1
|
Sakref Y, Rivoire O. On the exclusion of exponential autocatalysts by sub-exponential autocatalysts. J Theor Biol 2024; 579:111714. [PMID: 38128753 DOI: 10.1016/j.jtbi.2023.111714] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2023] [Revised: 12/14/2023] [Accepted: 12/15/2023] [Indexed: 12/23/2023]
Abstract
Selection among autocatalytic species fundamentally depends on their growth law: exponential species, whose number of copies grows exponentially, are mutually exclusive, while sub-exponential ones, whose number of copies grows polynomially, can coexist. Here we consider competitions between autocatalytic species with different growth laws and make the simple yet counterintuitive observation that sub-exponential species can exclude exponential ones while the reverse is, in principle, impossible. This observation has implications for scenarios pertaining to the emergence of natural selection.
Collapse
Affiliation(s)
- Yann Sakref
- Gulliver, CNRS, ESPCI Paris, Université PSL, 75005 Paris, France.
| | - Olivier Rivoire
- Gulliver, CNRS, ESPCI Paris, Université PSL, 75005 Paris, France.
| |
Collapse
|
2
|
Ganyani T, Faes C, Hens N. Inference of the generalized-growth model via maximum likelihood estimation: A reflection on the impact of overdispersion. J Theor Biol 2019; 484:110029. [PMID: 31568788 DOI: 10.1016/j.jtbi.2019.110029] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2019] [Revised: 07/15/2019] [Accepted: 09/26/2019] [Indexed: 01/17/2023]
Abstract
Recently, the generalized-growth model was introduced as a flexible approach to characterize growth dynamics of disease outbreaks during the early ascending phase. In this work, by using classical maximum likelihood estimation to obtain parameter estimates, we evaluate the impact of varying levels of overdispersion on the inference of the growth scaling parameter through comparing Poisson and Negative binomial models. In particular, under exponential and sub-exponential growth scenarios, we evaluate, via simulations, the error rate of making an incorrect characterization of early outbreak growth patterns. Simulation results show that the ability to correctly identify early outbreak growth patterns can be affected by overdispersion even when accounted for using the Negative binomial model. We exemplify our findings using data on five different outbreaks. Overall, our results show that estimates should be interpreted with caution when data are overdispersed.
Collapse
Affiliation(s)
- Tapiwa Ganyani
- Interuniversity Institute for Biostatistics and statistical Bioinformatics, UHasselt (Hasselt University), Diepenbeek, Belgium.
| | - Christel Faes
- Interuniversity Institute for Biostatistics and statistical Bioinformatics, UHasselt (Hasselt University), Diepenbeek, Belgium
| | - Niel Hens
- Interuniversity Institute for Biostatistics and statistical Bioinformatics, UHasselt (Hasselt University), Diepenbeek, Belgium; Centre for Health Economics Research and Modelling Infectious Diseases, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium
| |
Collapse
|
3
|
Shanafelt DW, Jones G, Lima M, Perrings C, Chowell G. Forecasting the 2001 Foot-and-Mouth Disease Epidemic in the UK. Ecohealth 2018; 15:338-347. [PMID: 29238900 PMCID: PMC6132414 DOI: 10.1007/s10393-017-1293-2] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2017] [Revised: 07/20/2017] [Accepted: 07/24/2017] [Indexed: 05/24/2023]
Abstract
Near real-time epidemic forecasting approaches are needed to respond to the increasing number of infectious disease outbreaks. In this paper, we retrospectively assess the performance of simple phenomenological models that incorporate early sub-exponential growth dynamics to generate short-term forecasts of the 2001 foot-and-mouth disease epidemic in the UK. For this purpose, we employed the generalized-growth model (GGM) for pre-peak predictions and the generalized-Richards model (GRM) for post-peak predictions. The epidemic exhibits a growth-decelerating pattern as the relative growth rate declines inversely with time. The uncertainty of the parameter estimates [Formula: see text] narrows down and becomes more precise using an increasing amount of data of the epidemic growth phase. Indeed, using only the first 10-15 days of the epidemic, the scaling of growth parameter (p) displays wide uncertainty with the confidence interval for p ranging from values ~ 0.5 to 1.0, indicating that less than 15 epidemic days of data are not sufficient to discriminate between sub-exponential (i.e., p < 1) and exponential growth dynamics (i.e., p = 1). By contrast, using 20, 25, or 30 days of epidemic data, it is possible to recover estimates of p around 0.6 and the confidence interval is substantially below the exponential growth regime. Local and national bans on the movement of livestock and a nationwide cull of infected and contiguous premises likely contributed to the decelerating trajectory of the epidemic. The GGM and GRM provided useful 10-day forecasts of the epidemic before and after the peak of the epidemic, respectively. Short-term forecasts improved as the model was calibrated with an increasing length of the epidemic growth phase. Phenomenological models incorporating generalized-growth dynamics are useful tools to generate short-term forecasts of epidemic growth in near real time, particularly in the context of limited epidemiological data as well as information about transmission mechanisms and the effects of control interventions.
Collapse
Affiliation(s)
- David W Shanafelt
- Centre for Biodiversity, Theory and Modelling, Station d'Ecologie Théorique et Expérimentale du CNRS, Moulis, France
| | | | - Mauricio Lima
- Center of Applied Ecology and Sustainability (CAPES), Pontificia Universidad Católica de Chile, Casilla 114-D, 6513677, Santiago, Chile
| | - Charles Perrings
- School of Life Sciences, Arizona State University, Tempe, AZ, USA
| | - Gerardo Chowell
- School of Public Health, Georgia State University, Atlanta, GA, USA.
- Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD, USA.
| |
Collapse
|
4
|
Pell B, Phan T, Rutter EM, Chowell G, Kuang Y. Simple multi-scale modeling of the transmission dynamics of the 1905 plague epidemic in Bombay. Math Biosci 2018; 301:83-92. [PMID: 29673967 DOI: 10.1016/j.mbs.2018.04.003] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2018] [Revised: 04/10/2018] [Accepted: 04/10/2018] [Indexed: 01/14/2023]
Abstract
The first few disease generations of an infectious disease outbreak is the most critical phase to implement control interventions. The lack of accurate data and information during the early transmission phase hinders the application of complex compartmental models to make predictions and forecasts about important epidemic quantities. Thus, simpler models are often times better tools to understand the early dynamics of an outbreak particularly in the context of limited data. In this paper we mechanistically derive and fit a family of logistic models to spatial-temporal data of the 1905 plague epidemic in Bombay, India. We systematically compare parameter estimates, reproduction numbers, model fit, and short-term forecasts across models at different spatial resolutions. At the same time, we also assess the presence of sub-exponential growth dynamics at different spatial scales and investigate the role of spatial structure and data resolution (district level data and city level data) using simple structured models. Our results for the 1905 plague epidemic in Bombay indicates that it is possible for the growth of an epidemic in the early phase to be sub-exponential at sub-city level, while maintaining near exponential growth at an aggregated city level. We also show that the rate of movement between districts can have a significant effect on the final epidemic size.
Collapse
Affiliation(s)
- Bruce Pell
- Department of Mathematics, Statistics, and Computer Science, St. Olaf College, Minnesota, USA.
| | - Tin Phan
- School of Mathematical and Statistical Sciences, Arizona State University, Arizona, USA.
| | - Erica M Rutter
- Department of Mathematics, North Carolina State University, North Carolina, USA.
| | - Gerardo Chowell
- School of Public Health, Georgia State University, Georgia, USA.
| | - Yang Kuang
- School of Mathematical and Statistical Sciences, Arizona State University, Arizona, USA.
| |
Collapse
|
5
|
Dinh L, Chowell G, Rothenberg R. Growth scaling for the early dynamics of HIV/AIDS epidemics in Brazil and the influence of socio-demographic factors. J Theor Biol 2018; 442:79-86. [PMID: 29330056 DOI: 10.1016/j.jtbi.2017.12.030] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2017] [Revised: 12/25/2017] [Accepted: 12/29/2017] [Indexed: 12/13/2022]
Abstract
The early dynamics of an infectious disease outbreak can be affected by various factors including the transmission mode of the disease and host-specific factors. While recent works have highlighted the presence of sub-exponential growth patterns during the early phase of epidemics, empirical studies examining the contribution of different factors to early epidemic growth dynamics are lacking. Here we aim to characterize and explain the early incidence growth patterns of local HIV/AIDS epidemics in Brazil as a function of socio-demographic factors. For this purpose, we accessed annual AIDS incidence series and state-level socio-demographic variables from publicly available databases. To characterize the early growth dynamics of the HIV/AIDS epidemic, we employed the generalized-growth model to estimate with quantified uncertainty the scaling of growth parameter (p) which captures growth patterns ranging from constant incidence (p=0) to sub-exponential (0 < p < 1) and exponential growth dynamics (p=1) at three spatial scales: national, regional, and state levels. We evaluated the relationship between socio-demographic variables and epidemic growth patterns across 27 Brazilian states using mixed-effect regression analyses. We found wide variation in the early dynamics of the AIDS epidemic in Brazil, displaying sub-exponential growth patterns with the p parameter estimated substantially below 1.0. The mean p was estimated to be 0.81 at the national level, with a range of 0.72-0.85 at the regional level, and a range of 0.28-0.96 at the state level. Our findings support the notion that socio-demographic factors contribute to shaping the early growth dynamics of the epidemic at the local level. Gini index and socio-demographic index were negatively associated with the parameter p, whereas urbanicity was positively associated with p. The results could have theoretical significance in understanding differences in growth scaling across different sexually transmitted disease systems, and have public health implications to guide control.
Collapse
Affiliation(s)
- L Dinh
- Division of Epidemiology and Biostatistics, School of Public Health, Georgia State University, Atlanta, GA, USA.
| | - G Chowell
- Division of Epidemiology and Biostatistics, School of Public Health, Georgia State University, Atlanta, GA, USA; Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD, USA
| | - R Rothenberg
- Division of Epidemiology and Biostatistics, School of Public Health, Georgia State University, Atlanta, GA, USA
| |
Collapse
|
6
|
Chowell G, Viboud C, Simonsen L, Merler S, Vespignani A. Perspectives on model forecasts of the 2014-2015 Ebola epidemic in West Africa: lessons and the way forward. BMC Med 2017; 15:42. [PMID: 28245814 PMCID: PMC5331683 DOI: 10.1186/s12916-017-0811-y] [Citation(s) in RCA: 46] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/18/2016] [Accepted: 02/07/2017] [Indexed: 11/10/2022] Open
Abstract
The unprecedented impact and modeling efforts associated with the 2014-2015 Ebola epidemic in West Africa provides a unique opportunity to document the performances and caveats of forecasting approaches used in near-real time for generating evidence and to guide policy. A number of international academic groups have developed and parameterized mathematical models of disease spread to forecast the trajectory of the outbreak. These modeling efforts often relied on limited epidemiological data to derive key transmission and severity parameters, which are needed to calibrate mechanistic models. Here, we provide a perspective on some of the challenges and lessons drawn from these efforts, focusing on (1) data availability and accuracy of early forecasts; (2) the ability of different models to capture the profile of early growth dynamics in local outbreaks and the importance of reactive behavior changes and case clustering; (3) challenges in forecasting the long-term epidemic impact very early in the outbreak; and (4) ways to move forward. We conclude that rapid availability of aggregated population-level data and detailed information on a subset of transmission chains is crucial to characterize transmission patterns, while ensemble-forecasting approaches could limit the uncertainty of any individual model. We believe that coordinated forecasting efforts, combined with rapid dissemination of disease predictions and underlying epidemiological data in shared online platforms, will be critical in optimizing the response to current and future infectious disease emergencies.
Collapse
Affiliation(s)
- Gerardo Chowell
- School of Public Health, Georgia State University, Atlanta, GA, USA.
- Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD, USA.
| | - Cécile Viboud
- Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD, USA
| | - Lone Simonsen
- Department of Public Health, University of Copenhagen, Copenhagen, Denmark
- Department of Global Health, George Washington University, Washington DC, USA
| | | | - Alessandro Vespignani
- Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston, MA, USA
| |
Collapse
|