scholarly journals The nature of individual heterogeneity shape outbreak dynamics

2021 ◽  
Author(s):  
Baptiste Elie ◽  
Christian Selinger ◽  
Samuel Alizon
Keyword(s):  
Transmission Rate ◽  
Sir Model ◽  
Pathogen Transmission ◽  
Main Driver ◽  
Biological Sources ◽  
Stochastic Sir ◽  
Stochastic Sir Model ◽  
The Impact ◽  
Parasite Emergence

AbstractIt is now common-place that pathogen transmission during an outbreak can be more heterogeneous than what is commonly assumed, and that it can have major consequences on their dynamics. However, previous studies did not explore the impact of the different biological sources of heterogeneity while controlling for the resulting heterogeneity in the number of secondary cases. In this study, we explore the role of individual variation in infection duration and transmission rate on parasite emergence and spread in a population. We simulate outbreaks using a custom stochastic SIR model, with and without evolution of the parasite. We show that for a given mean, the variance in the number of secondary cases is the main driver of the outbreak probability, with or without evolution, while it does not play a role on the outbreak dynamic once it emerged. On the opposite, a smaller and more realistic variance in the infection duration causes a faster outbreak. It is therefore useful to take into consideration more realistic distributions when modelling infectious diseases outbreaks.

scholarly journals Modelling the spread of American foulbrood in honeybees

2013 ◽  
Vol 10 (88) ◽  
pp. 20130650 ◽  
Author(s):  
Samik Datta ◽  
James C. Bull ◽  
Giles E. Budge ◽  
Matt J. Keeling
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Control Strategies ◽  
Sir Model ◽  
Model Parameters ◽  
American Foulbrood ◽  
Inspection Period ◽  
Stochastic Sir ◽  
Stochastic Sir Model ◽  
The Impact

We investigate the spread of American foulbrood (AFB), a disease caused by the bacterium Paenibacillus larvae , that affects bees and can be extremely damaging to beehives. Our dataset comes from an inspection period carried out during an AFB epidemic of honeybee colonies on the island of Jersey during the summer of 2010. The data include the number of hives of honeybees, location and owner of honeybee apiaries across the island. We use a spatial SIR model with an underlying owner network to simulate the epidemic and characterize the epidemic using a Markov chain Monte Carlo (MCMC) scheme to determine model parameters and infection times (including undetected ‘occult’ infections). Likely methods of infection spread can be inferred from the analysis, with both distance- and owner-based transmissions being found to contribute to the spread of AFB. The results of the MCMC are corroborated by simulating the epidemic using a stochastic SIR model, resulting in aggregate levels of infection that are comparable to the data. We use this stochastic SIR model to simulate the impact of different control strategies on controlling the epidemic. It is found that earlier inspections result in smaller epidemics and a higher likelihood of AFB extinction.

scholarly journals Modelling and Analysis of 2019-nCov Epidemic in India : A study on Attack & Recovery Rate, Basic & Effective Reproductive Number, Herd Immunity Threshold & Case Fatality Ratio of Coronavirus Covid-19 in India.

2020 ◽  
Author(s):  
Tanishque Propkar Malik
Keyword(s):  
Herd Immunity ◽  
Case Fatality ◽  
Sir Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Case Fatality Ratio ◽  
Stochastic Sir ◽  
Novel Coronavirus ◽  
Stochastic Sir Model ◽  
The Impact

Mathematical modelling of any epidemic plays a crucial role in quantifying the impact of such pathogens. This paper focuses on building a Stochastic SIR Model with non-linear parameters (to account for the effect of lockdowns) to gain a broader cognition of the 2019 novel Coronavirus pathogen (2019-nCov), widely known as Covid-19, in India. Such models help in gauging the virulence and fecundity of pathogens. Based on early transmission dynamics the basic reproductive number (R0) is computed to be 1.605. Whereas, effective reproductive number (Rt) is computed to be 4.880 as on 19 March, 2.756 as on 19 April, and 1.995 as on 19 May. Furthermore, the proportion of population that needs to be immunized (through inoculation, recovery, or death) to halt the infection spread is estimated to be 37.69%, ergo, the Herd Immunity Threshold is estimated to be 51.36 crores recoveries, if the Rt remains below 2. Rt is expected to fall below 2, and the Case Fatality Ratio (CFR) to fall to 2.14%, circa early-September (assuming minimal or no medical breakthroughs). The formulated model also provides inferential evidence manifesting the extent to which lockdowns contained the spread of the virus.

scholarly journals Global to USA County Scale Analysis of Weather, Urban Density, Mobility, Homestay, and Mask Use on COVID-19

2020 ◽  
Vol 17 (21) ◽  
pp. 7847
Author(s):  
Sajad Jamshidi ◽  
Maryam Baniasad ◽  
Dev Niyogi
Keyword(s):  
Transmission Rate ◽  
Climate Impact ◽  
Relative Importance ◽  
Urban Density ◽  
Spatial And Temporal Scales ◽  
Urban Dynamics ◽  
Causal Processes ◽  
The Impact ◽  
The Relationship

Prior evaluations of the relationship between COVID-19 and weather indicate an inconsistent role of meteorology (weather) in the transmission rate. While some effects due to weather may exist, we found possible misconceptions and biases in the analysis that only consider the impact of meteorological variables alone without considering the urban metabolism and environment. This study highlights that COVID-19 assessments can notably benefit by incorporating factors that account for urban dynamics and environmental exposure. We evaluated the role of weather (considering equivalent temperature that combines the effect of humidity and air temperature) with particular consideration of urban density, mobility, homestay, demographic information, and mask use within communities. Our findings highlighted the importance of considering spatial and temporal scales for interpreting the weather/climate impact on the COVID-19 spread and spatiotemporal lags between the causal processes and effects. On global to regional scales, we found contradictory relationships between weather and the transmission rate, confounded by decentralized policies, weather variability, and the onset of screening for COVID-19, highlighting an unlikely impact of weather alone. At a finer spatial scale, the mobility index (with the relative importance of 34.32%) was found to be the highest contributing factor to the COVID-19 pandemic growth, followed by homestay (26.14%), population (23.86%), and urban density (13.03%). The weather by itself was identified as a noninfluential factor (relative importance < 3%). The findings highlight that the relation between COVID-19 and meteorology needs to consider scale, urban density and mobility areas to improve predictions.

scholarly journals Stochastic SIR model with jumps

2013 ◽  
Vol 26 (8) ◽  
pp. 867-874 ◽  
Author(s):  
Xianghua Zhang ◽  
Ke Wang
Keyword(s):  
Sir Model ◽  
Stochastic Sir ◽  
Stochastic Sir Model

scholarly journals The use of mixture-density networks in the emulation of complex epidemiological individual-based models

2019 ◽  
Author(s):  
Christopher N Davis ◽  
T Deirdre Hollingsworth ◽  
Quentin Caudron ◽  
Michael A Irvine
Keyword(s):  
Neural Network ◽  
Infectious Disease ◽  
Negative Binomial ◽  
Sir Model ◽  
Discrete Distributions ◽  
Individual Based Model ◽  
Mixture Density ◽  
Individual Based Models ◽  
Stochastic Sir ◽  
Stochastic Sir Model

AbstractComplex, highly computational, individual-based models are abundant in epidemiology. For epidemics such as macro-parasitic diseases, detailed modelling of human behaviour and pathogen life-cycle are required in order to produce accurate results. This can often lead to models that are computationally-expensive to analyse and perform model fitting, and often require many simulation runs in order to build up sufficient statistics. Emulation can provide a more computationally-efficient output of the individual-based model, by approximating it using a statistical model. Previous work has used Gaussian processes in order to achieve this, but these can not deal with multi-modal, heavy-tailed, or discrete distributions. Here, we introduce the concept of a mixture density network (MDN) in its application in the emulation of epidemiological models. MDNs incorporate both a mixture model and a neural network to provide a flexible tool for emulating a variety of models and outputs. We develop an MDN emulation methodology and demonstrate its use on a number of simple models incorporating both normal, gamma and beta distribution outputs. We then explore its use on the stochastic SIR model to predict the final size distribution and infection dynamics. MDNs have the potential to faithfully reproduce multiple outputs of an individual-based model and allow for rapid analysis from a range of users. As such, an open-access library of the method has been released alongside this manuscript.Author summaryInfectious disease modellers have a growing need to expose their models to a variety of stakeholders in interactive, engaging ways that allow them to explore different scenarios. This approach can come with a considerable computational cost that motivates providing a simpler representation of the complex model. We propose the use of mixture density networks as a solution to this problem. These are highly flexible, deep neural network-based models that can emulate a variety of data, including counts and over-dispersion. We explore their use firstly through emulating a negative-binomial distribution, which arises in many places in ecology and parasite epidemiology. We then explore the approach using a stochastic SIR model. We also provide an accompanying Python library with code for all examples given in the manuscript. We believe that the use of emulation will provide a method to package an infectious disease model such that it can be disseminated to the widest audience possible.

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