Jonathan Dushoff
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Jonathan Dushoff has a total of 221 co-authors. Here are the top co-authors by number of shared publications:
- Joshua S. Weitz
Department of Biology, University of Maryland, College Park, MD 20742, USA
24 shared publications - Sang Woo Park
School of Biological Sciences, Seoul National University, Seoul, Korea
19 shared publications - David J. D. Earn
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
16 shared publications - Benjamin Michael Bolker
McMaster University
14 shared publications - David Champredon
Public Health Agency of Canada
13 shared publications - Michael Li
Public Health Agency of Canada
8 shared publications
Latest Publications
- Open Access
- 1 July 2026
- Published by Oxford University Press (OUP) in Virus Evolution
- Vol. 12 (1)
Differences in codon usage between host-species-specific rabies virus clades are driven by non-GC3 nucleotide composition
Viral genes sometimes use certain codons more than others due to their nucleotide content, translational efficiency, and selection pressure from the host immune system. The rabies virus (RABV) is a negative strand RNA virus which can infect a broad range of mammalian hosts, with many of its clades circulating predominantly in specific host species. Previous work on codon usage in RABV has focused only on broader viral clades. We use publicly available RABV nucleoprotein gene sequences to investigate how dinucleotide content and codon usage biases differ between host-associated clades, and what drives these differences. We found that codon usage varies most between bat- and carnivore-associated RABV clades, and more subtly between host-species-specific minor clades within these groups. C1, GA3 and GT3 content were found to have a strong influence over codon usage patterns, and CpG content was higher in carnivore-associated RABV clades than in bat-associated clades. This, along with lower numbers of zinc-finger antiviral protein binding motifs than would be expected based on (di)nucleotide composition in bat-associated RABV sequences, suggests that bat-associated RABV clades may be under higher selection pressure from the host’s zinc-finger antiviral protein than carnivore-associated clades are, warranting further investigation of the mechanism underpinning this change.
- 1 July 2026
- Published by Oxford University Press (OUP) in Virus Evolution
- Vol. 12 (1)
Open AccessDifferences in codon usage between host-species-specific rabies virus clades are driven by non-GC3 nucleotide composition
Viral genes sometimes use certain codons more than others due to their nucleotide content, translational efficiency, and selection pressure from the host immune system. The rabies virus (RABV) is a negative strand RNA virus which can infect a broad range of mammalian hosts, with many of its clades circulating predominantly in specific host species. Previous work on codon usage in RABV has focused only on broader viral clades. We use publicly available RABV nucleoprotein gene sequences to investigate how dinucleotide content and codon usage biases differ between host-associated clades, and what drives these differences. We found that codon usage varies most between bat- and carnivore-associated RABV clades, and more subtly between host-species-specific minor clades within these groups. C1, GA3 and GT3 content were found to have a strong influence over codon usage patterns, and CpG content was higher in carnivore-associated RABV clades than in bat-associated clades. This, along with lower numbers of zinc-finger antiviral protein binding motifs than would be expected based on (di)nucleotide composition in bat-associated RABV sequences, suggests that bat-associated RABV clades may be under higher selection pressure from the host’s zinc-finger antiviral protein than carnivore-associated clades are, warranting further investigation of the mechanism underpinning this change.
- Open Access
A simple method of estimating rabies outbreak sizes from phylogenies
The ability to estimate the size of a disease outbreak is beneficial both for coordinating an outbreak response and for retrospectively evaluating the effectiveness of response measures and surveillance. Methods such as seroprevalence surveys and epidemiological modelling can be used for this purpose, but are not suitable for every outbreak. We develop a simple formula to estimate the proportion of outbreak cases sequenced, using only the per-generation substitution rate and the length of a phylogenetic tree. This proportion can then be used to estimate the outbreak size. We validate this method using subsampled data from fully observed simulated outbreaks, and then apply it to an ongoing rabies outbreak in the Philippines. We find that this method produces accurate estimates of outbreak size and can be applied to outbreaks with substitution rates and R0 values within the estimated range for rabies. We estimated that approximately 19% of cases from the outbreak in the Philippines had been sequenced, suggesting better than average case detection, with a resulting outbreak size estimate consistent with previous analyses. With this method and the associated R package POSER (https://github.com/RowanDurrant/poser), we aim to make rabies outbreak size estimation more accessible, but further work is required to improve its applicability to other diseases.
Open AccessA simple method of estimating rabies outbreak sizes from phylogenies
The ability to estimate the size of a disease outbreak is beneficial both for coordinating an outbreak response and for retrospectively evaluating the effectiveness of response measures and surveillance. Methods such as seroprevalence surveys and epidemiological modelling can be used for this purpose, but are not suitable for every outbreak. We develop a simple formula to estimate the proportion of outbreak cases sequenced, using only the per-generation substitution rate and the length of a phylogenetic tree. This proportion can then be used to estimate the outbreak size. We validate this method using subsampled data from fully observed simulated outbreaks, and then apply it to an ongoing rabies outbreak in the Philippines. We find that this method produces accurate estimates of outbreak size and can be applied to outbreaks with substitution rates and R0 values within the estimated range for rabies. We estimated that approximately 19% of cases from the outbreak in the Philippines had been sequenced, suggesting better than average case detection, with a resulting outbreak size estimate consistent with previous analyses. With this method and the associated R package POSER (https://github.com/RowanDurrant/poser), we aim to make rabies outbreak size estimation more accessible, but further work is required to improve its applicability to other diseases.
- Open Access
- 3 June 2026
- Published by The Royal Society in Royal Society Open Science
- Vol. 13 (6)
Emerging frontiers in infectious disease modelling: reassessing the data-driven feedback loop between human behaviour and disease dynamics
Mathematical models have produced important insights into the relationships between disease transmission, risk perception, and human behaviour. However, the increase in scale and complexity of health and behavioural data accelerated by the COVID-19 pandemic demands a critical evaluation of the realism and readiness of mathematical models of infectious disease dynamics to inform preparation and response to (re)emerging public health threats. In this scoping review, we identify five thematic frontiers in extending coupled models of disease dynamics and human behaviour, spanning (1) information quality and scale, (2) data-driven versus perceived risk, (3) social influence, (4) barriers related to fatigue and access, and (5) disruptive events. For each frontier, we summarize key modelling approaches and results, identify knowledge gaps and provide recommendations on future directions with a focus on integrating big data into epidemiological models, incorporating social behavioural theory and accounting for heterogeneity within populations. In turn, each of these frontiers involves challenges that call for new analytical and technical developments. We close by providing general recommendations for modelers with a focus on interdisciplinary collaboration with social and behavioural scientists and establishing best practices for data collection and management to improve the public health relevance of infectious disease models.
- 3 June 2026
- Published by The Royal Society in Royal Society Open Science
- Vol. 13 (6)
Open AccessEmerging frontiers in infectious disease modelling: reassessing the data-driven feedback loop between human behaviour and disease dynamics
Mathematical models have produced important insights into the relationships between disease transmission, risk perception, and human behaviour. However, the increase in scale and complexity of health and behavioural data accelerated by the COVID-19 pandemic demands a critical evaluation of the realism and readiness of mathematical models of infectious disease dynamics to inform preparation and response to (re)emerging public health threats. In this scoping review, we identify five thematic frontiers in extending coupled models of disease dynamics and human behaviour, spanning (1) information quality and scale, (2) data-driven versus perceived risk, (3) social influence, (4) barriers related to fatigue and access, and (5) disruptive events. For each frontier, we summarize key modelling approaches and results, identify knowledge gaps and provide recommendations on future directions with a focus on integrating big data into epidemiological models, incorporating social behavioural theory and accounting for heterogeneity within populations. In turn, each of these frontiers involves challenges that call for new analytical and technical developments. We close by providing general recommendations for modelers with a focus on interdisciplinary collaboration with social and behavioural scientists and establishing best practices for data collection and management to improve the public health relevance of infectious disease models.
- Open Access
Interpreting Breakthrough Infections Given Assortative Mixing of Partially Vaccinated Populations
Declining vaccine coverage across the United States has increased the risk of outbreaks of vaccine-preventable diseases. Even when vaccines have low primary failure rates, conventional epidemic theory predicts a strongly nonlinear, positive relationship between vaccine coverage and the fraction of breakthrough infections in vaccinated individuals. These breakthrough infections may generate misconceptions that vaccines are not working and accelerate declines in confidence and coverage. Here, we set out to test predictions of conventional epidemic theory that assumes random mixing between individuals irrespective of vaccine status. In contrast to expectations from random mixing models, we find a far lower fraction of breakthrough infections in measles outbreak data from seven states in the United States. To explore this discrepancy, we evaluate an alternative, compartmental disease model that accounts for preferential mixing (‘assortativity’) between people with the same vaccination status. The model with assortativity predicts significantly lower fractions of breakthrough infections than conventional models, consistent with observations from measles outbreak data, even when accounting for potential biases in case reporting. Next, we leverage the deviation between statewide and school-level vaccine MMR coverage across kindergartens in sixteen states, finding substantial assortativity in all cases. Our model accounting for preferential mixing predicts the total number of breakthrough infections is nonlinear, peaking at intermediate coverage below vaccine-derived herd immunity. Nationally, more than 90% of counties that report MMR coverage are above the model-predicted breakthrough-maximizing coverage, suggesting that they are at risk for increasing breakthrough infections if coverage declines. Vaccination outreach and monitoring campaigns should develop proactive strategies to contextualize breakthrough infections before low levels of primary failure contributes to population-scale increases in preventable disease.
Open AccessInterpreting Breakthrough Infections Given Assortative Mixing of Partially Vaccinated Populations
Declining vaccine coverage across the United States has increased the risk of outbreaks of vaccine-preventable diseases. Even when vaccines have low primary failure rates, conventional epidemic theory predicts a strongly nonlinear, positive relationship between vaccine coverage and the fraction of breakthrough infections in vaccinated individuals. These breakthrough infections may generate misconceptions that vaccines are not working and accelerate declines in confidence and coverage. Here, we set out to test predictions of conventional epidemic theory that assumes random mixing between individuals irrespective of vaccine status. In contrast to expectations from random mixing models, we find a far lower fraction of breakthrough infections in measles outbreak data from seven states in the United States. To explore this discrepancy, we evaluate an alternative, compartmental disease model that accounts for preferential mixing (‘assortativity’) between people with the same vaccination status. The model with assortativity predicts significantly lower fractions of breakthrough infections than conventional models, consistent with observations from measles outbreak data, even when accounting for potential biases in case reporting. Next, we leverage the deviation between statewide and school-level vaccine MMR coverage across kindergartens in sixteen states, finding substantial assortativity in all cases. Our model accounting for preferential mixing predicts the total number of breakthrough infections is nonlinear, peaking at intermediate coverage below vaccine-derived herd immunity. Nationally, more than 90% of counties that report MMR coverage are above the model-predicted breakthrough-maximizing coverage, suggesting that they are at risk for increasing breakthrough infections if coverage declines. Vaccination outreach and monitoring campaigns should develop proactive strategies to contextualize breakthrough infections before low levels of primary failure contributes to population-scale increases in preventable disease.
- Open Access
Differences in codon usage between host-species-specific rabies virus clades are driven by non-GC3 nucleotide composition
Viral genes sometimes use certain codons more than others due to their nucleotide content, translational efficiency, and selection pressure from the host immune system. The rabies virus (RABV) is a negative strand RNA virus which can infect a broad range of mammalian hosts, with many of its clades circulating predominantly in specific host species. Previous work on codon usage in RABV has focused only on broader viral clades. We use publicly available RABV nucleoprotein gene sequences to investigate how dinucleotide content and codon usage biases differ between host-associated clades, and what drives these differences. We found that codon usage varies most between bat- and carnivore-associated RABV clades, and more subtly between host-species-specific minor clades within these groups. C1, GA3 and GT3 content were found to have a strong influence over codon usage patterns, and CpG content was higher in carnivore-associated RABV clades than in bat-associated clades. This, along with lower numbers of zinc-finger antiviral protein binding motifs than would be expected based on (di)nucleotide composition in bat-associated RABV sequences, suggests that bat-associated RABV clades may be under higher selection pressure from the host’s zinc-finger antiviral protein than carnivore-associated clades are, warranting further investigation of the mechanism underpinning this change.
Open AccessDifferences in codon usage between host-species-specific rabies virus clades are driven by non-GC3 nucleotide composition
Viral genes sometimes use certain codons more than others due to their nucleotide content, translational efficiency, and selection pressure from the host immune system. The rabies virus (RABV) is a negative strand RNA virus which can infect a broad range of mammalian hosts, with many of its clades circulating predominantly in specific host species. Previous work on codon usage in RABV has focused only on broader viral clades. We use publicly available RABV nucleoprotein gene sequences to investigate how dinucleotide content and codon usage biases differ between host-associated clades, and what drives these differences. We found that codon usage varies most between bat- and carnivore-associated RABV clades, and more subtly between host-species-specific minor clades within these groups. C1, GA3 and GT3 content were found to have a strong influence over codon usage patterns, and CpG content was higher in carnivore-associated RABV clades than in bat-associated clades. This, along with lower numbers of zinc-finger antiviral protein binding motifs than would be expected based on (di)nucleotide composition in bat-associated RABV sequences, suggests that bat-associated RABV clades may be under higher selection pressure from the host’s zinc-finger antiviral protein than carnivore-associated clades are, warranting further investigation of the mechanism underpinning this change.
- Open Access
- 23 July 2025
- Published by Elsevier in Journal of Theoretical Biology
- Vol. 613, 112211
Infections are not alike: The effects of covariation between individual susceptibility and transmissibility on epidemic dynamics
- 23 July 2025
- Published by Elsevier in Journal of Theoretical Biology
- Vol. 613, 112211
Open AccessInfections are not alike: The effects of covariation between individual susceptibility and transmissibility on epidemic dynamics
- 29 May 2025
- Published by American Association for the Advancement of Science (AAAS) in Science
- Vol. 388 (6750) , eadt3880
Attenuation of virulence in Yersinia pestis across three plague pandemics
Yersinia pestis has spilled over from wild rodent reservoirs to commensal rodents and humans, causing three historically recorded pandemics. Depletion in the copy number of the plasmid-encoded virulence gene pla occurred in later-dated strains of the first and second pandemics, yet the biological relevance of the pla deletion has been difficult to test. We identified modern Y. pestis strains that independently acquired the same pla depletion as ancient strains and herein show that excision of pla from the multicopy pPCP1 plasmid is accompanied by the integration of a separate full pPCP1 harboring pla into the single-copy pCD1 plasmid, reducing pla dosage. Moreover, we demonstrate that this depletion decreases the mortality of mice in models of bubonic plague but not in the pneumonic and septicemic forms of the disease. We hypothesize that pla depletion may have been selectively advantageous in bubonic plague, owing to rodent fragmentation after pandemic-induced mortality.
- 29 May 2025
- Published by American Association for the Advancement of Science (AAAS) in Science
- Vol. 388 (6750) , eadt3880
Attenuation of virulence in Yersinia pestis across three plague pandemics
Yersinia pestis has spilled over from wild rodent reservoirs to commensal rodents and humans, causing three historically recorded pandemics. Depletion in the copy number of the plasmid-encoded virulence gene pla occurred in later-dated strains of the first and second pandemics, yet the biological relevance of the pla deletion has been difficult to test. We identified modern Y. pestis strains that independently acquired the same pla depletion as ancient strains and herein show that excision of pla from the multicopy pPCP1 plasmid is accompanied by the integration of a separate full pPCP1 harboring pla into the single-copy pCD1 plasmid, reducing pla dosage. Moreover, we demonstrate that this depletion decreases the mortality of mice in models of bubonic plague but not in the pneumonic and septicemic forms of the disease. We hypothesize that pla depletion may have been selectively advantageous in bubonic plague, owing to rodent fragmentation after pandemic-induced mortality.
- Open Access
- 2 January 2025
- Published by Public Library of Science (PLoS) in PLOS ONE
- Vol. 20 (1) , e0315476
A generalised catalytic model to assess changes in risk for multiple reinfections with SARS-CoV-2
Background: Monitoring trends in multiple infections with SARS-CoV-2, following several pandemic waves, provides insight into the biological characteristics of new variants, but also necessitates methods to understand the risk of multiple reinfections. Objectives: We generalised a catalytic model designed to detect increases in the risk of SARS-CoV-2 reinfection, to assess the population-level risk of multiple reinfections. Methods: The catalytic model assumes the risk of reinfection is proportional to observed infections and uses a Bayesian approach to fit model parameters to the number of nth infections among individuals that occur at least 90 days after a previous infection. Using a posterior draw from the fitted model parameters, a 95% projection interval of daily nth infections is calculated under the assumption of a constant nth infection hazard coefficient. An additional model parameter was incorporated for the increased reinfection risk detected during the Omicron wave. The generalised model’s performance was then assessed using simulation-based validation. Key findings: No additional increase in the risk of third infection was detected after the increase detected during the Omicron wave. Using simulation-based validation, we show that the model can successfully detect increases in the risk of third infections under different scenarios. Limitations: Even though the generalised model is intended to detect the risk of nth infections, it is validated specifically for third infections, with its applicability for four or more infections being unconfirmed. Furthermore, the method’s sensitivity to low counts of nth infections, limits application in settings with small epidemics, limited testing coverage or early in an outbreak. Conclusions: The catalytic model was successfully adapted to detect increases in the risk of nth infections, enhancing our capacity to identify future changes in the risk of nth infections by SARS-CoV-2 or other similar pathogens.
- 2 January 2025
- Published by Public Library of Science (PLoS) in PLOS ONE
- Vol. 20 (1) , e0315476
Open AccessA generalised catalytic model to assess changes in risk for multiple reinfections with SARS-CoV-2
Background: Monitoring trends in multiple infections with SARS-CoV-2, following several pandemic waves, provides insight into the biological characteristics of new variants, but also necessitates methods to understand the risk of multiple reinfections. Objectives: We generalised a catalytic model designed to detect increases in the risk of SARS-CoV-2 reinfection, to assess the population-level risk of multiple reinfections. Methods: The catalytic model assumes the risk of reinfection is proportional to observed infections and uses a Bayesian approach to fit model parameters to the number of nth infections among individuals that occur at least 90 days after a previous infection. Using a posterior draw from the fitted model parameters, a 95% projection interval of daily nth infections is calculated under the assumption of a constant nth infection hazard coefficient. An additional model parameter was incorporated for the increased reinfection risk detected during the Omicron wave. The generalised model’s performance was then assessed using simulation-based validation. Key findings: No additional increase in the risk of third infection was detected after the increase detected during the Omicron wave. Using simulation-based validation, we show that the model can successfully detect increases in the risk of third infections under different scenarios. Limitations: Even though the generalised model is intended to detect the risk of nth infections, it is validated specifically for third infections, with its applicability for four or more infections being unconfirmed. Furthermore, the method’s sensitivity to low counts of nth infections, limits application in settings with small epidemics, limited testing coverage or early in an outbreak. Conclusions: The catalytic model was successfully adapted to detect increases in the risk of nth infections, enhancing our capacity to identify future changes in the risk of nth infections by SARS-CoV-2 or other similar pathogens.
- Open Access
A century of weekly notifiable disease incidence data by province in Canada
Background Canadian notifiable disease surveillance provides data on the incidence of communicable diseases, dating back to the late 19th century. The Public Health Agency of Canada offers summaries of these data (from 1924–2022) through an online portal. These summaries provide historical context for Canadian health researchers, but lack information on intra-annual and inter-provincial patterns. Sub-annual and sub-national data can be found in published documents, or requested from archives of government agencies, but are only available in typewritten or handwritten hard copies. We digitized and collated these data sources to create a resource for epidemiology and public health. Methods We manually entered data from scans of hard copies into spreadsheets resembling the originals, facilitating accurate transcription through easier cross-checking. We developed open-source pipelines to harmonize these spreadsheets into CSV files that blend data across sources. Results We assembled and processed 1,631,380 incidence values from 1903–2021. Focusing on sub-annual and sub-national data and removing redundancy yielded 934,009 weekly, monthly, or quarterly incidence values broken down by province/territory, containing 139 diseases. We give two examples of sub-annual and sub-national patterns: strong annual cycles of poliomyelitis that peaked simultaneously across provinces, and spatially heterogeneous resurgence of whooping cough in the 1990s. Interpretation Canada’s history of infectious disease surveillance has produced a detailed record of sub-annual and sub-national disease incidence patterns that remains largely unexplored. This important record is now available as the Canadian Disease Incidence Dataset (CANDID), hosted on a publicly accessible website along with the pipelines used to create it and scans of the original sources.
Open AccessA century of weekly notifiable disease incidence data by province in Canada
Background Canadian notifiable disease surveillance provides data on the incidence of communicable diseases, dating back to the late 19th century. The Public Health Agency of Canada offers summaries of these data (from 1924–2022) through an online portal. These summaries provide historical context for Canadian health researchers, but lack information on intra-annual and inter-provincial patterns. Sub-annual and sub-national data can be found in published documents, or requested from archives of government agencies, but are only available in typewritten or handwritten hard copies. We digitized and collated these data sources to create a resource for epidemiology and public health. Methods We manually entered data from scans of hard copies into spreadsheets resembling the originals, facilitating accurate transcription through easier cross-checking. We developed open-source pipelines to harmonize these spreadsheets into CSV files that blend data across sources. Results We assembled and processed 1,631,380 incidence values from 1903–2021. Focusing on sub-annual and sub-national data and removing redundancy yielded 934,009 weekly, monthly, or quarterly incidence values broken down by province/territory, containing 139 diseases. We give two examples of sub-annual and sub-national patterns: strong annual cycles of poliomyelitis that peaked simultaneously across provinces, and spatially heterogeneous resurgence of whooping cough in the 1990s. Interpretation Canada’s history of infectious disease surveillance has produced a detailed record of sub-annual and sub-national disease incidence patterns that remains largely unexplored. This important record is now available as the Canadian Disease Incidence Dataset (CANDID), hosted on a publicly accessible website along with the pipelines used to create it and scans of the original sources.
- Open Access
Infections are not alike: the effects of covariation between individual susceptibility and transmissibility on epidemic dynamics
Individual-level variation in susceptibility to infection and transmissibility of infection can affect population-level dynamics in epidemic outbreaks. Prior work has incorporated independent variation in susceptibility or transmissibility of individuals into epidemic compartmental models. Here, we develop and assess a mathematical framework that includes covariation in susceptibility and transmissibility. We show that uncorrelated variation in susceptibility and transmissibility leads to an effective transmissibility distribution that has a constant coefficient of variation such that the epidemic dynamics match those with variation in susceptibility alone, providing a baseline for comparison across different correlation structures. Increasing the correlation between susceptibility and transmissibility increases both the speed and strength of the outbreak – and is indicative of outbreaks which might be strongly structured by contact rate variation. In contrast, negative correlations between susceptibility and transmissibility lead to overall weaker outbreaks – with the caveat that the strength of effective transmission increases over time. In either case, correlations can shift the transmissibility distribution, thereby modifying the speed of the epidemic as the susceptible population is depleted. Overall, this work demonstrates how (often unaccounted) covariation in susceptibility and transmission can shape the course of outbreaks and final outbreak sizes. Highlights Developed models incorporating susceptibility and transmissibility covariation. Identified eigendistributions of the force of infection. Uncorrelated transmissibility reduces to variation in susceptibility alone. Positive correlations lead to increases in the basic reproduction number. Positive correlations give faster, stronger, more likely outbreaks. Effective transmission rates increase over time with negative correlations.
Open AccessInfections are not alike: the effects of covariation between individual susceptibility and transmissibility on epidemic dynamics
Individual-level variation in susceptibility to infection and transmissibility of infection can affect population-level dynamics in epidemic outbreaks. Prior work has incorporated independent variation in susceptibility or transmissibility of individuals into epidemic compartmental models. Here, we develop and assess a mathematical framework that includes covariation in susceptibility and transmissibility. We show that uncorrelated variation in susceptibility and transmissibility leads to an effective transmissibility distribution that has a constant coefficient of variation such that the epidemic dynamics match those with variation in susceptibility alone, providing a baseline for comparison across different correlation structures. Increasing the correlation between susceptibility and transmissibility increases both the speed and strength of the outbreak – and is indicative of outbreaks which might be strongly structured by contact rate variation. In contrast, negative correlations between susceptibility and transmissibility lead to overall weaker outbreaks – with the caveat that the strength of effective transmission increases over time. In either case, correlations can shift the transmissibility distribution, thereby modifying the speed of the epidemic as the susceptible population is depleted. Overall, this work demonstrates how (often unaccounted) covariation in susceptibility and transmission can shape the course of outbreaks and final outbreak sizes. Highlights Developed models incorporating susceptibility and transmissibility covariation. Identified eigendistributions of the force of infection. Uncorrelated transmissibility reduces to variation in susceptibility alone. Positive correlations lead to increases in the basic reproduction number. Positive correlations give faster, stronger, more likely outbreaks. Effective transmission rates increase over time with negative correlations.