<div><p>(A) The three curves refer, respectively, to strong (<i>K<sub>dd′... more <div><p>(A) The three curves refer, respectively, to strong (<i>K<sub>dd′</sub></i> = 0.01 nM, blue), medium (<i>K<sub>dd′</sub></i> = 1 nM, red), and weak (<i>K<sub>dd′</sub></i> = 100 nM, black) binding between UmuD and UmuD′.</p><p>(B) The effects of changing the binding constant between the UmuD′ homodimer and UmuC: as binding strength 1/<i>K</i> in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030041#pcbi-0030041-e012" target="_blank">Equation 12</a> increases (<i>K</i> = 100,10,1 nM for the green, blue, and red curves, respectively), the Pol V concentration saturates at the 200 nM value set by the maximum cellular level of UmuC.</p><p>(C) For strong binding (<i>K<sub>dd′</sub></i> = 0.01 nM), the three curves show the effect of increasing the degradation rate <i>γ<sub>dd′</sub></i> of UmuD′ by ClpX. As a default, the degradation rate is set equal to the dilution rate <i>γ<sub>dil</sub></i> (blue). The rate is half of the dilution rate for the red curve, whereas it is zero for the black curve. For the green curve, the degradation rate is double that of the dilution rate, which—at this level of UV damage—results in almost no Pol V.</p><p>(D) The effect of removing the Pol V to RecA* feedback. The blue curve is when there is feedback (as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030041#pcbi-0030041-g007" target="_blank">Figure 7</a> A–C). The green curve is when there is no feedback, i.e., τ<i><sub>stalled</sub></i> = τ<i>stalled</i>(0), irrespective of the Pol V level.</p></div
<p>(A) A simple modification scheme previously shown to be capable of giving heritable bist... more <p>(A) A simple modification scheme previously shown to be capable of giving heritable bistability <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002643#pcbi.1002643-Micheelsen1" target="_blank">[24]</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002643#pcbi.1002643-Dodd2" target="_blank">[25]</a> in which one residue per nucleosome is either unmodified (0) or modified (1), generating two nucleosome types, each associated with a distinct epigenetic regulatory state (E1 or E2). The grey box indicates the nucleosome type (R) that is added after DNA replication, which causes roughly half of the nucleosomes in the system to be converted to the R type. Interconversion reactions (red arrows) may occur at a rate that is unaffected by nearby nucleosomes (dashed red arrows) or are stimulated by enzymes recruited by other nucleosomes (green arrows). The green double-tailed arrow indicates direct cooperativity due to recruitment by two nucleosomes. (B) A three nucleosome-type scheme also shown to give heritable bistability <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002643#pcbi.1002643-Dodd1" target="_blank">[11]</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002643#pcbi.1002643-Sneppen1" target="_blank">[21]</a>, in which a single residue per nucleosome can exist in three modification states (e.g. H3K9ac, H3K9 and H3K9me). (C) Extended scheme analyzed here in which each nucleosome can be modified (1) or not (0) at two different histone positions, making a total of 4 nucleosome types (00, 10, 01, 11; e.g. H3K4K9, H3K4meK9, H3K4K9me, H3K4meK9me). [Note that our model effectively only considers the modification combinations for each half-nucleosome (one copy of each histone protein), whereas two binary modifications on each half nucleosome give 10 different full-nucleosome types (00/00, 00/01, 00/10, 00/11, 01/01, 01/10, 01/11, 10/10, 10/11, 11/11)]. Enzymatic transitions between types are by addition or removal of one modification. Each of the patterns of recruitment-reaction connections are defined by a specific circuit code that lists the recruiting nucleosome (0, 1, 2, 3) for each of the eight reactions; non-recruited ‘noise’ transitions are denoted ‘x’. We term the specific circuit shown in (C) the “classical” motif due to its similarity with the previously studied three nucleosome-type motif shown in (B). (D) Time course displaying strong bistability for the circuit in (C), showing the numbers of E1 and E2 nucleosomes in a 30 nucleosome system (with noise level ).</p
<p>In each network and are co-transcribed. The upper two networks (<i>p.lyt.cII</i... more <p>In each network and are co-transcribed. The upper two networks (<i>p.lyt.cII</i>) work at the standard 6% noise level, while in the lower network CII production is shut off after the first replication (<i>cII shut-off</i>). This network functions at a 20% noise level. The left panels are as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0015037#pone-0015037-g003" target="_blank">Figure 3</a>. The right panels show the time development of CII. All times are shown in units of the phage genome replication time, whereas CII levels are shown in units of its binding constant for activation of Lys protein production.</p
<div><p>(A) Height of the first (blue curve) and second (red curve) peaks in LexA-reg... more <div><p>(A) Height of the first (blue curve) and second (red curve) peaks in LexA-regulated promoter activity, averaged more than 200 runs each with a different value of <i>N<sub>f</sub></i>, uniformly distributed between 1 and 3 (other parameters remained fixed as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030041#pcbi-0030041-g004" target="_blank">Figure 4</a>) as a function of the UV dose. Red circles and blue triangles show the corresponding data from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030041#pcbi-0030041-g004" target="_blank">Figure 4</a>C of [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030041#pcbi-0030041-b010" target="_blank">10</a>]. To facilitate comparison, the height of the red (blue) curve was normalized to match the maximum experimentally observed peak activity.</p><p>(B) The peak heights as a function of UV dose for a single run with <i>N<sub>f</sub></i> = 2, with the same normalization as in (A). The saturation of peak heights for increasing UV doses in our model is a consequence of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030041#pcbi-0030041-e003" target="_blank">Equation 3</a>.</p></div
Phages and bacteria manage to coexist and sustain ecosystems with a high diversity of strains, de... more Phages and bacteria manage to coexist and sustain ecosystems with a high diversity of strains, despite limited resources and heavy predation. This diversity can be explained by the “kill the winner” model where virulent phages predominantly prey on fast-growing bacteria and thereby suppress the competitive exclusion of slower-growing bacteria. Here we computationally investigate the robustness of these systems against invasions, where new phages or bacteria may interact with more than one of the resident strains. The resulting interaction networks were found to self-organize into a network with strongly interacting specialized predator-prey pairs, resembling that of the “kill the winner” model. Furthermore, the “kill the winner” dynamics is enforced with the occasional elimination of even the fastest-growing bacteria strains due to a phage infecting the fast and slow growers. The frequency of slower-growing strains was increased with the introduction of even a few non-diagonal inter...
The West African Ebola (2014-2016) epidemic caused an estimated 11.310 deaths and massive social ... more The West African Ebola (2014-2016) epidemic caused an estimated 11.310 deaths and massive social and economic disruption. The epidemic was comprised of many local outbreaks of varying sizes. However, often local outbreaks recede before the arrival of international aid or susceptible depletion. We modeled Ebola virus transmission under the effect of behavior changes acting as a local inhibitor. A spatial model is used to simulate Ebola epidemics. Our findings suggest that behavior changes can explain why local Ebola outbreaks recede before substantial international aid was mobilized during the 2014-2016 epidemic.
Although coronavirus disease 2019 (COVID-19) has caused severe suffering in many countries around... more Although coronavirus disease 2019 (COVID-19) has caused severe suffering in many countries around the world, the efficacy of non-pharmaceutical interventions such as policies of social distancing has been greater than models have predicted. Meanwhile, evidence is mounting that the pandemic is characterized by superspreading, where a small fraction account for the majority of infections. Capturing this phenomenon theoretically requires modeling at the scale of individuals. Using a mathematical model, we show that superspreading represents an Achilles' heel of COVID-19, and drastically improves the efficacy of mitigations which reduce the personal contact number, even when this is done without changing the average social contact time.
Raul Donangelo, ∗ Mogens H. Jensen, † Ingve Simonsen, 4, ‡ and Kim Sneppen § Instituto de Fisica ... more Raul Donangelo, ∗ Mogens H. Jensen, † Ingve Simonsen, 4, ‡ and Kim Sneppen § Instituto de Fisica da UFRJ, Caixa Postal 68528, 21941-972 Rio de Janeiro, Brazil The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark Department of physics, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway NORDITA, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark (Dated: February 2, 2008)
The SARS-CoV-2 ancestral strain has caused pronounced super-spreading events, reflecting a diseas... more The SARS-CoV-2 ancestral strain has caused pronounced super-spreading events, reflecting a disease characterized by overdispersion, where about 10% of infected people causes 80% of infections. New variants of the disease have different person-to-person variations in viral load, suggesting for example that the Alpha (B.1.1.7) variant is more infectious but relatively less prone to superspreading. Meanwhile, mitigation of the pandemic has focused on limiting social contacts (lockdowns, regulations on gatherings) and decreasing transmission risk through mask wearing and social distancing. Using a mathematical model, we show that the competitive advantage of disease variants may heavily depend on the restrictions imposed. In particular, we find that lockdowns exert an evolutionary pressure which favours variants with lower levels of overdispersion. We find that overdispersion is an evolutionarily unstable trait, with a tendency for more homogeneously spreading variants to eventually dom...
1Restriction-modification (RM) systems are the most ubiquitous bacterial defense system against b... more 1Restriction-modification (RM) systems are the most ubiquitous bacterial defense system against bacteriophages and an important part of controlling phage predation. Using genomic sequence data, we show that RM systems are often shared among bacterial strains in a structured way. Examining the network of interconnections between bacterial strains within each genus, we find that in many genera strains share more RM systems than expected from a random network. We also find that many genera have a larger than expected number of bacterial strains with unique RM systems. We use population dynamics models of closed and open phage-bacteria ecosystems to qualitatively understand the selection pressures that could lead to these non-random network structures with enhanced overlap or uniqueness. In our models we find that the phages impose a pressure that favours bacteria with more RM systems, and more overlap of RM systems with other strains, but in bacteria dominated states this is opposed by...
Proceedings of the National Academy of Sciences, 2021
Significance Evidence indicates that superspreading plays a dominant role in COVID-19 transmissio... more Significance Evidence indicates that superspreading plays a dominant role in COVID-19 transmission, so that a small fraction of infected people causes a large proportion of new COVID-19 cases. We developed an agent-based model that simulates a superspreading disease moving through a society with networks of both repeated contacts and nonrepeated, random contacts. The results indicate that superspreading is the virus’ Achilles’ heel: Reducing random contacts—such as those that occur at sporting events, restaurants, bars, and the like—can control the outbreak at population scales.
So far, the COVID-19 pandemic has been characterised by an initial rapid rise in new cases follow... more So far, the COVID-19 pandemic has been characterised by an initial rapid rise in new cases followed by a peak and a more erratic behaviour that varies between regions. This is not easy to reproduce with traditional SIR models, which predict a more symmetric epidemic. Here, we argue that superspreaders and population heterogeneity are the core factors explaining this discrepancy. We do so through an agent-based lattice model of a disease spreading in a heterogeneous population. We predict that an epidemic driven by superspreaders will spread rapidly in cities, but not in the countryside where the sparse population limits the maximal number of secondary infections. This suggests that mitigation strategies should include restrictions on venues where people meet a large number of strangers. Furthermore, mitigating the epidemic in cities and in the countryside may require different levels of restrictions.
BackgroundThe draconian measures used to control COVID-19 dissemination have been highly effectiv... more BackgroundThe draconian measures used to control COVID-19 dissemination have been highly effective but only at enormous socioeconomic cost. Evidence suggests that “superspreaders” who transmit the virus to a large number of people, play a substantial role in transmission; recent estimates suggest that about 1-20% of people with the virus are the source for about 80% of infections. We used an agent-based model to explore the interplay between social structure, mitigation and superspreading.MethodsWe developed an agent-based model with a subset of “superspreader” agents that transmit disease far more efficiently. These agents act in a social network that allows transmission during contacts in three sectors: “home,” “work/school” and “other”. We simulated the effect of various mitigation strategies that limit contacts in each of these sectors, and used the model to fit COVID-19 mortality data from Sweden.FindingsReducing contacts in the “other” sector had a far greater impact on epidem...
ABSTRACTThe international community has been put in an unprecedented situation by the COVID-19 pa... more ABSTRACTThe international community has been put in an unprecedented situation by the COVID-19 pandemic. Creating models to describe and quantify alternative mitigation strategies becomes increasingly urgent. In this study, we propose an agent-based model of disease transmission in a society divided into closely connected families, workplaces, and social groups. This allows us to discuss mitigation strategies, including targeted quarantine measures. We find that workplace and more diffuse social contacts are roughly equally important to disease spread, and that an effective lockdown must target both. We examine the cost-benefit of replacing a lockdown with tracing and quarantining contacts of the infected. Quarantine can contribute substantially to mitigation, even if it has short duration and is done within households. When reopening society, testing and quarantining is a strategy that is much cheaper in terms of lost workdays than a long lockdown of workplaces. A targeted quaranti...
Disease and predation are both highly important in ecology, and pathogens with multiple host spec... more Disease and predation are both highly important in ecology, and pathogens with multiple host species have turned out to be common. Nonetheless, the interplay between multi-host epidemics and predation has received relatively little attention. Here, we analyse a model of a predator-prey system with disease in both prey and predator populations and determine reasonable parameter values using allometric mass scaling relations. Our analysis focuses on the possibility of extinction events rather than the linear stability of the model equations. We find that if the predator is a specialist, epidemics frequently drive the predator species to extinction. If the predator has an additional, immune prey species, predators will usually survive. Coexistence of predator and disease is impossible in the single-prey model. We conclude that for the prey species, carrying a pathogen can be an effective weapon against predators, and that being a generalist is a major advantage for a predator.
Natural bacterial populations are subject to constant predation pressure by phages. Bacteria use ... more Natural bacterial populations are subject to constant predation pressure by phages. Bacteria use a variety of well-studied molecular mechanisms to defend themselves from phage predation. However, since phage are non-motile, perhaps the simplest defense against phage would be for bacteria to outrun their predators. In particular, chemotaxis, the active migration of bacteria up attractant gradients, may help the bacteria escape slowly diffusing phages. Here we study phage infection dynamics in migrating bacterial populations driven by chemotaxis through low viscosity agar plates. We find that expanding phage-bacteria populations support two migrating fronts, an outermost “bacterial” front driven by nutrient uptake and chemotaxis and an inner “phage” front at which bacterial population collapses due to phage predation. We show that with increasing adsorption rate and initial phage population, the rate of migration of the phage front increases, eventually overtaking the bacterial front ...
<div><p>(A) The three curves refer, respectively, to strong (<i>K<sub>dd′... more <div><p>(A) The three curves refer, respectively, to strong (<i>K<sub>dd′</sub></i> = 0.01 nM, blue), medium (<i>K<sub>dd′</sub></i> = 1 nM, red), and weak (<i>K<sub>dd′</sub></i> = 100 nM, black) binding between UmuD and UmuD′.</p><p>(B) The effects of changing the binding constant between the UmuD′ homodimer and UmuC: as binding strength 1/<i>K</i> in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030041#pcbi-0030041-e012" target="_blank">Equation 12</a> increases (<i>K</i> = 100,10,1 nM for the green, blue, and red curves, respectively), the Pol V concentration saturates at the 200 nM value set by the maximum cellular level of UmuC.</p><p>(C) For strong binding (<i>K<sub>dd′</sub></i> = 0.01 nM), the three curves show the effect of increasing the degradation rate <i>γ<sub>dd′</sub></i> of UmuD′ by ClpX. As a default, the degradation rate is set equal to the dilution rate <i>γ<sub>dil</sub></i> (blue). The rate is half of the dilution rate for the red curve, whereas it is zero for the black curve. For the green curve, the degradation rate is double that of the dilution rate, which—at this level of UV damage—results in almost no Pol V.</p><p>(D) The effect of removing the Pol V to RecA* feedback. The blue curve is when there is feedback (as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030041#pcbi-0030041-g007" target="_blank">Figure 7</a> A–C). The green curve is when there is no feedback, i.e., τ<i><sub>stalled</sub></i> = τ<i>stalled</i>(0), irrespective of the Pol V level.</p></div
<p>(A) A simple modification scheme previously shown to be capable of giving heritable bist... more <p>(A) A simple modification scheme previously shown to be capable of giving heritable bistability <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002643#pcbi.1002643-Micheelsen1" target="_blank">[24]</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002643#pcbi.1002643-Dodd2" target="_blank">[25]</a> in which one residue per nucleosome is either unmodified (0) or modified (1), generating two nucleosome types, each associated with a distinct epigenetic regulatory state (E1 or E2). The grey box indicates the nucleosome type (R) that is added after DNA replication, which causes roughly half of the nucleosomes in the system to be converted to the R type. Interconversion reactions (red arrows) may occur at a rate that is unaffected by nearby nucleosomes (dashed red arrows) or are stimulated by enzymes recruited by other nucleosomes (green arrows). The green double-tailed arrow indicates direct cooperativity due to recruitment by two nucleosomes. (B) A three nucleosome-type scheme also shown to give heritable bistability <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002643#pcbi.1002643-Dodd1" target="_blank">[11]</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002643#pcbi.1002643-Sneppen1" target="_blank">[21]</a>, in which a single residue per nucleosome can exist in three modification states (e.g. H3K9ac, H3K9 and H3K9me). (C) Extended scheme analyzed here in which each nucleosome can be modified (1) or not (0) at two different histone positions, making a total of 4 nucleosome types (00, 10, 01, 11; e.g. H3K4K9, H3K4meK9, H3K4K9me, H3K4meK9me). [Note that our model effectively only considers the modification combinations for each half-nucleosome (one copy of each histone protein), whereas two binary modifications on each half nucleosome give 10 different full-nucleosome types (00/00, 00/01, 00/10, 00/11, 01/01, 01/10, 01/11, 10/10, 10/11, 11/11)]. Enzymatic transitions between types are by addition or removal of one modification. Each of the patterns of recruitment-reaction connections are defined by a specific circuit code that lists the recruiting nucleosome (0, 1, 2, 3) for each of the eight reactions; non-recruited ‘noise’ transitions are denoted ‘x’. We term the specific circuit shown in (C) the “classical” motif due to its similarity with the previously studied three nucleosome-type motif shown in (B). (D) Time course displaying strong bistability for the circuit in (C), showing the numbers of E1 and E2 nucleosomes in a 30 nucleosome system (with noise level ).</p
<p>In each network and are co-transcribed. The upper two networks (<i>p.lyt.cII</i... more <p>In each network and are co-transcribed. The upper two networks (<i>p.lyt.cII</i>) work at the standard 6% noise level, while in the lower network CII production is shut off after the first replication (<i>cII shut-off</i>). This network functions at a 20% noise level. The left panels are as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0015037#pone-0015037-g003" target="_blank">Figure 3</a>. The right panels show the time development of CII. All times are shown in units of the phage genome replication time, whereas CII levels are shown in units of its binding constant for activation of Lys protein production.</p
<div><p>(A) Height of the first (blue curve) and second (red curve) peaks in LexA-reg... more <div><p>(A) Height of the first (blue curve) and second (red curve) peaks in LexA-regulated promoter activity, averaged more than 200 runs each with a different value of <i>N<sub>f</sub></i>, uniformly distributed between 1 and 3 (other parameters remained fixed as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030041#pcbi-0030041-g004" target="_blank">Figure 4</a>) as a function of the UV dose. Red circles and blue triangles show the corresponding data from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030041#pcbi-0030041-g004" target="_blank">Figure 4</a>C of [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030041#pcbi-0030041-b010" target="_blank">10</a>]. To facilitate comparison, the height of the red (blue) curve was normalized to match the maximum experimentally observed peak activity.</p><p>(B) The peak heights as a function of UV dose for a single run with <i>N<sub>f</sub></i> = 2, with the same normalization as in (A). The saturation of peak heights for increasing UV doses in our model is a consequence of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030041#pcbi-0030041-e003" target="_blank">Equation 3</a>.</p></div
Phages and bacteria manage to coexist and sustain ecosystems with a high diversity of strains, de... more Phages and bacteria manage to coexist and sustain ecosystems with a high diversity of strains, despite limited resources and heavy predation. This diversity can be explained by the “kill the winner” model where virulent phages predominantly prey on fast-growing bacteria and thereby suppress the competitive exclusion of slower-growing bacteria. Here we computationally investigate the robustness of these systems against invasions, where new phages or bacteria may interact with more than one of the resident strains. The resulting interaction networks were found to self-organize into a network with strongly interacting specialized predator-prey pairs, resembling that of the “kill the winner” model. Furthermore, the “kill the winner” dynamics is enforced with the occasional elimination of even the fastest-growing bacteria strains due to a phage infecting the fast and slow growers. The frequency of slower-growing strains was increased with the introduction of even a few non-diagonal inter...
The West African Ebola (2014-2016) epidemic caused an estimated 11.310 deaths and massive social ... more The West African Ebola (2014-2016) epidemic caused an estimated 11.310 deaths and massive social and economic disruption. The epidemic was comprised of many local outbreaks of varying sizes. However, often local outbreaks recede before the arrival of international aid or susceptible depletion. We modeled Ebola virus transmission under the effect of behavior changes acting as a local inhibitor. A spatial model is used to simulate Ebola epidemics. Our findings suggest that behavior changes can explain why local Ebola outbreaks recede before substantial international aid was mobilized during the 2014-2016 epidemic.
Although coronavirus disease 2019 (COVID-19) has caused severe suffering in many countries around... more Although coronavirus disease 2019 (COVID-19) has caused severe suffering in many countries around the world, the efficacy of non-pharmaceutical interventions such as policies of social distancing has been greater than models have predicted. Meanwhile, evidence is mounting that the pandemic is characterized by superspreading, where a small fraction account for the majority of infections. Capturing this phenomenon theoretically requires modeling at the scale of individuals. Using a mathematical model, we show that superspreading represents an Achilles' heel of COVID-19, and drastically improves the efficacy of mitigations which reduce the personal contact number, even when this is done without changing the average social contact time.
Raul Donangelo, ∗ Mogens H. Jensen, † Ingve Simonsen, 4, ‡ and Kim Sneppen § Instituto de Fisica ... more Raul Donangelo, ∗ Mogens H. Jensen, † Ingve Simonsen, 4, ‡ and Kim Sneppen § Instituto de Fisica da UFRJ, Caixa Postal 68528, 21941-972 Rio de Janeiro, Brazil The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark Department of physics, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway NORDITA, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark (Dated: February 2, 2008)
The SARS-CoV-2 ancestral strain has caused pronounced super-spreading events, reflecting a diseas... more The SARS-CoV-2 ancestral strain has caused pronounced super-spreading events, reflecting a disease characterized by overdispersion, where about 10% of infected people causes 80% of infections. New variants of the disease have different person-to-person variations in viral load, suggesting for example that the Alpha (B.1.1.7) variant is more infectious but relatively less prone to superspreading. Meanwhile, mitigation of the pandemic has focused on limiting social contacts (lockdowns, regulations on gatherings) and decreasing transmission risk through mask wearing and social distancing. Using a mathematical model, we show that the competitive advantage of disease variants may heavily depend on the restrictions imposed. In particular, we find that lockdowns exert an evolutionary pressure which favours variants with lower levels of overdispersion. We find that overdispersion is an evolutionarily unstable trait, with a tendency for more homogeneously spreading variants to eventually dom...
1Restriction-modification (RM) systems are the most ubiquitous bacterial defense system against b... more 1Restriction-modification (RM) systems are the most ubiquitous bacterial defense system against bacteriophages and an important part of controlling phage predation. Using genomic sequence data, we show that RM systems are often shared among bacterial strains in a structured way. Examining the network of interconnections between bacterial strains within each genus, we find that in many genera strains share more RM systems than expected from a random network. We also find that many genera have a larger than expected number of bacterial strains with unique RM systems. We use population dynamics models of closed and open phage-bacteria ecosystems to qualitatively understand the selection pressures that could lead to these non-random network structures with enhanced overlap or uniqueness. In our models we find that the phages impose a pressure that favours bacteria with more RM systems, and more overlap of RM systems with other strains, but in bacteria dominated states this is opposed by...
Proceedings of the National Academy of Sciences, 2021
Significance Evidence indicates that superspreading plays a dominant role in COVID-19 transmissio... more Significance Evidence indicates that superspreading plays a dominant role in COVID-19 transmission, so that a small fraction of infected people causes a large proportion of new COVID-19 cases. We developed an agent-based model that simulates a superspreading disease moving through a society with networks of both repeated contacts and nonrepeated, random contacts. The results indicate that superspreading is the virus’ Achilles’ heel: Reducing random contacts—such as those that occur at sporting events, restaurants, bars, and the like—can control the outbreak at population scales.
So far, the COVID-19 pandemic has been characterised by an initial rapid rise in new cases follow... more So far, the COVID-19 pandemic has been characterised by an initial rapid rise in new cases followed by a peak and a more erratic behaviour that varies between regions. This is not easy to reproduce with traditional SIR models, which predict a more symmetric epidemic. Here, we argue that superspreaders and population heterogeneity are the core factors explaining this discrepancy. We do so through an agent-based lattice model of a disease spreading in a heterogeneous population. We predict that an epidemic driven by superspreaders will spread rapidly in cities, but not in the countryside where the sparse population limits the maximal number of secondary infections. This suggests that mitigation strategies should include restrictions on venues where people meet a large number of strangers. Furthermore, mitigating the epidemic in cities and in the countryside may require different levels of restrictions.
BackgroundThe draconian measures used to control COVID-19 dissemination have been highly effectiv... more BackgroundThe draconian measures used to control COVID-19 dissemination have been highly effective but only at enormous socioeconomic cost. Evidence suggests that “superspreaders” who transmit the virus to a large number of people, play a substantial role in transmission; recent estimates suggest that about 1-20% of people with the virus are the source for about 80% of infections. We used an agent-based model to explore the interplay between social structure, mitigation and superspreading.MethodsWe developed an agent-based model with a subset of “superspreader” agents that transmit disease far more efficiently. These agents act in a social network that allows transmission during contacts in three sectors: “home,” “work/school” and “other”. We simulated the effect of various mitigation strategies that limit contacts in each of these sectors, and used the model to fit COVID-19 mortality data from Sweden.FindingsReducing contacts in the “other” sector had a far greater impact on epidem...
ABSTRACTThe international community has been put in an unprecedented situation by the COVID-19 pa... more ABSTRACTThe international community has been put in an unprecedented situation by the COVID-19 pandemic. Creating models to describe and quantify alternative mitigation strategies becomes increasingly urgent. In this study, we propose an agent-based model of disease transmission in a society divided into closely connected families, workplaces, and social groups. This allows us to discuss mitigation strategies, including targeted quarantine measures. We find that workplace and more diffuse social contacts are roughly equally important to disease spread, and that an effective lockdown must target both. We examine the cost-benefit of replacing a lockdown with tracing and quarantining contacts of the infected. Quarantine can contribute substantially to mitigation, even if it has short duration and is done within households. When reopening society, testing and quarantining is a strategy that is much cheaper in terms of lost workdays than a long lockdown of workplaces. A targeted quaranti...
Disease and predation are both highly important in ecology, and pathogens with multiple host spec... more Disease and predation are both highly important in ecology, and pathogens with multiple host species have turned out to be common. Nonetheless, the interplay between multi-host epidemics and predation has received relatively little attention. Here, we analyse a model of a predator-prey system with disease in both prey and predator populations and determine reasonable parameter values using allometric mass scaling relations. Our analysis focuses on the possibility of extinction events rather than the linear stability of the model equations. We find that if the predator is a specialist, epidemics frequently drive the predator species to extinction. If the predator has an additional, immune prey species, predators will usually survive. Coexistence of predator and disease is impossible in the single-prey model. We conclude that for the prey species, carrying a pathogen can be an effective weapon against predators, and that being a generalist is a major advantage for a predator.
Natural bacterial populations are subject to constant predation pressure by phages. Bacteria use ... more Natural bacterial populations are subject to constant predation pressure by phages. Bacteria use a variety of well-studied molecular mechanisms to defend themselves from phage predation. However, since phage are non-motile, perhaps the simplest defense against phage would be for bacteria to outrun their predators. In particular, chemotaxis, the active migration of bacteria up attractant gradients, may help the bacteria escape slowly diffusing phages. Here we study phage infection dynamics in migrating bacterial populations driven by chemotaxis through low viscosity agar plates. We find that expanding phage-bacteria populations support two migrating fronts, an outermost “bacterial” front driven by nutrient uptake and chemotaxis and an inner “phage” front at which bacterial population collapses due to phage predation. We show that with increasing adsorption rate and initial phage population, the rate of migration of the phage front increases, eventually overtaking the bacterial front ...
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Papers by Kim Sneppen