scholarly journals Geospatial Model of COVID-19 Spreading and Vaccination With Event Gillespie Algorithm

2021 ◽  
Author(s):  
Alexander Temerev ◽  
Liudmila Rozanova ◽  
Janne Estill ◽  
Olivia Keiser
Keyword(s):  
Population Density ◽  
Stochastic Simulations ◽  
Contact Network ◽  
Gillespie Algorithm ◽  
Simulation Code ◽  
Response Strategies ◽  
Development Scenarios ◽  
Local Environments ◽  
Epidemic Development ◽  
Surrogate Model Optimization

Abstract We developed a model and a software package for stochastic simulations of transmission of COVID-19 and other similar infectious diseases, that takes into account contact network structures and geographical distribution of population density, detailed up to a level of location of individuals. Our analysis framework includes a surrogate model optimization process for quick fitting of the model’s parameters to the observed epidemic curves for cases, hospitalizations and deaths. This set of instruments (the model, the simulation code, and the optimizer) is a useful tool for policymakers and epidemic response teams who can use it to forecast epidemic development scenarios in local environments (on the scale from towns to large countries) and design optimal response strategies. The simulation code also includes a geospatial visualization subsystem, presenting detailed views of epidemic scenarios directly on population density maps. We used the developed framework to draw predictions for COVID-19 spreading in the canton of Geneva, Switzerland.

scholarly journals Using network properties to predict disease dynamics on human contact networks

2011 ◽  
Vol 278 (1724) ◽  
pp. 3544-3550 ◽  
Author(s):  
Gregory M. Ames ◽  
Dylan B. George ◽  
Christian P. Hampson ◽  
Andrew R. Kanarek ◽  
Cayla D. McBee ◽  
...  
Keyword(s):  
Degree Distribution ◽  
Stochastic Simulations ◽  
Disease Spread ◽  
Contact Structures ◽  
Contact Network ◽  
Contact Networks ◽  
Human Contact ◽  
Differential Equation Models ◽  
Network Properties ◽  
Intermediate Density

Recent studies have increasingly turned to graph theory to model more realistic contact structures that characterize disease spread. Because of the computational demands of these methods, many researchers have sought to use measures of network structure to modify analytically tractable differential equation models. Several of these studies have focused on the degree distribution of the contact network as the basis for their modifications. We show that although degree distribution is sufficient to predict disease behaviour on very sparse or very dense human contact networks, for intermediate density networks we must include information on clustering and path length to accurately predict disease behaviour. Using these three metrics, we were able to explain more than 98 per cent of the variation in endemic disease levels in our stochastic simulations.

scholarly journals Stochastic challenges to interrupting helminth transmission

2019 ◽  
Author(s):  
Robert J. Hardwick ◽  
Marleen Werkman ◽  
James E. Truscott ◽  
Roy M. Anderson
Keyword(s):  
Drug Administration ◽  
Mass Drug Administration ◽  
Living Environment ◽  
Human Migration ◽  
Stochastic Simulations ◽  
Model Framework ◽  
Deterministic Models ◽  
Simulation Code ◽  
Infected People ◽  
And Control

AbstractPredicting the effect of different programmes designed to control both the morbidity induced by helminth infections and parasite transmission is greatly facilitated by the use of mathematical models of transmission and control impact. In such models, it is essential to account for as many sources of uncertainty— natural, or otherwise — to ensure robustness in prediction and to accurately depict variation around an expected outcome. In this paper, we investigate how well the standard deterministic models match the predictions made using individual-based stochastic simulations. We also explore how well concepts which derive from deterministic models, such as ‘breakpoints’ in transmission, apply in the stochastic world. Employing an individual based stochastic model framework we also investigate how transmission and control are affected by the migration of infected people into a defined community. To give our study focus we consider the control of soil-transmitted helminths (STH) by mass drug administration (MDA), though our methodology is readily applicable to the other helminth species such as the schistosome parasites and the filarial worms. We show it is possible to define a ‘stochastic breakpoint’ where much noise surrounds the expected deterministic breakpoint. We also discuss the concept of the ‘interruption of transmission’ independent of the ‘breakpoint’ concept where analyses of model behaviour illustrate the current limitations of deterministic models to account for the ‘fade-out’ or transmission extinction behaviour in simulations. The analyses based on migration confirm a relationship between the infected human migration rate per unit of time and the death rate of infective stages that are released into the free-living environment (eggs or larvae depending on the STH species) that create the reservoir of infection which in turn determines the likelihood that control activities aim at chemotherapeutic treatment of the human host will eliminate transmission. The development of a new stochastic simulation code for STH in the form of a publicly-available open-source python package which includes features to incorporate many population stratifications, different control interventions including mass drug administration (with defined frequency, coverage levels and compliance patterns) and inter-village human migration is also described.

scholarly journals Heterogeneity matters: Contact structure and individual variation shape epidemic dynamics

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0250050
Author(s):  
Gerrit Großmann ◽  
Michael Backenköhler ◽  
Verena Wolf
Keyword(s):  
Viral Load ◽  
Herd Immunity ◽  
Dynamical Evolution ◽  
Stochastic Simulations ◽  
Contact Network ◽  
Initial Increase ◽  
Epidemic Dynamics ◽  
Ode Models ◽  
Point Estimates ◽  
Model Complex

In the recent COVID-19 pandemic, mathematical modeling constitutes an important tool to evaluate the prospective effectiveness of non-pharmaceutical interventions (NPIs) and to guide policy-making. Most research is, however, centered around characterizing the epidemic based on point estimates like the average infectiousness or the average number of contacts. In this work, we use stochastic simulations to investigate the consequences of a population’s heterogeneity regarding connectivity and individual viral load levels. Therefore, we translate a COVID-19 ODE model to a stochastic multi-agent system. We use contact networks to model complex interaction structures and a probabilistic infection rate to model individual viral load variation. We observe a large dependency of the dispersion and dynamical evolution on the population’s heterogeneity that is not adequately captured by point estimates, for instance, used in ODE models. In particular, models that assume the same clinical and transmission parameters may lead to different conclusions, depending on different types of heterogeneity in the population. For instance, the existence of hubs in the contact network leads to an initial increase of dispersion and the effective reproduction number, but to a lower herd immunity threshold (HIT) compared to homogeneous populations or a population where the heterogeneity stems solely from individual infectivity variations.

scholarly journals Contact Tracing Evaluation for COVID-19 Transmission during the Reopening Phase in a Rural College Town

2020 ◽  
Author(s):  
Sifat Afroj Moon ◽  
Caterina Scoglio
Keyword(s):  
Epidemic Model ◽  
Infected Individual ◽  
Vital Role ◽  
Stochastic Simulations ◽  
Contact Tracing ◽  
Contact Network ◽  
Unknown Parameters ◽  
Interesting Phenomenon ◽  
Epidemic Size ◽  
The Usa

AbstractContact tracing can play a vital role in controlling human-to-human transmission of a highly contagious disease such as COVID-19. To investigate the benefits and costs of contact tracing, we develop an individual-based contact-network model and a susceptible-exposed-infected-confirmed (SEIC) epidemic model for the stochastic simulations of COVID-19 transmission. We estimate the unknown parameters (reproductive ratio R0 and confirmed rate δ2) by using observed confirmed case data. After a two month-lockdown, states in the USA have started the reopening process. We provide simulations for four different reopening situations: under “stay-at-home” order or no reopening, 25 % reopening, 50 % reopening, and 75 % reopening. We model contact tracing in a two-layer network by modifying the basic SEIC epidemic model. The two-layer network is composed by the contact network in the first layer and the tracing network in the second layer. Since the full contact list of an infected individual patient can be hard to obtain, then we consider different fractions of contacts from 60% to 5%. The goal of this paper is to assess the effectiveness of contact tracing to control the COVID-19 spreading in the reopening process. In terms of benefits, simulation results show that increasing the fraction of traced contacts decreases the size of the epidemic. For example, tracing 20% of the contacts is enough for all four reopening scenarios to reduce the epidemic size by half. Considering the act of quarantining susceptible households as the contact tracing cost, we have observed an interesting phenomenon. When we increase the fraction of traced contacts from 5% to 20%, the number of quarantined susceptible people increases because each individual confirmed case is mentioning more contacts. However, when we increase the fraction of traced contacts from 20% to 60%, the number of quarantined susceptible people decreases because the increment of the mentioned contacts is balanced by a reduced number of confirmed cases. The main contribution of this research lies in the investigation of the effectiveness of contact tracing for the containment of COVID-19 spreading during the initial phase of the reopening process of the USA.

scholarly journals Why ODE models for COVID-19 fail: Heterogeneity shapes epidemic dynamics

2021 ◽  
Author(s):  
Gerrit Großmann ◽  
Michael Backenköhler ◽  
Verena Wolf
Keyword(s):  
Viral Load ◽  
Herd Immunity ◽  
Age Groups ◽  
Stochastic Simulations ◽  
Contact Network ◽  
Initial Increase ◽  
Epidemic Dynamics ◽  
Ode Models ◽  
Point Estimates ◽  
Model Complex

AbstractIn the recent COVID-19 pandemic, mathematical modeling constitutes an important tool to evaluate the prospective effectiveness of non-pharmaceutical interventions (NPIs) and to guide policy-making. Most research is, however, centered around characterizing the epidemic based on point estimates like the average infectiousness or the average number of contacts.In this work, we use stochastic simulations to investigate the consequences of a population’s heterogeneity regarding connectivity and individual viral load levels.Therefore, we translate a COVID-19 ODE model to a stochastic multi-agent system. We use contact networks to model complex interaction structures and a probabilistic infection rate to model individual viral load variation.We observe a large dependency of the dispersion and dynamical evolution on the population’s heterogeneity that is not adequately captured by point estimates, for instance, used in ODE models. In particular, models that assume the same clinical and transmission parameters may lead to different conclusions, depending on different types of heterogeneity in the population. For instance, the existence of hubs in the contact network leads to an initial increase of dispersion and the effective reproduction number, but to a lower herd immunity threshold (HIT) compared to homogeneous populations or a population where the heterogeneity stems solely from individual infectivity variations.Author summaryComputational modeling can support decision-making in the face of pandemics like COVID-19. Models help to understand transmission data and predict important epidemiological properties (e.g., When will herd immunity be reached?). They can also examine the effectiveness of certain measures, and—to a limited extent—extrapolate the dynamics under specific assumptions. In all these cases, the heterogeneity of the population plays an important role. For instance, it is known that connectivity differences in (and among) age groups influence the dynamics of epidemic propagation. Here we focus on two types of differences among individuals: their social interactions and on how infectious they are. We show that only considering population averages (e.g., What is the average number of contacts of an individual?) may lead to misleading conclusions, because the individual differences (such as those related to the epidemic (over-)dispersion) play an important role in shaping the epidemic dynamics. Many commonly used model classes, such as SEIR-type ODE compartmental models, ignore differences within a population to a large extent. This omission bears the potential of misleading conclusions.

scholarly journals Using multiple infection history to infer contact network structure

2019 ◽  
Author(s):  
Christian Selinger ◽  
Samuel Alizon
Keyword(s):  
Infectious Diseases ◽  
Disease Transmission ◽  
Multiple Infection ◽  
Contact Network ◽  
Multiple Infections ◽  
Human Populations ◽  
Gillespie Algorithm ◽  
Epidemiological Modeling ◽  
Contact Patterns ◽  
Recent Developments

The structure of host interactions within a population shapes the spread of infectious diseases but contact patterns between hosts are difficult to access. We hypothesised that key properties of these patterns can be inferred by using multiple infections data from individual longitudinal follow-ups. To show this, we simulated multiple infections on a contact network in an unbiased way by implementing a non-Markovian extension of the Gillespie algorithm for a community of parasites spreading on this network. We then analysed the resulting individual infection time series in an original way by introducing the concept of ‘infection barcodes’ to represent the infection history in each host. We find that, depending on infection multiplicity and immunity assumptions, knowledge about the barcode topology makes it possible to recover key properties of the network topology and even of individual nodes. The combination of individual-based simulations and barcode analysis of infection histories opens promising perspectives for the study of infectious disease transmission networks.Significance StatementThe way hosts interact with each other is known to shape epidemics spread. However, these interactions are difficult to infer, especially in human populations. Using recent developments in stochastic epidemiological modeling and barcode theory, we show that the diversity of infections each host has undergone over time contains key information about contact network between hosts. This means that longitudinal follow-ups of some individuals in a population can tell us how hosts are in contact with each other. It can also inform us on how connected a particular individual is. This opens new possibilities regarding the use of genetic diversity of infectious diseases in epidemiology.

scholarly journals Risk assessment of Ebola virus disease spreading in Uganda using a two-layer temporal network

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Mahbubul H. Riad ◽  
Musa Sekamatte ◽  
Felix Ocom ◽  
Issa Makumbi ◽  
Caterina M. Scoglio
Keyword(s):  
Risk Assessment ◽  
Ebola Virus ◽  
Democratic Republic Of Congo ◽  
Virus Disease ◽  
Physical Contact ◽  
Ebola Virus Disease ◽  
Contact Network ◽  
Gillespie Algorithm ◽  
Temporal Network ◽  
Simulation Results

Abstract Network-based modelling of infectious diseases apply compartmental models on a contact network, which makes the epidemic process crucially dependent on the network structure. For highly contagious diseases such as Ebola virus disease (EVD), interpersonal contact plays the most vital role in human-to-human transmission. Therefore, for accurate representation of EVD spreading, the contact network needs to resemble the reality. Prior research has mainly focused on static networks (only permanent contacts) or activity-driven networks (only temporal contacts) for Ebola spreading. A comprehensive network for EVD spreading should include both these network structures, as there are always some permanent contacts together with temporal contacts. Therefore, we propose a two-layer temporal network for Uganda, which is at risk of an Ebola outbreak from the neighboring Democratic Republic of Congo (DRC) epidemic. The network has a permanent layer representing permanent contacts among individuals within the family level, and a data-driven temporal network for human movements motivated by cattle trade, fish trade, or general communications. We propose a Gillespie algorithm with the susceptible-infected-recovered (SIR) compartmental model to simulate the evolution of EVD spreading as well as to evaluate the risk throughout our network. As an example, we applied our method to a network consisting of 23 districts along different movement routes in Uganda starting from bordering districts of the DRC to Kampala. Simulation results show that some regions are at higher risk of infection, suggesting some focal points for Ebola preparedness and providing direction to inform interventions in the field. Simulation results also show that decreasing physical contact as well as increasing preventive measures result in a reduction of chances to develop an outbreak. Overall, the main contribution of this paper lies in the novel method for risk assessment, which can be more precise with an increasing volume of accurate data for creating the network model.

scholarly journals Introducing and benchmarking the accuracy of cayenne: a Python package for stochastic simulations

2020 ◽  
Author(s):  
Dileep Kishore ◽  
Srikiran Chandrasekaran
Keyword(s):  
Stochastic Simulation ◽  
Analytical Solutions ◽  
Adaptive Algorithm ◽  
Direct Method ◽  
Stochastic Simulations ◽  
Gillespie Algorithm ◽  
Trade Off ◽  
Link Type ◽  
Stochastic Simulation Algorithms ◽  
Python Package

AbstractBiological systems are intrinsically noisy and this noise may determine the qualitative outcome of the system. In the absence of analytical solutions to mathematical models incorporating noise, stochastic simulation algorithms are useful to explore the possible trajectories of these systems. Algorithms used for such stochastic simulations include the Gillespie algorithm and its approximations. In this study we introduce cayenne, an easy to use Python package containing accurate and fast implementations of the Gillespie algorithm (direct method), the tau-leaping algorithm and a tau-adaptive algorithm. We compare the accuracy of cayenne with other stochastic simulation libraries (BioSimulator.jl, GillespieSSA and Tellurium) and find that cayenne offers the best trade-off between accuracy and speed. Additionally, we highlight the importance of performing accuracy tests for stochastic simulation libraries, and hope that it becomes standard practice when developing the same.The cayenne package can be found at https://github.com/Heuro-labs/cayenne while the bench-marks can be found at https://github.com/Heuro-labs/cayenne-benchmarks

scholarly journals Risk assessment of Ebola virus disease spreading in Uganda using a multilayer temporal network

2019 ◽  
Author(s):  
Mahbubul H Riad ◽  
Musa Sekamatte ◽  
Felix Ocom ◽  
Issa Makumbi ◽  
Caterina M Scoglio
Keyword(s):  
Risk Assessment ◽  
Ebola Virus ◽  
Virus Disease ◽  
Research Work ◽  
Ebola Virus Disease ◽  
Personal Contact ◽  
Contact Network ◽  
Gillespie Algorithm ◽  
Temporal Network ◽  
Simulation Results

ABSTRACTNetwork-based modelling of infectious diseases apply compartmental models on a contact network, which makes the epidemic process crucially dependent on the network structure. For highly contagious diseases such as Ebola virus disease (EVD), the inter-personal contact plays the most vital role in the human to human transmission. Therefore, for accurate representation of the EVD spreading, the contact network needs to resemble the reality. Prior research work has mainly focused on static networks (only permanent contacts) or activity driven networks (only temporal contacts) for Ebola spreading. A comprehensive network for EVD spreading should include both these network structures, as there are always some permanent contacts together with temporal contacts. Therefore, we propose a multilayer temporal network for Uganda, which is at risk of Ebola outbreak from the neighboring Democratic Republic of Congo (DRC) epidemic. The network has a permanent layer representing permanent contacts among individuals within family level, and a data driven temporal network for human movements motivated by cattle trade, fish trade, or general communications. We propose a Gillespie algorithm with the susceptible-infected-recovered (SIR) compartmental model to simulate the evolution of the EVD spreading as well as to evaluate the risk throughout our network. As an example, we applied our method to a multilayer network consisting of 23 districts along different movement routes in Uganda starting from bordering districts of DRC to Kampala. Simulation results shows that some regions are at higher risk of infection, suggesting some focal points for Ebola preparedness and providing direction to inform interventions in the field. Simulation results also shows that decreasing physical contacts as well as increasing preventive measures result in a reduction of chances to develop an outbreak. Overall, the main contribution of this paper lies in the novel method for risk assessment, the accuracy of which can be increased by increasing the amount and the accuracy of the data used to build the network and the model.

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