A random-walk based epidemiological model

ABSTRACTRandom walkers on a two-dimensional square lattice are used to explore the spatio-temporal growth of an epidemic. We have found that a simple random-walk system generates nontrivial dynamics compared with traditional well-mixed models. Phase diagrams characterizing the long-term behaviors of the epidemics are calculated numerically. The phase boundary separating those sets of parameters leading to outbreaks dying out and those leading to indefinite growth is mapped out in detail. The functional dependence of the basic reproductive number R0 on the model’s defining parameters reveals the role of spatial fluctuations and leads to a novel expression for R0. Special attention is given to simulations of inter-regional transmission of the contagion. The attack rate and the (growing) radius of gyration of the affected zones are used as measures of the severity of the outbreaks, in cases where R0 is not sufficiently prescriptive to chart the epidemic dynamics.

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A random-walk-based epidemiological model

Scientific Reports ◽

10.1038/s41598-021-98211-5 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Andrew Chu ◽

Greg Huber ◽

Aaron McGeever ◽

Boris Veytsman ◽

David Yllanes

Keyword(s):

Random Walk ◽

Functional Dependence ◽

Universality Class ◽

Simple Random Walk ◽

Basic Reproductive Number ◽

Square Lattice ◽

Reproductive Number ◽

Random Walkers ◽

Spatial Fluctuations ◽

Spatio Temporal

AbstractRandom walkers on a two-dimensional square lattice are used to explore the spatio-temporal growth of an epidemic. We have found that a simple random-walk system generates non-trivial dynamics compared with traditional well-mixed models. Phase diagrams characterizing the long-term behaviors of the epidemics are calculated numerically. The functional dependence of the basic reproductive number $$R_{0}$$ R 0 on the model’s defining parameters reveals the role of spatial fluctuations and leads to a novel expression for $$R_{0}$$ R 0 . Special attention is given to simulations of inter-regional transmission of the contagion. The scaling of the epidemic with respect to space and time scales is studied in detail in the critical region, which is shown to be compatible with the directed-percolation universality class.

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Strong spatial embedding of social networks generates nonstandard epidemic dynamics independent of degree distribution and clustering

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1910181117 ◽

2020 ◽

Vol 117 (38) ◽

pp. 23636-23642

Author(s):

David J. Haw ◽

Rachael Pung ◽

Jonathan M. Read ◽

Steven Riley

Keyword(s):

Spatial Correlation ◽

Dynamic Models ◽

Peak Height ◽

Single Parameter ◽

Clustering Coefficient ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Human Pathogens ◽

Final Size ◽

Epidemic Dynamics

Some directly transmitted human pathogens, such as influenza and measles, generate sustained exponential growth in incidence and have a high peak incidence consistent with the rapid depletion of susceptible individuals. Many do not. While a prolonged exponential phase typically arises in traditional disease-dynamic models, current quantitative descriptions of nonstandard epidemic profiles are either abstract, phenomenological, or rely on highly skewed offspring distributions in network models. Here, we create large socio-spatial networks to represent contact behavior using human population-density data, a previously developed fitting algorithm, and gravity-like mobility kernels. We define a basic reproductive numberR0for this system, analogous to that used for compartmental models. Controlling forR0, we then explore networks with a household–workplace structure in which between-household contacts can be formed with varying degrees of spatial correlation, determined by a single parameter from the gravity-like kernel. By varying this single parameter and simulating epidemic spread, we are able to identify how more frequent local movement can lead to strong spatial correlation and, thus, induce subexponential outbreak dynamics with lower, later epidemic peaks. Also, the ratio of peak height to final size was much smaller when movement was highly spatially correlated. We investigate the topological properties of our networks via a generalized clustering coefficient that extends beyond immediate neighborhoods, identifying very strong correlations between fourth-order clustering and nonstandard epidemic dynamics. Our results motivate the observation of both incidence and socio-spatial human behavior during epidemics that exhibit nonstandard incidence patterns.

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Emergence of an Adaptive Movement from a Subjective Inference about Resource Distribution

10.21203/rs.3.rs-103602/v1 ◽

2020 ◽

Author(s):

Tomoko Sakiyama

Keyword(s):

Random Walk ◽

Search Strategy ◽

Resource Distribution ◽

Simple Random Walk ◽

Food Distribution ◽

Local Resource ◽

Random Walkers ◽

Resource Searching ◽

Proposed Model ◽

Global Food

Abstract Background: In animal foraging, the optimal search strategy in an unknown environment varies according to the context. When food is distributed sparsely and randomly, super-diffusive walks outperform normal-diffusive walks. However, super-diffusive walks are no longer advantageous when random walkers forage in a resource-rich environment. It is not currently clear whether a relationship exists between an agent’s use of local information to make subjective inferences about global food distribution and an optimal random walk strategy. Methods: Therefore, I investigated how flexible exploration is achieved if an agent alters its directional rule based on local resource distribution. In the proposed model, the agent, a Brownian-like walker, estimates global resource distribution using local resource patterns and makes a decision by altering its rules. Results: I showed that the agent behaved like a non-Brownian walker and the model adaptively switched between diffusive properties depending on the resource density. This led to a more effective resource-searching performance compared with that of a simple random-walk model. Conclusion: These results demonstrate a process of optimal searching dependent on context.

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THE IMPACT OF HUMAN LOCATION-SPECIFIC CONTACT PATTERN ON THE SIR EPIDEMIC TRANSMISSION BETWEEN POPULATIONS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127413500958 ◽

2013 ◽

Vol 23 (05) ◽

pp. 1350095 ◽

Cited By ~ 28

Author(s):

LIN WANG ◽

YAN ZHANG ◽

ZHEN WANG ◽

XIANG LI

Keyword(s):

Population Model ◽

Disease Incidence ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Contact Pattern ◽

Structured Population Model ◽

Epidemic Dynamics ◽

Sir Epidemic ◽

Structured Population ◽

The Impact

The structured-population model is extensively used to study the complexity of epidemic dynamics. In many seminal researches, the impact of human mobility on the outbreak threshold has been profoundly studied, with the general assumption that the human contact pattern is mixing homogeneously. As the individual contact is assumed uniform among different subpopulations, the basic reproductive number, R0, which relates to the stability at the disease-free equilibrium, is equal to the same constant on separate locations. However, recent studies have shown that there may exist location-related factors driving the variance of disease incidence between populations, in reality. Therefore, in this study, the location-specific heterogeneous contact pattern has been introduced into a famous phenomenological structured-population model, where bidirectional recurrent commuting flows couple two typical subpopulations, to study the complex dynamics behaviors of spatial transmission of epidemics. Besides the usual SIR epidemic dynamics with birth and death processes, we take into account the contact process by assigning each member from a given subpopulation with a characteristic contact rate. Through theoretical arguments and agent-based computer simulations, we unveil that the stressed element dramatically affects the epidemic threshold of the system.

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Epidemic Dynamics and Patterns of Plant Diseases

Phytopathology ◽

10.1094/phyto.2001.91.10.1001 ◽

2001 ◽

Vol 91 (10) ◽

pp. 1001-1010 ◽

Cited By ~ 68

Author(s):

J. Segarra ◽

M. J. Jeger ◽

F. van den Bosch

Keyword(s):

Plant Diseases ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Disease Rate ◽

Epidemic Threshold ◽

Differential Delay Equation ◽

Differential Delay ◽

Epidemic Curve ◽

Epidemic Dynamics ◽

Special Cases

The general Kermack and McKendrick epidemic model (K&M) is derived with an appropriate terminology for plant diseases. The epidemic dynamics and patterns of special cases of the K&M model, such as the Vanderplank differential-delay equation; the compartmental healthy (H), latent (L), infectious (S), and postinfectious (R) model; and the K&M model with a delay-gamma-distributed sporulation curve were compared. The characteristics of the disease cycle are summarized by the basic reproductive number, R0, and the normalized sporulation curve, i(τ). We show how R0 and the normalized sporulation curve can be calculated from data in the literature. There are equivalences in the values of the basic reproductive number, R0, the epidemic threshold, and the final disease level across the different models.However, they differ in expressions for the initial disease rate, r, and the initial infection, Q, because the values depend on the sporulation curve. Expressions for r and Q were obtained for each model and can be used to approximate the epidemic curve by the logistic equation.

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THRESHOLD AND STABILITY RESULTS FOR AN SIRS EPIDEMIC MODEL WITH A GENERAL PERIODIC VACCINATION STRATEGY

Journal of Biological System ◽

10.1142/s0218339005001446 ◽

2005 ◽

Vol 13 (02) ◽

pp. 131-150 ◽

Cited By ~ 29

Author(s):

I. A. MONEIM ◽

D. GREENHALGH

Keyword(s):

Epidemic Model ◽

Vaccination Strategy ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Contact Rate ◽

Globally Asymptotically Stable ◽

Epidemic Dynamics ◽

Sirs Epidemic Model ◽

Sirs Model ◽

Periodic Disease

An SIRS epidemic model with general periodic vaccination strategy is analyzed. This periodic vaccination strategy is discussed first for an SIRS model with seasonal variation in the contact rate of period T = 1 year. We start with the case where the vaccination strategy and the contact rate have the same period and then discuss the case where the period of the vaccination strategy is LT, where L is an integer. We investigate whether a periodic vaccination strategy may force the epidemic dynamics to have periodic behavior. We prove that our SIRS model has a unique periodic disease free solution (DFS) whose period is the same as that of the vaccination strategy, which is globally asymptotically stable when the basic reproductive number R0 is less than or equal to one in value. When R0 > 1, we prove that there exists a non-trivial periodic solution of period the same as that of the vaccination strategy. Some persistence results are also discussed. Threshold conditions for these periodic vaccination strategies to ensure that R0 ≤ 1 are derived.

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Social networks with strong spatial embedding generate non-standard epidemic dynamics driven by higher-order clustering

10.1101/714006 ◽

2019 ◽

Cited By ~ 1

Author(s):

David J. Haw ◽

Rachael Pung ◽

Jonathan M. Read ◽

Steven Riley

Keyword(s):

Social Networks ◽

Spatial Correlation ◽

Dynamic Models ◽

Single Parameter ◽

Clustering Coefficient ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Epidemic Dynamics ◽

Contact Behaviour ◽

The Way

AbstractSome directly transmitted human pathogens such as influenza and measles generate sustained exponential growth in incidence, and have a high peak incidence consistent with the rapid depletion of susceptible individuals. Many do not. While a prolonged exponential phase typically arises in traditional disease-dynamic models, current quantitative descriptions of non-standard epidemic profiles are either abstract, phenomenological or rely on highly skewed offspring distributions in network models. Here, we create large socio-spatial networks to represent contact behaviour using human population density data, a previously developed fitting algorithm, and gravity-like mobility kernels. We define a basic reproductive number R0 for this system analogous to that used for compartmental models. Controlling for R0, we then explore networks with a household-workplace structure in which between-household contacts can be formed with varying degrees of spatial correlation, determined by a single parameter from the gravity-like kernel. By varying this single parameter and simulating epidemic spread, we are able to identify how more frequent local movement can lead to strong spatial correlation and thus induce sub-exponential outbreak dynamics with lower, later epidemic peaks. Also, the ratio of peak height to final size was much smaller when movement was highly spatially correlated. We investigate the topological properties of our networks via a generalized clustering coefficient that extends beyond immediate neighbourhoods, identifying very strong correlations between 4th order clustering and non-standard epidemic dynamics. Our results motivate the joint observation of incidence and socio-spatial human behaviour during epidemics that exhibit non-standard incidence patterns.Author SummaryEpidemics are typically described using a standard set of mathematical models that do not capture social interactions or the way those interactions are determined by geography. Here we propose a model that can reflect social networks influenced strongly by the way people travel and we show that they lead to very different epidemic profiles. This type of model will likely be useful for forecasting.

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Epidemic Dynamics of COVID-19 Based on SEAIUHR Model Considering Asymptomatic Cases in Henan Province, China

10.21203/rs.3.rs-50050/v1 ◽

2020 ◽

Author(s):

Chunyu Li ◽

Yuchen Zhu ◽

Chang Qi ◽

Lili Liu ◽

Dandan Zhang ◽

...

Keyword(s):

Early Stage ◽

Henan Province ◽

Control Measures ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Infected People ◽

Epidemic Dynamics ◽

Global Pandemic ◽

Prevention And Control Measures ◽

Novel Coronavirus

Abstract Background New coronavirus disease (COVID-19), an infectious disease caused by a type of novel coronavirus, has emerged in various countries since the end of 2019 and caused a global pandemic. Many infected people went undetected because their symptoms were mild or asymptomatic, but the proportion and infectivity of asymptomatic infections remained unknown. Therefore, in this paper, we analyzed the proportion and infectivity of asymptomatic cases, as we as the prevalence of COVID-19 in Henan province. Methods We constructed SEAIUHR model based on COVID-19 cases reported from 21 January to 26 February 2020 in Henan province to estimate the proportion and infectivity of asymptomatic cases, as we as the change of effective reproductive number, ${R}_{t}$. At the same time, we simulated the changes of cases in different scenarios by changing the time and intensity of the implementation of prevention and control measures. Results The proportion of asymptomatic cases among COVID-19 infected individuals was 42% and infectivity of asymptomatic cases was 10% of that symptomatic ones. The basic reproductive number${R}_{0}$=2.73, and ${R}_{t}$ dropped below 1 on 1 February under a series of measures. If measures were taken five days earlier, the number of cases would be reduced by 2/3, and after 5 days the number would more than triple. Conclusions In Henan Province, the COVID-19 epidemic spread rapidly in the early stage, and there were a large number of asymptomatic infected individuals with relatively low infectivity. However, the epidemic was quickly brought under control with national measures, and the earlier measures were implemented, the better.

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Gillis' Random Walks on Graphs

Journal of Applied Probability ◽

10.1239/jap/1110381390 ◽

2005 ◽

Vol 42 (1) ◽

pp. 295-301 ◽

Cited By ~ 1

Author(s):

Nadine Guillotin-Plantard

Keyword(s):

Random Walk ◽

Green Function ◽

Random Walks ◽

Regular Graph ◽

Simple Random Walk ◽

Square Lattice ◽

Random Walker ◽

Unit Step ◽

Random Walks On Graphs ◽

The Green Function

We consider a random walker on a d-regular graph. Starting from a fixed vertex, the first step is a unit step in any one of the d directions, with common probability 1/d for each one. At any later step, the random walker moves in any one of the directions, with probability q for a reversal of direction and probability p for any other direction. This model was introduced and first studied by Gillis (1955), in the case when the graph is a d-dimensional square lattice. We prove that the Gillis random walk on a d-regular graph is recurrent if and only if the simple random walk on the graph is recurrent. The Green function of the Gillis random walk will be also given, in terms of that of the simple random walk.

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Hand, Foot, and Mouth Disease in Thailand: A Comprehensive Modelling of Epidemic Dynamics

10.21203/rs.3.rs-77402/v1 ◽

2020 ◽

Author(s):

Suraj Verma ◽

Mohammad Abdur Razzaque ◽

U Sangtongdee ◽

C Arpnikanondt ◽

Boonrat Tassaneetrithep ◽

...

Keyword(s):

Learning Algorithm ◽

Foot And Mouth Disease ◽

Mouth Disease ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Public Health Issue ◽

Seasonal Effect ◽

Epidemic Dynamics ◽

Foot And Mouth ◽

Asian Pacific

Abstract Background Hand Foot and Mouth Disease (HFMD) is a highly contagious disease and has become an epidemic in many Asian-Pacific countries, including Thailand. With such epidemic characteristics and potential economic impact, HFMD is a significant public health issue. Comprehensive modelling of HFMD’s epidemic dynamics can be useful in understanding and predicting any potential outbreak of it, and manage its impact efficiently and effectively. Generally, the transmission dynamics of infectious diseases vary across geolocations due to different socio-economic situations, demography, and people’s lifestyles. However, there is no nation-wide and comprehensive (i.e., the inclusion of reinfections in the model) modelling of HFDM dynamics in Thailand. We aim to develop a nation-wide comprehensive modelling of HFMD’s epidemic dynamics and understand the reinfection cases in Thailand.Methods We have formulated Susceptible - Exposed - Infectious - Recovered - Susceptible (SEIRS) epidemiological model with dynamic vitals, including reinfections, to investigate the transmission of this disease in Thailand. We also introduced periodic seasonality to model the seasonal effect. According to the model, the spread of this disease is uneven throughout the provinces in Thailand. So, we have grouped the provinces into three clusters (i.e., highly, moderately and least affected provinces) using K-means unsupervised machine learning algorithm for better estimation of the parameters and fitting the model. We collected data from three local hospitals in Thailand to analyze the reinfection cases.Results The result from the analysis of HFMD recorded cases from three hospital (years 2012 to 2016) shows that 11% (approximately) are reinfections. By fitting the model with HFMD confirmed cases (years 2011 to 2019) and considering the reinfections, the basic reproductive number (R0) was estimated to be 2.643, 1.91 and 3.246 for three clustered provinces.Conclusion In a conclusion, it is found that HFMD is re-infectious disease in Thailand. It is also found that the spread of HFMD is not uniform across the provinces in Thailand. The basic reproductive number R 0 was estimated to be greater than 1 for all the three clusters. This indicates that under the same social and environmental condition, this disease will persist in coming years.

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