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Wang X, Mei J, Zhang F, Wei M, Xie Y, Bayoude A, Liu X, Zhang B, Yu B. A ternary correlation multi-symptom network strategy based on in vivo chemical profile identification and metabolomics to explore the molecular basis of Ephedra herb against viral pneumonia. J Sep Sci 2024; 47:e2400090. [PMID: 38819782 DOI: 10.1002/jssc.202400090] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Revised: 04/08/2024] [Accepted: 04/24/2024] [Indexed: 06/01/2024]
Abstract
Ephedra herb (EH), an important medicine prescribed in herbal formulas by Traditional Chinese Medicine practitioners, has been widely used in the treatment of viral pneumonia in China. However, the molecular basis of EH in viral pneumonia remains unclear. In this study, a ternary correlation multi-symptom network strategy was established based on in vivo chemical profile identification and metabolomics to explore the molecular basis of EH against viral pneumonia. Results showed that 143 compounds of EH and 70 prototype components were identified in vivo. EH could reduce alveolar-capillary barrier disruption in rats with viral pneumonia and significantly downregulate the expression of inflammatory factors and bronchoalveolar lavage fluid. Plasma metabolomics revealed that EH may be involved in the regulation of arachidonic acid, tryptophan, tyrosine, nicotinate, and nicotinamide metabolism. The multi-symptom network showed that 12 compounds have an integral function in the treatment of viral pneumonia by intervening in many pathways related to viruses, immunity and inflammation, and lung injury. Further verification demonstrated that sinapic acid and frambinone can regulate the expression of related genes. It has been shown to be a promising representative of the pharmacological constituents of ephedra.
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Affiliation(s)
- Xiaoyan Wang
- State Key Laboratory of Natural Medicines, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
- Jiangsu Key Laboratory of TCM Evaluation and Translational Research, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
| | - Jie Mei
- State Key Laboratory of Natural Medicines, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
- Jiangsu Key Laboratory of TCM Evaluation and Translational Research, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
| | - Fan Zhang
- State Key Laboratory of Natural Medicines, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
- Jiangsu Key Laboratory of TCM Evaluation and Translational Research, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
| | - Miaomiao Wei
- State Key Laboratory of Natural Medicines, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
- Jiangsu Key Laboratory of TCM Evaluation and Translational Research, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
| | - Yujun Xie
- State Key Laboratory of Natural Medicines, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
- Jiangsu Key Laboratory of TCM Evaluation and Translational Research, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
| | - Alamusi Bayoude
- State Key Laboratory of Natural Medicines, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
- Jiangsu Key Laboratory of TCM Evaluation and Translational Research, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
| | - Xiufeng Liu
- State Key Laboratory of Natural Medicines, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
- Jiangsu Key Laboratory of TCM Evaluation and Translational Research, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
- Research Center for Traceability and Standardization of TCMs, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
| | - Boli Zhang
- State Key Laboratory of Component-Based Chinese Medicine, School of Chinese Medicine, Tianjin University of Traditional Chinese Medicine, Tianjin, China
| | - Boyang Yu
- State Key Laboratory of Natural Medicines, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
- Jiangsu Key Laboratory of TCM Evaluation and Translational Research, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
- Research Center for Traceability and Standardization of TCMs, School of Chinese Materia Medica, China Pharmaceutical University, Nanjing, China
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2
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Feng T, Milne R, Wang H. Variation in environmental stochasticity dramatically affects viability and extinction time in a predator-prey system with high prey group cohesion. Math Biosci 2023; 365:109075. [PMID: 37734536 DOI: 10.1016/j.mbs.2023.109075] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Revised: 08/13/2023] [Accepted: 09/06/2023] [Indexed: 09/23/2023]
Abstract
Understanding how tipping points arise is critical for population protection and ecosystem robustness. This work evaluates the impact of environmental stochasticity on the emergence of tipping points in a predator-prey system subject to the Allee effect and Holling type IV functional response, modeling an environment in which the prey has high group cohesion. We analyze the relationship between stochasticity and the probability and time that predator and prey populations in our model tip between different steady states. We evaluate the safety from extinction of different population values for each species, and accordingly assign extinction warning levels to these population values. Our analysis suggests that the effects of environmental stochasticity on tipping phenomena are scenario-dependent but follow a few interpretable trends. The probability of tipping towards a steady state in which one or both species go extinct generally monotonically increased with noise intensity, while the probability of tipping towards a more favorable steady state (in which more species were viable) usually peaked at intermediate noise intensity. For tipping between two equilibria where a given species was at risk of extinction in one equilibrium but not the other, noise affecting that species had greater impact on tipping probability than noise affecting the other species. Noise in the predator population facilitated quicker tipping to extinction equilibria, whereas prey noise instead often slowed down extinction. Changes in warning level for initial population values due to noise were most apparent near attraction basin boundaries, but noise of sufficient magnitude (especially in the predator population) could alter risk even far away from these boundaries. Our model provides critical theoretical insights for the conservation of population diversity: management criteria and early warning signals can be developed based on our results to keep populations away from destructive critical thresholds.
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Affiliation(s)
- Tao Feng
- School of Mathematical Science, Yangzhou University, Yangzhou, Jiangsu 225002, PR China.
| | - Russell Milne
- Department of Mathematical and Statistical Sciences & Interdisciplinary Lab for Mathematical Ecology and Epidemiology, University of Alberta, Edmonton, AB T6G 2G1, Canada.
| | - Hao Wang
- Department of Mathematical and Statistical Sciences & Interdisciplinary Lab for Mathematical Ecology and Epidemiology, University of Alberta, Edmonton, AB T6G 2G1, Canada.
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3
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O'Neill X, White A, Boots M. The evolution of parasite virulence under targeted culling and harvesting in wildlife and livestock. Evol Appl 2023; 16:1697-1707. [PMID: 38020874 PMCID: PMC10660816 DOI: 10.1111/eva.13594] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2023] [Revised: 07/27/2023] [Accepted: 09/01/2023] [Indexed: 12/01/2023] Open
Abstract
There is a clear need to understand the effect of human intervention on the evolution of infectious disease. In particular, culling and harvesting of both wildlife and managed livestock populations are carried out in a wide range of management practices, and they have the potential to impact the evolution of a broad range of disease characteristics. Applying eco-evolutionary theory we show that once culling/harvesting becomes targeted on specific disease classes, the established result that culling selects for higher virulence is only found when sufficient infected individuals are culled. If susceptible or recovered individuals are targeted, selection for lower virulence can occur. An important implication of this result is that when culling to eradicate an infectious disease from a population, while it is optimal to target infected individuals, the consequent evolution can increase the basic reproductive ratio of the infection, R 0 , and make parasite eradication more difficult. We show that increases in evolved virulence due to the culling of infected individuals can lead to excess population decline when sustainably harvesting a population. In contrast, culling susceptible or recovered individuals can select for decreased virulence and a reduction in population decline through culling. The implications to the evolution of virulence are typically the same in wildlife populations, that are regulated by the parasite, and livestock populations, that have a constant population size where restocking balances the losses due to mortality. However, the well-known result that vertical transmission selects for lower virulence and transmission in wildlife populations is less marked in livestock populations for parasites that convey long-term immunity since restocking can enhance the density of the immune class. Our work emphasizes the importance of understanding the evolutionary consequences of intervention strategies and the different ecological feedbacks that can occur in wildlife and livestock populations.
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Affiliation(s)
- Xander O'Neill
- Department of MathematicsMaxwell Institute for Mathematical Sciences, Heriot‐Watt UniversityEdinburghUK
| | - Andy White
- Department of MathematicsMaxwell Institute for Mathematical Sciences, Heriot‐Watt UniversityEdinburghUK
| | - Mike Boots
- Department of Integrative BiologyUniversity of CaliforniaBerkeleyCaliforniaUSA
- Centre for Ecology and Conservation, BiosciencesUniversity of ExeterCornwallUK
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4
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Hoyer-Leitzel A, Iams S, Haslam-Hyde A, Zeeman M, Fefferman N. An immuno-epidemiological model for transient immune protection: A case study for viral respiratory infections. Infect Dis Model 2023; 8:855-864. [PMID: 37502609 PMCID: PMC10369473 DOI: 10.1016/j.idm.2023.07.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2022] [Revised: 06/14/2023] [Accepted: 07/08/2023] [Indexed: 07/29/2023] Open
Abstract
The dynamics of infectious disease in a population critically involves both within-host pathogen replication and between host pathogen transmission. While modeling efforts have recently explored how within-host dynamics contribute to shaping population transmission, fewer have explored how ongoing circulation of an epidemic infectious disease can impact within-host immunological dynamics. We present a simple, influenza-inspired model that explores the potential for re-exposure during a single, ongoing outbreak to shape individual immune response and epidemiological potential in non-trivial ways. We show how even a simplified system can exhibit complex ongoing dynamics and sensitive thresholds in behavior. We also find epidemiological stochasticity likely plays a critical role in reinfection or in the maintenance of individual immunological protection over time.
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Affiliation(s)
- A. Hoyer-Leitzel
- Department of Mathematics and Statistics, Mount Holyoke College, 50 College St, South Hadley, MA, 01075, USA
| | - S.M. Iams
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, USA
| | - A.J. Haslam-Hyde
- Department of Mathematics and Statistics, Boston University, USA
| | - M.L. Zeeman
- Department of Mathematics, Bowdoin College, USA
| | - N.H. Fefferman
- Dept of Mathematics & Dept of Ecology and Evolutionary Biology & NIMBioS, University of Tennessee, Knoxville, USA
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5
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Gao S, Shen M, Wang X, Wang J, Martcheva M, Rong L. A multi-strain model with asymptomatic transmission: Application to COVID-19 in the US. J Theor Biol 2023; 565:111468. [PMID: 36940811 PMCID: PMC10027298 DOI: 10.1016/j.jtbi.2023.111468] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2022] [Revised: 02/08/2023] [Accepted: 03/16/2023] [Indexed: 03/23/2023]
Abstract
COVID-19, induced by the SARS-CoV-2 infection, has caused an unprecedented pandemic in the world. New variants of the virus have emerged and dominated the virus population. In this paper, we develop a multi-strain model with asymptomatic transmission to study how the asymptomatic or pre-symptomatic infection influences the transmission between different strains and control strategies that aim to mitigate the pandemic. Both analytical and numerical results reveal that the competitive exclusion principle still holds for the model with the asymptomatic transmission. By fitting the model to the COVID-19 case and viral variant data in the US, we show that the omicron variants are more transmissible but less fatal than the previously circulating variants. The basic reproduction number for the omicron variants is estimated to be 11.15, larger than that for the previous variants. Using mask mandate as an example of non-pharmaceutical interventions, we show that implementing it before the prevalence peak can significantly lower and postpone the peak. The time of lifting the mask mandate can affect the emergence and frequency of subsequent waves. Lifting before the peak will result in an earlier and much higher subsequent wave. Caution should also be taken to lift the restriction when a large portion of the population remains susceptible. The methods and results obtained her e may be applied to the study of the dynamics of other infectious diseases with asymptomatic transmission using other control measures.
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Affiliation(s)
- Shasha Gao
- School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, 330000, China; Department of Mathematics, University of Florida, Gainesville, FL 32611, United States of America
| | - Mingwang Shen
- China-Australia Joint Research Centre for Infectious Diseases, School of Public Health, Xi'an Jiaotong University Health Science Center, Xi'an, Shaanxi, China
| | - Xueying Wang
- Department of Mathematics and Statistics, Washington State University, Pullman, WA 99163, United States of America
| | - Jin Wang
- Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States of America
| | - Maia Martcheva
- Department of Mathematics, University of Florida, Gainesville, FL 32611, United States of America
| | - Libin Rong
- Department of Mathematics, University of Florida, Gainesville, FL 32611, United States of America.
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6
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Social dilemmas of sociality due to beneficial and costly contagion. PLoS Comput Biol 2022; 18:e1010670. [DOI: 10.1371/journal.pcbi.1010670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2022] [Revised: 12/05/2022] [Accepted: 10/20/2022] [Indexed: 11/22/2022] Open
Abstract
Levels of sociality in nature vary widely. Some species are solitary; others live in family groups; some form complex multi-family societies. Increased levels of social interaction can allow for the spread of useful innovations and beneficial information, but can also facilitate the spread of harmful contagions, such as infectious diseases. It is natural to assume that these contagion processes shape the evolution of complex social systems, but an explicit account of the dynamics of sociality under selection pressure imposed by contagion remains elusive. We consider a model for the evolution of sociality strategies in the presence of both a beneficial and costly contagion. We study the dynamics of this model at three timescales: using a susceptible-infectious-susceptible (SIS) model to describe contagion spread for given sociality strategies, a replicator equation to study the changing fractions of two different levels of sociality, and an adaptive dynamics approach to study the long-time evolution of the population level of sociality. For a wide range of assumptions about the benefits and costs of infection, we identify a social dilemma: the evolutionarily-stable sociality strategy (ESS) is distinct from the collective optimum—the level of sociality that would be best for all individuals. In particular, the ESS level of social interaction is greater (respectively less) than the social optimum when the good contagion spreads more (respectively less) readily than the bad contagion. Our results shed light on how contagion shapes the evolution of social interaction, but reveals that evolution may not necessarily lead populations to social structures that are good for any or all.
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7
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Serra M, Al-Mosleh S, Prasath G, Raju V, Mantena S, Chandra J, Iams S, Mahadevan L. Optimal policies for mitigating pandemic costs: a minimal model. Phys Biol 2022; 19. [PMID: 35790172 DOI: 10.1088/1478-3975/ac7e9e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2021] [Accepted: 07/05/2022] [Indexed: 11/11/2022]
Abstract
There have been a number of pharmaceutical and non-pharmaceutical interventions associated with COVID-19 over the past two years. Of the various non-pharmaceutical interventions that were proposed and implemented to control the spread of the COVID-19 pandemic partial and complete lockdowns were used repeatedly in an attempt to minimize the costs associated with mortality, economic losses and social factors, while being subject to constraints such as finite hospital capacity. Here, we use a minimal model to understand the costs and benefits of these strategies that mitigate pandemic costs subject to constraints, we adopt the language of optimal control theory. This allows us to determine top-down policies for the nature and dynamics of social contact rates given an age-structured model for the dynamics of the disease. Depending on the relative weights allocated to mortality and socioeconomic losses, we see that the optimal strategies range from long-term social-distancing only for the most vulnerable, to partial lockdown to ensure not over-running hospitals, to alternating-shifts with significant reduction in mortality and/or socioeconomic losses. Crucially, commonly used strategies that involve long periods of broad lockdown are almost never optimal, as they are highly unstable to reopening {and entail high socioeconomic costs}. Using parameter estimates from data available for Germany and the USA early in the pandemic, we quantify these policies and use sensitivity analysis in the relevant model parameters and initial conditions to determine the range of robustness of our policies. Finally we also discuss how bottom-up behavioral changes affect the dynamics of the pandemic and show they can work in tandem with top-down control policies to mitigate pandemic costs even more effectively.
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Affiliation(s)
- Mattia Serra
- Harvard University, Pierce Hall, Cambridge, Cambridge, 02138, UNITED STATES
| | - Salem Al-Mosleh
- School of Engineering and Applied Sciences, Harvard University, Pierce Hall, Cambridge, Cambridge, 02138, UNITED STATES
| | - Ganga Prasath
- School of Engineering and Applied Sciences, Harvard University, 29 Oxford St, Cambridge, Cambridge, Massachusetts, 02138, UNITED STATES
| | - Vidya Raju
- School of Engineering and Applied Sciences, Harvard University, 29 Oxford St, Cambridge, Cambridge, Massachusetts, 02138, UNITED STATES
| | - Sreekar Mantena
- School of Engineering and Applied Sciences, Harvard University, 29 Oxford St, Cambridge, Cambridge, 02138, UNITED STATES
| | - Jay Chandra
- School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, 02138, UNITED STATES
| | - Sarah Iams
- Harvard University, 29 Oxford Street, Cambridge, 02138, UNITED STATES
| | - L Mahadevan
- Harvard University, 29 Oxford Street, Cambridge, Massachusetts, 02138, UNITED STATES
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8
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Dong R, Hu T, Zhang Y, Li Y, Zhou XH. Assessing the Transmissibility of the New SARS-CoV-2 Variants: From Delta to Omicron. Vaccines (Basel) 2022; 10:496. [PMID: 35455246 PMCID: PMC9026126 DOI: 10.3390/vaccines10040496] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2022] [Revised: 03/15/2022] [Accepted: 03/21/2022] [Indexed: 02/06/2023] Open
Abstract
Omicron, the latest SARS-CoV-2 Variant of Concern (VOC), first appeared in Africa in November 2021. At present, the question of whether a new VOC will out-compete the currently predominant variant is important for governments seeking to determine if current surveillance strategies and responses are appropriate and reasonable. Based on both virus genomes and daily-confirmed cases, we compare the additive differences in growth rates and reproductive numbers (R0) between VOCs and their predominant variants through a Bayesian framework and phylo-dynamics analysis. Faced with different variants, we evaluate the effects of current policies and vaccinations against VOCs and predominant variants. The model also predicts the date on which a VOC may become dominant based on simulation and real data in the early stage. The results suggest that the overall additive difference in growth rates of B.1.617.2 and predominant variants was 0.44 (95% confidence interval, 95% CI: -0.38, 1.25) in February 2021, and that the VOC had a relatively high R0. The additive difference in the growth rate of BA.1 in the United Kingdom was 6.82 times the difference between Delta and Alpha, and the model successfully predicted the dominating process of Alpha, Delta and Omicron. Current vaccination strategies remain similarly effective against Delta compared to the previous variants. Our model proposes a reliable Bayesian framework to predict the spread trends of VOCs based on early-stage data, and evaluates the effects of public health policies, which may help us better prepare for the upcoming Omicron variant, which is now spreading at an unprecedented speed.
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Affiliation(s)
- Rui Dong
- Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China;
- Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, China
| | - Taojun Hu
- Department of Biostatistics, School of Public Health, Peking University, Beijing 100191, China; (T.H.); (Y.Z.)
| | - Yunjun Zhang
- Department of Biostatistics, School of Public Health, Peking University, Beijing 100191, China; (T.H.); (Y.Z.)
| | - Yang Li
- Chongqing School, University of Chinese Academy of Sciences, Chongqing 400020, China;
| | - Xiao-Hua Zhou
- Department of Biostatistics, School of Public Health, Peking University, Beijing 100191, China; (T.H.); (Y.Z.)
- Beijing International Center for Mathematical Research, Peking University, Beijing 100191, China
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9
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Greischar MA. Modern Epidemics: From the Spanish Flu to COVID-19. Emerg Infect Dis 2021. [DOI: 10.3201/eid2712.1312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
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10
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Alizon S, Sofonea MT. SARS-CoV-2 virulence evolution: Avirulence theory, immunity and trade-offs. J Evol Biol 2021; 34:1867-1877. [PMID: 34196431 PMCID: PMC8447366 DOI: 10.1111/jeb.13896] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2021] [Revised: 06/15/2021] [Accepted: 06/21/2021] [Indexed: 12/21/2022]
Abstract
The COVID-19 pandemic has led to a resurgence of the debate on whether host-parasite interactions should evolve towards avirulence. In this review, we first show that SARS-CoV-2 virulence is evolving, before explaining why some expect the mortality caused by the epidemic to converge towards that of human seasonal alphacoronaviruses. Leaning on existing theory, we then include viral evolution into the picture and discuss hypotheses explaining why the virulence has increased since the beginning of the pandemic. Finally, we mention some potential scenarios for the future.
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Affiliation(s)
- Samuel Alizon
- MIVEGECCNRS, IRD, Univ. MontpellierMontpellierFrance
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11
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Modern Epidemics: From the Spanish Flu to COVID-19. Emerg Infect Dis 2021. [PMCID: PMC8632183 DOI: 10.3201/eid2712.211312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
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12
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Kokko H. The stagnation paradox: the ever-improving but (more or less) stationary population fitness. Proc Biol Sci 2021; 288:20212145. [PMID: 34784767 PMCID: PMC8596016 DOI: 10.1098/rspb.2021.2145] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Fisher's fundamental theorem states that natural selection improves mean fitness. Fitness, in turn, is often equated with population growth. This leads to an absurd prediction that life evolves to ever-faster growth rates, yet no one seriously claims generally slower population growth rates in the Triassic compared with the present day. I review here, using non-technical language, how fitness can improve yet stay constant (stagnation paradox), and why an unambiguous measure of population fitness does not exist. Subfields use different terminology for aspects of the paradox, referring to stasis, cryptic evolution or the difficulty of choosing an appropriate fitness measure; known resolutions likewise use diverse terms from environmental feedback to density dependence and ‘evolutionary environmental deterioration’. The paradox vanishes when these concepts are understood, and adaptation can lead to declining reproductive output of a population when individuals can improve their fitness by exploiting conspecifics. This is particularly readily observable when males participate in a zero-sum game over paternity and population output depends more strongly on female than male fitness. Even so, the jury is still out regarding the effect of sexual conflict on population fitness. Finally, life-history theory and genetic studies of microevolutionary change could pay more attention to each other.
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Affiliation(s)
- Hanna Kokko
- Department of Evolutionary Biology and Environmental Studies, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
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13
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Bärwolff G. Modeling of COVID-19 propagation with compartment models. MATHEMATISCHE SEMESTERBERICHTE 2021; 68:181-219. [PMID: 34795464 PMCID: PMC8564799 DOI: 10.1007/s00591-021-00312-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/09/2021] [Accepted: 10/08/2021] [Indexed: 12/05/2022]
Abstract
The current pandemic is a great challenge for several research areas. In addition to virology research, mathematical models and simulations can be a valuable contribution to the understanding of the dynamics of the pandemic and can give recommendations to both physicians and politicians. In this paper we give an overview about mathematical models to describe the pandemic by differential equations. As a matter of principle the historic origin of the epidemic growth models will be remembered. Moreover we discuss models for the actual pandemic of 2020/2021. This will be done based on actual data of people infected with COVID-19 from the European Centre for Disease Prevention and Control (ECDC), input parameters of mathematical models will be determined and applied. These parameters will be estimated for the UK, Italy, Spain, and Germany and used in a SIR-type model. As a basis for the model's calibration, the initial exponential growth phase of the COVID-19 pandemic in the named countries is used. Strategies for the commencing and ending of social and economic shutdown measures are discussed. To respect heterogeneity of the people density in the different federal states of Germany diffusion effects are considered.
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Affiliation(s)
- Günter Bärwolff
- Inst. f. Math., Technische Universität Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany
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14
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Visher E, Evensen C, Guth S, Lai E, Norfolk M, Rozins C, Sokolov NA, Sui M, Boots M. The three Ts of virulence evolution during zoonotic emergence. Proc Biol Sci 2021; 288:20210900. [PMID: 34375554 PMCID: PMC8354747 DOI: 10.1098/rspb.2021.0900] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Accepted: 07/16/2021] [Indexed: 12/21/2022] Open
Abstract
There is increasing interest in the role that evolution may play in current and future pandemics, but there is often also considerable confusion about the actual evolutionary predictions. This may be, in part, due to a historical separation of evolutionary and medical fields, but there is a large, somewhat nuanced body of evidence-supported theory on the evolution of infectious disease. In this review, we synthesize this evolutionary theory in order to provide a framework for clearer understanding of the key principles. Specifically, we discuss the selection acting on zoonotic pathogens' transmission rates and virulence at spillover and during emergence. We explain how the direction and strength of selection during epidemics of emerging zoonotic disease can be understood by a three Ts framework: trade-offs, transmission, and time scales. Virulence and transmission rate may trade-off, but transmission rate is likely to be favoured by selection early in emergence, particularly if maladapted zoonotic pathogens have 'no-cost' transmission rate improving mutations available to them. Additionally, the optimal virulence and transmission rates can shift with the time scale of the epidemic. Predicting pathogen evolution, therefore, depends on understanding both the trade-offs of transmission-improving mutations and the time scales of selection.
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Affiliation(s)
- Elisa Visher
- Department of Integrative Biology, University of California, Berkeley, CA 94720, USA
| | - Claire Evensen
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
| | - Sarah Guth
- Department of Integrative Biology, University of California, Berkeley, CA 94720, USA
| | - Edith Lai
- College of Natural Resources, University of California, Berkeley, CA 94720, USA
| | - Marina Norfolk
- College of Letters and Sciences, University of California, Berkeley, CA 94720, USA
| | - Carly Rozins
- Department of Science and Technology Studies, Division of Natural Science, York University, Toronto, Ontario, Canada M3J 1P3
| | - Nina A. Sokolov
- Department of Integrative Biology, University of California, Berkeley, CA 94720, USA
| | - Melissa Sui
- College of Letters and Sciences, University of California, Berkeley, CA 94720, USA
| | - Michael Boots
- Department of Integrative Biology, University of California, Berkeley, CA 94720, USA
- Centre for Ecology and Conservation, College of Life and Environmental Sciences, University of Exeter, Penryn Campus, Penryn TR10 9FE, UK
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15
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Saad-Roy CM, Grenfell BT, Levin SA, van den Driessche P, Wingreen NS. Evolution of an asymptomatic first stage of infection in a heterogeneous population. J R Soc Interface 2021; 18:20210175. [PMID: 34129793 PMCID: PMC8205539 DOI: 10.1098/rsif.2021.0175] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 05/24/2021] [Indexed: 11/12/2022] Open
Abstract
Pathogens evolve different life-history strategies, which depend in part on differences in their host populations. A central feature of hosts is their population structure (e.g. spatial). Additionally, hosts themselves can exhibit different degrees of symptoms when newly infected; this latency is a key life-history property of pathogens. With an evolutionary-epidemiological model, we examine the role of population structure on the evolutionary dynamics of latency. We focus on specific power-law-like formulations for transmission and progression from the first infectious stage as a function of latency, assuming that the across-group to within-group transmission ratio increases if hosts are less symptomatic. We find that simple population heterogeneity can lead to local evolutionarily stable strategies (ESSs) at zero and infinite latency in situations where a unique ESS exists in the corresponding homogeneous case. Furthermore, there can exist more than one interior evolutionarily singular strategy. We find that this diversity of outcomes is due to the (possibly slight) advantage of across-group transmission for pathogens that produce fewer symptoms in a first infectious stage. Thus, our work reveals that allowing individuals without symptoms to travel can have important unintended evolutionary effects and is thus fundamentally problematic in view of the evolutionary dynamics of latency.
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Affiliation(s)
- Chadi M. Saad-Roy
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
| | - Bryan T. Grenfell
- Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, USA
- Princeton School of Public and International Affairs, Princeton University, Princeton, NJ, USA
| | - Simon A. Levin
- Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, USA
| | - P. van den Driessche
- Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada
| | - Ned S. Wingreen
- Department of Molecular Biology, Princeton University, Princeton, NJ, USA
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Saad-Roy CM, Grenfell BT, Levin SA, Pellis L, Stage HB, van den Driessche P, Wingreen NS. Superinfection and the evolution of an initial asymptomatic stage. ROYAL SOCIETY OPEN SCIENCE 2021; 8:202212. [PMID: 33614103 PMCID: PMC7890506 DOI: 10.1098/rsos.202212] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/04/2020] [Accepted: 12/16/2020] [Indexed: 06/12/2023]
Abstract
Pathogens have evolved a variety of life-history strategies. An important strategy consists of successful transmission by an infected host before the appearance of symptoms, that is, while the host is still partially or fully asymptomatic. During this initial stage of infection, it is possible for another pathogen to superinfect an already infected host and replace the previously infecting pathogen. Here, we study the effect of superinfection during the first stage of an infection on the evolutionary dynamics of the degree to which the host is asymptomatic (host latency) in that same stage. We find that superinfection can lead to major differences in evolutionary behaviour. Most strikingly, the duration of immunity following infection can significantly influence pathogen evolutionary dynamics, whereas without superinfection the outcomes are independent of host immunity. For example, changes in host immunity can drive evolutionary transitions from a fully symptomatic to a fully asymptomatic first infection stage. Additionally, if superinfection relative to susceptible infection is strong enough, evolution can lead to a unique strategy of latency that corresponds to a local fitness minimum, and is therefore invasible by nearby mutants. Thus, this strategy is a branching point, and can lead to coexistence of pathogens with different latencies. Furthermore, in this new framework with superinfection, we also find that there can exist two interior singular strategies. Overall, new evolutionary outcomes can cascade from superinfection.
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Affiliation(s)
- Chadi M. Saad-Roy
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
| | - Bryan T. Grenfell
- Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, USA
- Princeton School of Public and International Affairs, Princeton University, Princeton, NJ, USA
- Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD, USA
| | - Simon A. Levin
- Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, USA
| | - Lorenzo Pellis
- Department of Mathematics, University of Manchester, Manchester, UK
- The Alan Turing Institute, London, UK
| | - Helena B. Stage
- Department of Mathematics, University of Manchester, Manchester, UK
| | - P. van den Driessche
- Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada
| | - Ned S. Wingreen
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
- Department of Molecular Biology, Princeton University, Princeton, NJ, USA
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Ansumali S, Kaushal S, Kumar A, Prakash MK, Vidyasagar M. Modelling a pandemic with asymptomatic patients, impact of lockdown and herd immunity, with applications to SARS-CoV-2. ANNUAL REVIEWS IN CONTROL 2020; 50:432-447. [PMID: 33071595 PMCID: PMC7546280 DOI: 10.1016/j.arcontrol.2020.10.003] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Revised: 09/30/2020] [Accepted: 10/05/2020] [Indexed: 05/15/2023]
Abstract
The SARS-CoV-2 is a type of coronavirus that has caused the pandemic known as the Coronavirus Disease of 2019, or COVID-19. In traditional epidemiological models such as SEIR (Susceptible, Exposed, Infected, Removed), the exposed group E does not infect the susceptible group S. A distinguishing feature of COVID-19 is that, unlike with previous viral diseases, there is a distinct "asymptomatic" group A, which does not show any symptoms, but can nevertheless infect others, at the same rate as infected symptomatic patients. This situation is captured in a model known as SAIR (Susceptible, Asymptomatic, Infected, Removed), introduced in Robinson and Stillianakis (2013). The dynamical behavior of the SAIR model is quite different from that of the SEIR model. In this paper, we use Lyapunov theory to establish the global asymptotic stabililty of the SAIR model, both without and with vital dynamics. Then we develop compartmental SAIR models to cater to the migration of population across geographic regions, and once again establish global asymptotic stability. Next, we go beyond long-term asymptotic analysis and present methods for estimating the parameters in the SAIR model. We apply these estimation methods to data from several countries including India, and demonstrate that the predicted trajectories of the disease closely match actual data. We show that "herd immunity" (defined as the time when the number of infected persons is maximum) can be achieved when the total of infected, symptomatic and asymptomatic persons is as low as 25% of the population. Previous estimates are typically 50% or higher. We also conclude that "lockdown" as a way of greatly reducing inter-personal contact has been very effective in checking the progress of the disease.
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Affiliation(s)
- Santosh Ansumali
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India
| | - Shaurya Kaushal
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India
| | - Aloke Kumar
- Indian Institute of Science, Bangalore, India
| | - Meher K Prakash
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India
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Abstract
The current pandemic is a great challenge for several research areas. In addition to virology research, mathematical models and simulations can be a valuable contribution to the understanding of the dynamics of the pandemic and can give recommendations to physicians and politicians. Based on actual data of people infected with COVID-19 from the European Center for Disease Prevention and Control (ECDC), input parameters of mathematical models will be determined and applied. These parameters will be estimated for the UK, Italy, Spain, and Germany and used in an S I R -type model. As a basis for the model’s calibration, the initial exponential growth phase of the COVID-19 pandemic in the named countries is used. Strategies for the commencing and ending of social and economic shutdown measures are discussed.
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