The signal is not flushed away: Inferring the effective reproduction number from wastewater data in small populations.

This paper presents a novel numerical technique for the identification of effective and basic reproduction numbers, Re and R0, for long-term epidemics, using an inverse problem approach. The method is based on the direct integration of the SIR (Susceptible-Infectious-Removed) system of ordinary differential equations and the least-squares method. Simulations were conducted using official COVID-19 data for the United States and Canada, and for the states of Georgia, Texas, and Louisiana, for a period of two years and ten months. The results demonstrate the applicability of the method in simulating the dynamics of the epidemic and reveal an interesting relationship between the number of currently infectious individuals and the effective reproduction number, which is a useful tool for predicting the epidemic dynamics. For all conducted experiments, the results show that the local maximum (and minimum) values of the time-dependent effective reproduction number occur approximately three weeks before the local maximum (and minimum) values of the number of currently infectious individuals. This work provides a novel and efficient approach for the identification of time-dependent epidemics parameters.

The effective reproduction number (ℜt) 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 ℜt 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.

Impact of climate on COVID-19 transmission: A study over Indian states

Three variants of COVID-19 had been found in Indonesia. A control strategy may rely on the transmission rate of the variant. This study aims to investigate how the variants spread in Indonesia by computing a basic and effective reproduction number on the national and province scale. The basic reproduction number shows the indicator of initial transmission rate of alpha variant computed by an exponential growth rate model. The effective reproduction number describes the dynamic of the transmission rate estimated based on a Bayesian approach. This study revealed that each variant shows different characteristics. The alpha variant of COVID-19 in Indonesia was mainly initiated from big cities, then it spread to all provinces quickly because the control strategies were not established well at the beginning. A rapid increase of the effective reproduction number about July 2021 showed a novel delta variant, but it could be managed quite well by a large number of testing and stronger restrictions. Before the end of 2021, a novel variant omicron was also shown by the steeper change of the effective reproduction number. Thus, the variant spread rate can be estimated by how steep the effective reproduction number change is.

1 - Epidemic theory: Studying the effective and basic reproduction numbers, epidemic thresholds and techniques for the analysis of infectious diseases with particular emphasis on tuberculosis

This paper examines the effect of screening and HIV therapy on the dynamics of the spread of HIV in a population. In modeling of the dynamics of HIV, the population is divided into five subpopulations: susceptible, unaware infectives, screened infectives, therapy infectives, and AIDS patients.The effective reproduction numbers are calculated using the next generation matrix method. A sensitivity analysis discovers parameters that have a high impact on effective reproduction number and should be targeted by intervention strategies. Sensitivity indices is used to measure the relative change in the effective reproduction number if a parameter change. The results shows that the disease-free equilibrium point is asymptotically stable when the effective reproduction number is less than one and unstable when the effective reproduction number is greater than one. According to the analysis, screening of unaware infectives and trerapy of screened HIV infectives have the effect of reducing the transmission of the disease. Finally, numerical simulation of the model shows that the most sensitive parameter is contact rate of unaware infectives with susceptibles, allowed by the rate of progression of unaware infectives to screened infectives.

We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process (MJP), computational cost can be prohibitive for networks of realistic size and complexity. In this paper, we consider an inference scheme based on a novel hybrid simulator that classifies reactions as either ‘fast’ or ‘slow’ with fast reactions evolving as a continuous Markov process whilst the remaining slow reaction occurrences are modelled through a MJP with time-dependent hazards. A linear noise approximation (LNA) of fast reaction dynamics is employed and slow reaction events are captured by exploiting the ability to solve the stochastic differential equation driving the LNA. This simulation procedure is used as a proposal mechanism inside a particle MCMC scheme, thus allowing Bayesian inference for the model parameters. We apply the scheme to a simple application and compare the output with an existing hybrid approach and also a scheme for performing inference for the underlying discrete stochastic model.

This work considers an epidemic model with saturated incidence rate and saturated isolation and treatment functions. The incidence function (as well as the treatment and isolation functions) is of the Holling type II form, where, in the cases of treatment and isolation, these functions describes the effect of delayed treatment and isolation with large number of infected individuals in a population especially in situations where isolation facilities are available but fewer medical personnel. It is shown that the disease-free equilibrium (DFE) is locally-asymptotically stable whenever the effective reproduction number is less than unity. However, it is shown that the global-asymptotic stability of the disease-free equilibrium was largely dictated by the delay in treatment (of non-isolated infected individuals) and isolation of infected individuals; when such delay effect is weak, then the DFE is globally asymptotically stable when the effective reproduction number is less than unity. When the delay effect is strong, it is shown that there is the possibility of the existence of the backward bifurcation phenomenon whereby the DFE will co-exists with two endemic equilibria, when the effective reproduction number is less than unity. The backward bifurcation phenomenon existed when the delays occurred either singly or jointly. Mathematical analysis provides threshold conditions that allows for the global stability of the endemic equilibrium whenever the associated reproduction number is greater than unity. The results suggests that with timely isolation of infected individuals (for treatment under isolation) and treatment of non-isolated infectious cases, the ultimate goal of disease eradication is possible.

Concentrations of pathogen genomes measured in wastewater have recently become available as a new data source to use when modeling the spread of infectious diseases. One promising use for this data source is inference of the effective reproduction number, the average number of individuals a newly infected person will infect. We propose a model where new infections arrive according to a time-varying immigration rate which can be interpreted as an average number of secondary infections produced by one infectious individual per unit time. This model allows us to estimate the effective reproduction number from concentrations of pathogen genomes, while avoiding difficulty to verify assumptions about the dynamics of the susceptible population. As a byproduct of our primary goal, we also produce a new model for estimating the effective reproduction number from case data using the same framework. We test this modeling framework in an agent-based simulation study with a realistic data generating mechanism which accounts for the time-varying dynamics of pathogen shedding. Finally, we apply our new model to estimating the effective reproduction number of SARS-CoV-2, the causative agent of COVID-19, in Los Angeles, CA, using pathogen RNA concentrations collected from a large wastewater treatment facility.

Chopping the tail: How preventing superspreading can help to maintain COVID-19 control

Estimating effective reproduction numbers using wastewater data from multiple sewersheds for SARS-CoV-2 in California counties.

Mathematical analysis of HIV/AIDS stochastic dynamic models

In this research has been carried out the stability analysis of HIV/AIDS epidemic model with a public health educational through the expansion of the SI (susceptible-infected) model. In modeling of HIV/AIDS epidemic, the population is divided into six subpopulations: uneducated susceptible individuals, educated susceptible individuals, uneducated infected individuals without AIDS symptoms, educated infected individuals with AIDS symptoms, uneducated infected individuals with AIDS symptoms and educated infected individuals with AIDS symptoms. The disease-free equilibrium point of the HIV transmission model with education program is locally asymptotically stable if the basic reproduction number is less than unity and unstable if the basic reproduction number is greater than unity. The endemic equilibrium point is exist if the effective reproduction number is greater than unity and stability of endemic equilibrium point has been determined using the Center manifold theory. The center manifold theory can be used to analyze the stability near the disease-free equilibrium point (the effective reproduction number is equal to unity). The impact of a public health education on the spread of HIV/AIDS, the sensitivity analysis on effective reproduction numbers respect to all the parameters which drive the disease dynamics.

Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJPs), but are computationally challenging as imperfect surveillance, lack of subject-level information, and temporal coarseness of the data obscure the true epidemic. Analytic integration over the latent epidemic process is impossible, and integration via Markov chain Monte Carlo (MCMC) is cumbersome due to the dimensionality and discreteness of the latent state space. Simulation-based computational approaches can address the intractability of the MJP likelihood, but are numerically fragile and prohibitively expensive for complex models. A linear noise approximation (LNA) that approximates the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large-population settings, but requires modification for analyzing incidence counts without assuming that the data are normally distributed. We demonstrate how to reparameterize SEMs to appropriately analyze incidence data, and fold the LNA into a data augmentation MCMC framework that outperforms deterministic methods, statistically, and simulation-based methods, computationally. Our framework is computationally robust when the model dynamics are complex and applies to a broad class of SEMs. We evaluate our method in simulations that reflect Ebola, influenza, and SARS-CoV-2 dynamics, and apply our method to national surveillance counts from the 2013-2015 West Africa Ebolaoutbreak.

Recently-proposed particle MCMC methods provide a flexible way of performing Bayesian inference for parameters governing stochastic kinetic models defined as Markov (jump) processes (MJPs). Each iteration of the scheme requires an estimate of the marginal likelihood calculated from the output of a sequential Monte Carlo scheme (also known as a particle filter). Consequently, the method can be extremely computationally intensive. We therefore aim to avoid most instances of the expensive likelihood calculation through use of a fast approximation. We consider two approximations: the chemical Langevin equation diffusion approximation (CLE) and the linear noise approximation (LNA). Either an estimate of the marginal likelihood under the CLE, or the tractable marginal likelihood under the LNA can be used to calculate a first step acceptance probability. Only if a proposal is accepted under the approximation do we then run a sequential Monte Carlo scheme to compute an estimate of the marginal likelihood under the true MJP and construct a second stage acceptance probability that permits exact (simulation based) inference for the MJP. We therefore avoid expensive calculations for proposals that are likely to be rejected. We illustrate the method by considering inference for parameters governing a Lotka-Volterra system, a model of gene expression and a simple epidemic process.