the average electricity intensity of transmitting data through the Internet (measured as kilowatt‐hours per gigabyte [kWh/GB]). This study identifies representative estimates for the average electricity intensity of fixed‐line Internet transmission networks over time and suggests criteria for making accurate estimates in the future. Differences in system boundary, assumptions used, and year to which the data apply significantly affect such estimates. Surprisingly, methodology used is not a major source of error, as has been suggested in the past. This article derives criteria to identify accurate estimates over time and provides a new estimate of 0.06 kWh/GB for 2015. By retroactively applying our criteria to existing studies, we were able to determine that the electricity intensity of data transmission (core and fixed‐line access networks) has decreased by half approximately every 2 years since 2000 (for developed countries), a rate of change comparable to that found in the efficiency of computing more generally.     

Warmer temperatures reduce the vectorial capacity of malaria mosquitoes

The development rate of parasites and pathogens within vectors typically increases with temperature. Accordingly, transmission intensity is generally assumed to be higher under warmer conditions. However, development is only one component of parasite/pathogen life history and there has been little research exploring the temperature sensitivity of other traits that contribute to transmission intensity. Here, using a rodent malaria, we show that vector competence (the maximum proportion of infectious mosquitoes, which implicitly includes parasite survival across the incubation period) tails off at higher temperatures, even though parasite development rate increases. We also show that the standard measure of the parasite incubation period (i.e. time until the first mosquitoes within a cohort become infectious following an infected blood-meal) is incomplete because parasite development follows a cumulative distribution, which itself varies with temperature. Including these effects in a simple model dramatically alters estimates of transmission intensity and reduces the optimum temperature for transmission. These results highlight the need to understand the interactive effects of environmental temperature on multiple host-disease life-history traits and challenge the assumptions of many current disease models that ignore this complexity.     

Simplified Resting Metabolic Rate—Predicting Formulas for Normal‐Sized and Obese Individuals

Objective: Resting metabolic rate (RMR) is known to be proportional to body weight and to follow allometric scaling principles. We hypothesized that RMR can be predicted from an allometric formula with weight alone as an independent variable. Research Methods and Procedures: An allometric, power‐law scaling model was fit to RMR measurements obtained from a cohort of patients being treated for weight loss. This, as well as many of the commonly used RMR‐predicting formulas, was tested for RMR prediction ability against a large publicly available RMR database. Bland‐Altman analysis was used to determine the efficacy of the various RMR‐predicting formulas in obese and non‐obese subjects. Results: Power law modeling of the RMR—body weight relationship yielded the following RMR‐predicting equations: RMR_Women = 248 × Weight^0.4356 ? (5.09 × Age) and RMR_Men = 293 × Weight^0.4330 ? (5.92 × Age). Partial correlation analysis revealed that age significantly contributed to RMR variance and was necessary to include in RMR prediction formulas. The James, allometric, and Harris‐Benedict formulas all yielded reasonable RMR predictions for normal sized and obese subjects. Discussion: A simple power formula relating RMR to body weight can be a reasonable RMR estimator for normal‐sized and obese individuals but still requires an age term and separate formulas for men and women for the best possible RMR estimates. The apparent performance of RMR‐predicting formulas is highly dependent on the methodology employed to compare the various formulas.     

Infection-age structured epidemic models with behavior change or treatment

We formulate infection-age structured susceptible-infective-removed (SIR) models with behavior change or treatment of infections. Individuals change their behavior or have treatment after they are infected. Using infection age as a continuous variable, and dividing infectives into discrete groups with different infection stages, respectively, we formulate a partial differential equation model and an ordinary differential equation model with behavior change or treatment. We derive explicit formulas for the reproductive number by linear stability analysis of the infection-free equilibrium, and explicit formulas for the unique endemic equilibrium, when it exists, for both models. These formulas provide mathematical theoretical frameworks for analysis of impact of behavior change or treatment of infection to the transmission dynamics of infectious diseases. We study several special cases and provide sensitivity analysis for the reproductive numbers with respect to model parameters based on those formulas.     

Measuring and estimating GFR and treatment effect in ADPKD patients: results and implications of a longitudinal cohort study

Trials failed to demonstrate protective effects of investigational treatments on glomerular filtration rate (GFR) reduction in Autosomal Dominant Polycystic Kidney Disease (ADPKD). To assess whether above findings were explained by unreliable GFR estimates, in this academic study we compared GFR values centrally measured by iohexol plasma clearance with corresponding values estimated by Chronic Kidney Disease Epidemiology Collaboration (CKD-Epi) and abbreviated Modification of Diet in Renal Disease (aMDRD) formulas in ADPKD patients retrieved from four clinical trials run by a Clinical Research Center and five Nephrology Units in Italy. Measured baseline GFRs and one-year GFR changes averaged 78.6±26.7 and 8.4±10.3 mL/min/1.73 m(2) in 111 and 71 ADPKD patients, respectively. CKD-Epi significantly overestimated and aMDRD underestimated baseline GFRs. Less than half estimates deviated by <10% from measured values. One-year estimated GFR changes did not detect measured changes. Both formulas underestimated GFR changes by 50%. Less than 9% of estimates deviated <10% from measured changes. Extent of deviations even exceeded that of measured one-year GFR changes. In ADPKD, prediction formulas unreliably estimate actual GFR values and fail to detect their changes over time. Direct kidney function measurements by appropriate techniques are needed to adequately evaluate treatment effects in clinics and research.     

Epidemiological parameters of White Spot Syndrome Virus infections in Litopenaeus vannamei and L. setiferus

An experimental protocol based on a mathematical epidemiology model was developed to study the transmission, virulence, and recovery rates of White Spot Syndrome Virus (WSSV). Two modes of transmission were compared for WSSV in Litopenaeus vannamei. We compared transmission by ingestion of infected cadavers to transmission by cohabitation with infected animals. In addition, we compared the ingestion transmission of WSSV in L. vannamei and in L. setiferus. Finally, we compared the virulence and recovery rates of WSSV in L. vannamei and L. setiferus. The transmission rate of WSSV to L. vannamei by cohabitation was 0.01. The transmission rate by ingestion of infected cadavers was over an order of magnitude larger at 0.46, suggesting that cohabitation is a much less important mode of transmission for WSSV. A statistically significant difference was detected between the estimates of ingestion transmission of L. vannamei (0.46) and those of L. setiferus (0.84), yet no differences in the virulence or recovery rates were detected between hosts. The overall estimated virulence rate was 0.34, and the overall estimated recovery rate from a WSSV infection was 0.007 for both species. According to epidemiological theory the threshold density of hosts necessary for an epidemic to occur is directly related to the virulence and recovery rates and inversely related to the transmission rate. Therefore, the epidemic threshold density may be lower for ingestion transmission than cohabitation transmission and lower for L. setiferus than for L. vannamei.     

Inferring the effective reproductive number from deterministic and semi-deterministic compartmental models using incidence and mobility data

The effective reproduction number (ℜ_t) is a theoretical indicator of the course of an infectious disease that allows policymakers to evaluate whether current or previous control efforts have been successful or whether additional interventions are necessary. This metric, however, cannot be directly observed and must be inferred from available data. One approach to obtaining such estimates is fitting compartmental models to incidence data. We can envision these dynamic models as the ensemble of structures that describe the disease’s natural history and individuals’ behavioural patterns. In the context of the response to the COVID-19 pandemic, the assumption of a constant transmission rate is rendered unrealistic, and it is critical to identify a mathematical formulation that accounts for changes in contact patterns. In this work, we leverage existing approaches to propose three complementary formulations that yield similar estimates for ℜ_t based on data from Ireland’s first COVID-19 wave. We describe these Data Generating Processes (DGP) in terms of State-Space models. Two (DGP1 and DGP2) correspond to stochastic process models whose transmission rate is modelled as Brownian motion processes (Geometric and Cox-Ingersoll-Ross). These DGPs share a measurement model that accounts for incidence and transmission rates, where mobility data is assumed as a proxy of the transmission rate. We perform inference on these structures using Iterated Filtering and the Particle Filter. The final DGP (DGP3) is built from a pool of deterministic models that describe the transmission rate as information delays. We calibrate this pool of models to incidence reports using Hamiltonian Monte Carlo. By following this complementary approach, we assess the tradeoffs associated with each formulation and reflect on the benefits/risks of incorporating proxy data into the inference process. We anticipate this work will help evaluate the implications of choosing a particular formulation for the dynamics and observation of the time-varying transmission rate.     

Infection-age structured epidemic models with behavior change or treatment

We formulate infection-age structured susceptible-infective-removed (SIR) models with behavior change or treatment of infections. Individuals change their behavior or have treatment after they are infected. Using infection age as a continuous variable, and dividing infectives into discrete groups with different infection stages, respectively, we formulate a partial differential equation model and an ordinary differential equation model with behavior change or treatment. We derive explicit formulas for the reproductive number by linear stability analysis of the infection-free equilibrium, and explicit formulas for the unique endemic equilibrium, when it exists, for both models. These formulas provide mathematical theoretical frameworks for analysis of impact of behavior change or treatment of infection to the transmission dynamics of infectious diseases. We study several special cases and provide sensitivity analysis for the reproductive numbers with respect to model parameters based on those formulas.     

Dating the time of viral subtype divergence

Precise dating of viral subtype divergence enables researchers to correlate divergence with geographic and demographic occurrences. When historical data are absent (that is, the overwhelming majority), viral sequence sampling on a time scale commensurate with the rate of substitution permits the inference of the times of subtype divergence. Currently, researchers use two strategies to approach this task, both requiring strong conditions on the molecular clock assumption of substitution rate. As the underlying structure of the substitution rate process at the time of subtype divergence is not understood and likely highly variable, we present a simple method that estimates rates of substitution, and from there, times of divergence, without use of an assumed molecular clock. We accomplish this by blending estimates of the substitution rate for triplets of dated sequences where each sequence draws from a distinct viral subtype, providing a zeroth-order approximation for the rate between subtypes. As an example, we calculate the time of divergence for three genes among influenza subtypes A-H3N2 and B using subtype C as an outgroup. We show a time of divergence approximately 100 years ago, substantially more recent than previous estimates which range from 250 to 3800 years ago.     

Estimating Xylella fastidiosa transmission parameters: decoupling sharpshooter number and feeding period

Compared to human- and wildlife-transmitted pathogens, less emphasis has been placed on developing models of plant pathogen transmission by insects. Here, we describe the transmission ecology of the bacterium Xylella fastidiosa Wells et al., the causal agent of Pierce's disease in grapevines, by its leafhopper vectors. First, we performed a meta-analysis of transmission studies of X. fastidiosa by its two most important vectors in the Western USA, the invasive glassy-winged sharpshooter, Homalodisca vitripennis Germar, and the native blue-green sharpshooter, Graphocephala atropunctata Signoret (both Hemiptera: Cicadellidae). The importance of vector number, pathogen acquisition period, and inoculation access period (IAP) for transmission differed between the two species. We fit these transmission datasets to two biologically derived transmission models, i.e., a binomial and a Poisson probability model. The Poisson model provided substantially better fit and produced estimates of H. vitripennis transmission efficiency that were dramatically lower than for G. atropunctata . We also conducted a separate pair of experiments that decoupled vector number from IAP. These experiments supported the results of the meta-analysis. Interestingly, high vector loads not only increased transmission rate, but also shortened X. fastidiosa incubation period in grapevines. This work provides quantitative estimates of transmission of an economically important pathogen that is analogous to risk models for arthropod-vectored human and wildlife diseases. In addition, this work suggests that heterogeneous vector loads may accelerate the disease cycle, increasing the potential for secondary spread in vineyards.     

Inferring Influenza Infection Attack Rate from Seroprevalence Data

Seroprevalence survey is the most practical method for accurately estimating infection attack rate (IAR) in an epidemic such as influenza. These studies typically entail selecting an arbitrary titer threshold for seropositivity (e.g. microneutralization [MN] 1∶40) and assuming the probability of seropositivity given infection (infection-seropositivity probability, ISP) is 100% or similar to that among clinical cases. We hypothesize that such conventions are not necessarily robust because different thresholds may result in different IAR estimates and serologic responses of clinical cases may not be representative. To illustrate our hypothesis, we used an age-structured transmission model to fully characterize the transmission dynamics and seroprevalence rises of 2009 influenza pandemic A/H1N1 (pdmH1N1) during its first wave in Hong Kong. We estimated that while 99% of pdmH1N1 infections became MN_1∶20 seropositive, only 72%, 62%, 58% and 34% of infections among age 3–12, 13–19, 20–29, 30–59 became MN_1∶40 seropositive, which was much lower than the 90%–100% observed among clinical cases. The fitted model was consistent with prevailing consensus on pdmH1N1 transmission characteristics (e.g. initial reproductive number of 1.28 and mean generation time of 2.4 days which were within the consensus range), hence our ISP estimates were consistent with the transmission dynamics and temporal buildup of population-level immunity. IAR estimates in influenza seroprevalence studies are sensitive to seropositivity thresholds and ISP adjustments which in current practice are mostly chosen based on conventions instead of systematic criteria. Our results thus highlighted the need for reexamining conventional practice to develop standards for analyzing influenza serologic data (e.g. real-time assessment of bias in ISP adjustments by evaluating the consistency of IAR across multiple thresholds and with mixture models), especially in the context of pandemics when robustness and comparability of IAR estimates are most needed for informing situational awareness and risk assessment. The same principles are broadly applicable for seroprevalence studies of other infectious disease outbreaks.     

Dynamics of malaria transmission model with sterile mosquitoes

In this paper, a malaria transmission model with sterile mosquitoes is considered. We first formulate a simple SEIR malaria transmission model as our baseline model. Then sterile mosquitoes are introduced into the baseline model. We consider the case that the release rate of sterile mosquitoes is proportional to the wild mosquito population size. To investigate the impact of releasing sterile mosquitoes on the malaria transmission, the dynamics of the baseline model and the models with the sterile mosquitoes are discussed. We derive formulas of the reproductive numbers and explore the existence of endemic equilibrium as the reproductive number is more than unity for these models. It is shown that both the baseline model and the models with the sterile mosquitoes undergo backward bifurcations. Based on theoretical analysis and numerical simulation, we investigate the impact of releasing sterile mosquitoes on malaria transmission.     

A computationally tractable birth-death model that combines phylogenetic and epidemiological data

Inferring the dynamics of pathogen transmission during an outbreak is an important problem in infectious disease epidemiology. In mathematical epidemiology, estimates are often informed by time series of confirmed cases, while in phylodynamics genetic sequences of the pathogen, sampled through time, are the primary data source. Each type of data provides different, and potentially complementary, insight. Recent studies have recognised that combining data sources can improve estimates of the transmission rate and the number of infected individuals. However, inference methods are typically highly specialised and field-specific and are either computationally prohibitive or require intensive simulation, limiting their real-time utility. We present a novel birth-death phylogenetic model and derive a tractable analytic approximation of its likelihood, the computational complexity of which is linear in the size of the dataset. This approach combines epidemiological and phylodynamic data to produce estimates of key parameters of transmission dynamics and the unobserved prevalence. Using simulated data, we show (a) that the approximation agrees well with existing methods, (b) validate the claim of linear complexity and (c) explore robustness to model misspecification. This approximation facilitates inference on large datasets, which is increasingly important as large genomic sequence datasets become commonplace.