Pub Date : 2017-01-01DOI: 10.1080/23737867.2017.1359697
L. Denholm, N. Beeton, L. Forbes, S. Carver
Abstract Ross River Disease is a mosquito-borne viral condition that affects pockets of the Australian human population, and can be debilitating in some instances. The evidence is that the virus reservoirs in marsupials, such as kangaroos, and this may account for the unpredictable outbreaks of the disease in humans. Accordingly, we present here a new model for the dynamics of Ross River Virus (RRV) in populations of mosquitoes and kangaroos. We calculate steady-state populations for the sub-groups in each species and demonstrate that naturally-occurring oscillations in the populations (limit cycles) do not occur. When seasonal forcing of vector populations and kangaroo birth rates is taken into account, however, the model may predict multi-annual outbreaks and chaos, perhaps explaining the unpredictability of some RRV disease epidemics, particularly across southern Australia. Detailed results in this case are presented.
{"title":"A model for the dynamics of Ross River Virus in the Australian environment","authors":"L. Denholm, N. Beeton, L. Forbes, S. Carver","doi":"10.1080/23737867.2017.1359697","DOIUrl":"https://doi.org/10.1080/23737867.2017.1359697","url":null,"abstract":"Abstract Ross River Disease is a mosquito-borne viral condition that affects pockets of the Australian human population, and can be debilitating in some instances. The evidence is that the virus reservoirs in marsupials, such as kangaroos, and this may account for the unpredictable outbreaks of the disease in humans. Accordingly, we present here a new model for the dynamics of Ross River Virus (RRV) in populations of mosquitoes and kangaroos. We calculate steady-state populations for the sub-groups in each species and demonstrate that naturally-occurring oscillations in the populations (limit cycles) do not occur. When seasonal forcing of vector populations and kangaroo birth rates is taken into account, however, the model may predict multi-annual outbreaks and chaos, perhaps explaining the unpredictability of some RRV disease epidemics, particularly across southern Australia. Detailed results in this case are presented.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"4 1","pages":"187 - 206"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2017.1359697","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44920221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-01-01DOI: 10.1080/23737867.2017.1302827
Katherine Snyder, B. Kohler, Luis F. Gordillo
Ideal gas models are a paradigm used in Biology for the phenomenological modelling of encounters between individuals of different types. These models have been used to approximate encounter rates given densities, velocities and distance within which an encounter certainly occurs. When using mass action in two-sex populations, however, it is necessary to recognize the difference between encounters and mating encounters. While the former refers in general to the (possibly simultaneous) collisions between particles, the latter represents pair formation that will produce offspring. The classical formulation of the law of mass action does not account this difference. In this short paper, we present an alternative derivation of the law of mass action that uses dimensional reduction together with simulated data. This straightforward approach allows to correct the expression for the rate of mating encounters between individuals in a two-sex population with relative ease. In addition, variability in mating encounter rates (due to environmental stochasticity) is numerically explored through random fluctuations on the new mass action proportionality constant. The simulations show how the conditioned time to extinction in a population subject to a reproductive Allee effect is affected.
{"title":"Mass action in two-sex population models: encounters, mating encounters and the associated numerical correction","authors":"Katherine Snyder, B. Kohler, Luis F. Gordillo","doi":"10.1080/23737867.2017.1302827","DOIUrl":"https://doi.org/10.1080/23737867.2017.1302827","url":null,"abstract":"Ideal gas models are a paradigm used in Biology for the phenomenological modelling of encounters between individuals of different types. These models have been used to approximate encounter rates given densities, velocities and distance within which an encounter certainly occurs. When using mass action in two-sex populations, however, it is necessary to recognize the difference between encounters and mating encounters. While the former refers in general to the (possibly simultaneous) collisions between particles, the latter represents pair formation that will produce offspring. The classical formulation of the law of mass action does not account this difference. In this short paper, we present an alternative derivation of the law of mass action that uses dimensional reduction together with simulated data. This straightforward approach allows to correct the expression for the rate of mating encounters between individuals in a two-sex population with relative ease. In addition, variability in mating encounter rates (due to environmental stochasticity) is numerically explored through random fluctuations on the new mass action proportionality constant. The simulations show how the conditioned time to extinction in a population subject to a reproductive Allee effect is affected.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"4 1","pages":"101 - 111"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2017.1302827","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48011768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-01-01DOI: 10.1080/23737867.2017.1401493
K. Larripa, A. Gallegos
Abstract New neurons are generated in the adult hippocampus throughout life by neural stem cells (NSCs) in a dynamic process responsive to external signalling cues. NSCs in the adult hippocampus divide infrequently, and it has been shown that bone morphogenetic protein (BMP) modulates their quiescence. Infusion of Noggin, a BMP antagonist, blocks this signalling. We investigate the balance of BMP and Noggin in this particular niche and qualitatively reproduce experimental results obtained and qualitatively reproduce experimental results with a one-dimensional reaction–diffusion model. We use the model to connect BMP signalling profiles with specific cellular outcomes and to determine whether the transient infusion of BMP leads to a signalling profile which can be reversed by the infusion of Noggin. Additionally, we analyse the role of diffusion in this system for generating signalling profiles with dramatically different cell-fate outcomes and show that diffusion-driven instability is not possible in our system of reaction–diffusion equations.
{"title":"A mathematical model of Noggin and BMP densities in adult neural stem cells","authors":"K. Larripa, A. Gallegos","doi":"10.1080/23737867.2017.1401493","DOIUrl":"https://doi.org/10.1080/23737867.2017.1401493","url":null,"abstract":"Abstract New neurons are generated in the adult hippocampus throughout life by neural stem cells (NSCs) in a dynamic process responsive to external signalling cues. NSCs in the adult hippocampus divide infrequently, and it has been shown that bone morphogenetic protein (BMP) modulates their quiescence. Infusion of Noggin, a BMP antagonist, blocks this signalling. We investigate the balance of BMP and Noggin in this particular niche and qualitatively reproduce experimental results obtained and qualitatively reproduce experimental results with a one-dimensional reaction–diffusion model. We use the model to connect BMP signalling profiles with specific cellular outcomes and to determine whether the transient infusion of BMP leads to a signalling profile which can be reversed by the infusion of Noggin. Additionally, we analyse the role of diffusion in this system for generating signalling profiles with dramatically different cell-fate outcomes and show that diffusion-driven instability is not possible in our system of reaction–diffusion equations.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"4 1","pages":"219 - 243"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2017.1401493","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49110229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-01-01DOI: 10.1080/23737867.2016.1248507
M. Kaplan, C. Manore, K. Bagamian
Abstract Behavioural and environmental heterogeneities among host populations can play an important role in hantavirus transmission. We designed an agent-based model to determine the relative role of direct and indirect transmission on Sin Nombre hantavirus (SNV) dynamics in deer mice, incorporating host heterogeneities. We parameterized the model to reproduce aggressive encounters, movement and excretions from field-based studies and lab experiments. Our model captured known properties of SNV spread and matched the outcomes of transmission experiments. Although the model was not fit to values, the distribution from our simulations was similar to values from other hantavirus models. We also found that a small per cent of mice were responsible for a high per cent of direct transmission. Our model indicated that mouse heterogeneity and environmental contamination are both important. Model extensions can explore larger ecosystem dynamics by incorporating temporal heterogeneity, to understand how changes in host characteristics and environment influence SNV transmission.
{"title":"Agent-based hantavirus transmission model incorporating host behavior and viral shedding heterogeneities derived from field transmission experiments","authors":"M. Kaplan, C. Manore, K. Bagamian","doi":"10.1080/23737867.2016.1248507","DOIUrl":"https://doi.org/10.1080/23737867.2016.1248507","url":null,"abstract":"Abstract Behavioural and environmental heterogeneities among host populations can play an important role in hantavirus transmission. We designed an agent-based model to determine the relative role of direct and indirect transmission on Sin Nombre hantavirus (SNV) dynamics in deer mice, incorporating host heterogeneities. We parameterized the model to reproduce aggressive encounters, movement and excretions from field-based studies and lab experiments. Our model captured known properties of SNV spread and matched the outcomes of transmission experiments. Although the model was not fit to values, the distribution from our simulations was similar to values from other hantavirus models. We also found that a small per cent of mice were responsible for a high per cent of direct transmission. Our model indicated that mouse heterogeneity and environmental contamination are both important. Model extensions can explore larger ecosystem dynamics by incorporating temporal heterogeneity, to understand how changes in host characteristics and environment influence SNV transmission.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"3 1","pages":"209 - 228"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2016.1248507","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60101947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-01-01DOI: 10.1080/23737867.2016.1221328
Kasthuri Kannan, A. Heguy
The mutant allele frequencies in oncogenes peak around .40 and rapidly decrease. In this article, we explain why this is the case. Invoking a key result from mathematical analysis in our model, namely, the inverse function theorem, we estimate the selection coefficients of the mutant alleles as a function of germline allele frequencies. Under complete dominance of oncogenic mutations, this selection function is expected to be linearly correlated with the distribution of the mutant alleles. We demonstrate that this is the case by investigating the allele frequencies of mutations in oncogenes across various cancer types, validating our model for mean effective selection. Consistent with the population genetics model of fitness, the selection function fits a gamma-distribution curve that accurately describes the trend of the mutant allele frequencies. While existing equations for selection explain evolution at low allele frequencies, our equations are general formulas for natural selection under complete dominance operating at all frequencies. We show that selection exhibits linear behaviour at all times, favouring dominant alleles with respect to the change in recessive allele frequencies. Also, these equations show, selection behaves like power law against the recessive alleles at low dominant allele frequencies.
{"title":"Why do mutant allele frequencies in oncogenes peak around .40 and rapidly decrease?","authors":"Kasthuri Kannan, A. Heguy","doi":"10.1080/23737867.2016.1221328","DOIUrl":"https://doi.org/10.1080/23737867.2016.1221328","url":null,"abstract":"The mutant allele frequencies in oncogenes peak around .40 and rapidly decrease. In this article, we explain why this is the case. Invoking a key result from mathematical analysis in our model, namely, the inverse function theorem, we estimate the selection coefficients of the mutant alleles as a function of germline allele frequencies. Under complete dominance of oncogenic mutations, this selection function is expected to be linearly correlated with the distribution of the mutant alleles. We demonstrate that this is the case by investigating the allele frequencies of mutations in oncogenes across various cancer types, validating our model for mean effective selection. Consistent with the population genetics model of fitness, the selection function fits a gamma-distribution curve that accurately describes the trend of the mutant allele frequencies. While existing equations for selection explain evolution at low allele frequencies, our equations are general formulas for natural selection under complete dominance operating at all frequencies. We show that selection exhibits linear behaviour at all times, favouring dominant alleles with respect to the change in recessive allele frequencies. Also, these equations show, selection behaves like power law against the recessive alleles at low dominant allele frequencies.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"3 1","pages":"200 - 208"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2016.1221328","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60101901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-01-01DOI: 10.1080/23737867.2016.1166075
Eric Eager
We study the equilibrium dynamics of a Lur’e system modelling a structured population, where adult conspecifics are assumed to have a negative density-dependent feedback on the recruitment of possible recruits. We find that, depending on the model’s parameter values, the population either goes extinct or has a positive equilibrium that is asymptotically stable, globally attracting or globally asymptotically stable. We apply our results to an integral projection model for the Platte thistle (Cirsium canescens) and highlight open aspects of this problem for future work.
{"title":"Modelling and analysis of population dynamics using Lur’e systems accounting for competition from adult conspecifics","authors":"Eric Eager","doi":"10.1080/23737867.2016.1166075","DOIUrl":"https://doi.org/10.1080/23737867.2016.1166075","url":null,"abstract":"We study the equilibrium dynamics of a Lur’e system modelling a structured population, where adult conspecifics are assumed to have a negative density-dependent feedback on the recruitment of possible recruits. We find that, depending on the model’s parameter values, the population either goes extinct or has a positive equilibrium that is asymptotically stable, globally attracting or globally asymptotically stable. We apply our results to an integral projection model for the Platte thistle (Cirsium canescens) and highlight open aspects of this problem for future work.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"3 1","pages":"41 - 58"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2016.1166075","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60102249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-01-01DOI: 10.1080/23737867.2016.1217757
David J. Gerberry, A. M. Philip
In modelling, the dynamics of infectious disease, the choice of the specific mathematical formulation of disease transmission (i.e. the incidence function) is one of the initial assumptions to be made. While inconsequential in many situations, we show that the incidence function can have an effect on the existence of backward bifurcation (the phenomenon where a disease can persist even when the basic reproductive number is less than 1). More specifically, we compare mass action (MA) and standard incidence (SI) (the most common incidence functions) versions of two hallmark models in the backward bifurcation literature and an original combination model. Our findings indicate that the SI formation of disease transmission is more conducive to backward bifurcation than MA, a trend seen in all the models analysed.
{"title":"The effect of the incidence function on the existence of backward bifurcation","authors":"David J. Gerberry, A. M. Philip","doi":"10.1080/23737867.2016.1217757","DOIUrl":"https://doi.org/10.1080/23737867.2016.1217757","url":null,"abstract":"In modelling, the dynamics of infectious disease, the choice of the specific mathematical formulation of disease transmission (i.e. the incidence function) is one of the initial assumptions to be made. While inconsequential in many situations, we show that the incidence function can have an effect on the existence of backward bifurcation (the phenomenon where a disease can persist even when the basic reproductive number is less than 1). More specifically, we compare mass action (MA) and standard incidence (SI) (the most common incidence functions) versions of two hallmark models in the backward bifurcation literature and an original combination model. Our findings indicate that the SI formation of disease transmission is more conducive to backward bifurcation than MA, a trend seen in all the models analysed.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"3 1","pages":"181 - 199"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2016.1217757","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60102334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-01-01DOI: 10.1080/23737867.2016.1213146
Banamali Maji, Joydeb Bhattacharyya, Samares Pal
The invasion of predatory lionfish (Pterois volitans) represents a major threat to the western Atlantic coral reef ecosystems. The proliferation of venomous, fast reproducing and aggressive P. volitans in coral reefs causes severe declines in the abundance and diversity of reef herbivores. There is also widespread cannibalism amongst P. volitans populations. A mathematical model is proposed to study the effects of predation on the biomass of herbivorous reef fishes by considering two life stages and intraguild predation of P. volitans population with harvesting of adult P. volitans. The system undergoes a supercritical Hopf bifurcation when the invasiveness of P. volitans crosses a certain critical value. It is observed that cannibalism of P. volitans induces stability in the system even with high invasiveness of adult P. volitans. The dynamic instability of the system due to higher invasiveness of P. volitans can be controlled by increasing the rate of harvesting of P. volitans. It is also proven that P. volitans goes extinct when the harvest rate is greater than some critical threshold value. These results indicate that the dynamical behaviour of the model is very sensitive to the harvesting of P. volitans, which in turn is useful in the conservation of reef herbivores.
{"title":"Potential effects of invasive Pterois volitans in coral reefs","authors":"Banamali Maji, Joydeb Bhattacharyya, Samares Pal","doi":"10.1080/23737867.2016.1213146","DOIUrl":"https://doi.org/10.1080/23737867.2016.1213146","url":null,"abstract":"The invasion of predatory lionfish (Pterois volitans) represents a major threat to the western Atlantic coral reef ecosystems. The proliferation of venomous, fast reproducing and aggressive P. volitans in coral reefs causes severe declines in the abundance and diversity of reef herbivores. There is also widespread cannibalism amongst P. volitans populations. A mathematical model is proposed to study the effects of predation on the biomass of herbivorous reef fishes by considering two life stages and intraguild predation of P. volitans population with harvesting of adult P. volitans. The system undergoes a supercritical Hopf bifurcation when the invasiveness of P. volitans crosses a certain critical value. It is observed that cannibalism of P. volitans induces stability in the system even with high invasiveness of adult P. volitans. The dynamic instability of the system due to higher invasiveness of P. volitans can be controlled by increasing the rate of harvesting of P. volitans. It is also proven that P. volitans goes extinct when the harvest rate is greater than some critical threshold value. These results indicate that the dynamical behaviour of the model is very sensitive to the harvesting of P. volitans, which in turn is useful in the conservation of reef herbivores.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"3 1","pages":"119 - 139"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2016.1213146","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60101877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-01-01DOI: 10.1080/23737867.2016.1157449
E. Agyingi, M. Ngwa, T. Wiandt
This paper presents a deterministic SIS model for the transmission dynamics of malaria, a life-threatening disease transmitted by mosquitos. Four species of the parasite genus Plasmodium are known to cause human malaria. Some species of the parasite have evolved into strains that are resistant to treatment. Although proportions of Plasmodium species vary considerably between geographic regions, multiple species and strains do coexist within some communities. The mathematical model derived here includes all available species and strains for a given community. The model has a disease-free equilibrium, which is a global attractor when the reproduction number of each species or strain is less than one. The model possesses quasi-endemic equilibria; local asymptotic stability is established for two species, and numerical simulations suggest that the species or strain with the highest reproduction number exhibits competitive exclusion.
{"title":"The dynamics of multiple species and strains of malaria","authors":"E. Agyingi, M. Ngwa, T. Wiandt","doi":"10.1080/23737867.2016.1157449","DOIUrl":"https://doi.org/10.1080/23737867.2016.1157449","url":null,"abstract":"This paper presents a deterministic SIS model for the transmission dynamics of malaria, a life-threatening disease transmitted by mosquitos. Four species of the parasite genus Plasmodium are known to cause human malaria. Some species of the parasite have evolved into strains that are resistant to treatment. Although proportions of Plasmodium species vary considerably between geographic regions, multiple species and strains do coexist within some communities. The mathematical model derived here includes all available species and strains for a given community. The model has a disease-free equilibrium, which is a global attractor when the reproduction number of each species or strain is less than one. The model possesses quasi-endemic equilibria; local asymptotic stability is established for two species, and numerical simulations suggest that the species or strain with the highest reproduction number exhibits competitive exclusion.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"52 1","pages":"29 - 40"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2016.1157449","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60102209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-01-01DOI: 10.1080/23737867.2016.1185979
C. Seibold, H. Callender
We will first provide a brief introduction to models of disease transmission on so-called contact networks, which can be represented by various structures from the mathematical field of graph theory. These models allow for exploration of stochastic effects and incorporation of more biological detail than the classical compartment-based ordinary differential equation models, which usually assume both homogeneity in the population and uniform mixing. In particular, we use an agent-based modelling platform to compare theoretical predictions from mathematical epidemiology to results obtained from simulations of disease transmission on a regular tree graph. We also demonstrate how this graph reveals connections between network structure and the spread of infectious diseases. Specifically, we discuss results for how certain properties of the tree graph, such as network diameter and density, alter the duration of an outbreak.
{"title":"Modeling epidemics on a regular tree graph","authors":"C. Seibold, H. Callender","doi":"10.1080/23737867.2016.1185979","DOIUrl":"https://doi.org/10.1080/23737867.2016.1185979","url":null,"abstract":"We will first provide a brief introduction to models of disease transmission on so-called contact networks, which can be represented by various structures from the mathematical field of graph theory. These models allow for exploration of stochastic effects and incorporation of more biological detail than the classical compartment-based ordinary differential equation models, which usually assume both homogeneity in the population and uniform mixing. In particular, we use an agent-based modelling platform to compare theoretical predictions from mathematical epidemiology to results obtained from simulations of disease transmission on a regular tree graph. We also demonstrate how this graph reveals connections between network structure and the spread of infectious diseases. Specifically, we discuss results for how certain properties of the tree graph, such as network diameter and density, alter the duration of an outbreak.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"3 1","pages":"59 - 74"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2016.1185979","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60102260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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