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Andreu-Vilarroig C, González-Parra G, Villanueva RJ. Mathematical Modeling of Influenza Dynamics: Integrating Seasonality and Gradual Waning Immunity. Bull Math Biol 2025; 87:75. [PMID: 40379989 DOI: 10.1007/s11538-025-01454-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2024] [Accepted: 04/09/2025] [Indexed: 05/19/2025]
Abstract
The dynamics of influenza virus spread is one of the most complex to model due to two crucial factors involved: seasonality and immunity. These factors have been typically addressed separately in mathematical modeling in epidemiology. In this paper, we present a mathematical modeling approach to consider simultaneously both forced-seasonality and gradual waning immunity. A seasonal SIRn model that integrates seasonality and gradual waning immunity is constructed. Seasonality has been modeled classically, by defining the transmission rate as a periodic function, with higher values in winter seasons. The progressive decline of immunity after infection has been introduced into the model structure by considering multiple recovered subpopulations or recovery states with transmission rates attenuated by a susceptibility factor that varies with the age of infection. To show the applicability of the proposed mathematical modeling approach to a real-world scenario, we have carried out a calibration of the model with the data series of influenza infections reported in the 2010-2020 period at the General Hospital of Castellón de la Plana, Spain. The results of the case study show the feasibility of the mathematical approach. We provide a discussion of the main features and insights of the proposed mathematical modeling approach presented in this study.
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Affiliation(s)
- Carlos Andreu-Vilarroig
- Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camí de Vera, s/n, Valencia, 46022, Spain
| | | | - Rafael-Jacinto Villanueva
- Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camí de Vera, s/n, Valencia, 46022, Spain
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Li S, Gulisija D, Carja O. The evolutionary cost of homophily: Social stratification facilitates stable variant coexistence and increased rates of evolution in host-associated pathogens. PLoS Comput Biol 2024; 20:e1012619. [PMID: 39576842 PMCID: PMC11623455 DOI: 10.1371/journal.pcbi.1012619] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2024] [Revised: 12/06/2024] [Accepted: 11/07/2024] [Indexed: 11/24/2024] Open
Abstract
Coexistence of multiple strains of a pathogen in a host population can present significant challenges to vaccine development or treatment efficacy. Here we discuss a novel mechanism that can increase rates of long-lived strain polymorphism, rooted in the presence of social structure in a host population. We show that social preference of interaction, in conjunction with differences in immunity between host subgroups, can exert varying selection pressure on pathogen strains, creating a balancing mechanism that supports stable viral coexistence, independent of other known mechanisms. We use population genetic models to study rates of pathogen heterozygosity as a function of population size, host population composition, mutant strain fitness differences and host social preferences of interaction. We also show that even small periodic epochs of host population stratification can lead to elevated strain coexistence. These results are robust to varying social preferences of interaction, overall differences in strain fitnesses, and spatial heterogeneity in host population composition. Our results highlight the role of host population social stratification in increasing rates of pathogen strain diversity, with effects that should be considered when designing policies or treatments with a long-term view of curbing pathogen evolution.
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Affiliation(s)
- Shuanger Li
- Computational Biology Department, School of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
| | - Davorka Gulisija
- Department of Biology, University of New Mexico, Albuquerque, New Mexico, United States of America
| | - Oana Carja
- Computational Biology Department, School of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
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Li S, Gulisija D, Carja O. The evolutionary cost of homophily: social stratification facilitates stable variant coexistence and increased rates of evolution in host-associated pathogens. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.07.14.603415. [PMID: 39071438 PMCID: PMC11275799 DOI: 10.1101/2024.07.14.603415] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/30/2024]
Abstract
Coexistence of multiple strains of a pathogen in a host population can present significant challenges to vaccine development or treatment efficacy. Here we discuss a novel mechanism that can increase rates of long-lived strain polymorphism, rooted in the presence of social structure in a host population. We show that social preference of interaction, in conjunction with differences in immunity between host subgroups, can exert varying selection pressure on pathogen strains, creating a balancing mechanism that supports stable viral coexistence, independent of other known mechanisms. We use population genetic models to study rates of pathogen heterozygosity as a function of population size, host population composition, mutant strain fitness differences and host social preferences of interaction. We also show that even small periodic epochs of host population stratification can lead to elevated strain coexistence. These results are robust to varying social preferences of interaction, overall differences in strain fitnesses, and spatial heterogeneity in host population composition. Our results highlight the role of host population social stratification in increasing rates of pathogen strain diversity, with effects that should be considered when designing policies or treatments with a long-term view of curbing pathogen evolution.
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Affiliation(s)
- Shuanger Li
- Computational Biology Department, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA
- Current affiliation: Ecology and Evolution Graduate Program, University of Chicago, Chicago, USA
| | - Davorka Gulisija
- Department of Biology, University of New Mexico, Albuquerque, NM, USA
| | - Oana Carja
- Computational Biology Department, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA
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Wilasang C, Suttirat P, Chadsuthi S, Wiratsudakul A, Modchang C. Competitive evolution of H1N1 and H3N2 influenza viruses in the United States: A mathematical modeling study. J Theor Biol 2022; 555:111292. [PMID: 36179800 DOI: 10.1016/j.jtbi.2022.111292] [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: 04/13/2022] [Revised: 08/17/2022] [Accepted: 09/21/2022] [Indexed: 01/14/2023]
Abstract
Seasonal influenza causes vast public health and economic impact globally. The prevention and control of the annual epidemics remain a challenge due to the antigenic evolution of the viruses. Here, we presented a novel modeling framework based on changes in amino acid sequences and relevant epidemiological data to retrospectively investigate the competitive evolution and transmission of H1N1 and H3N2 influenza viruses in the United States during October 2002 and April 2019. To do so, we estimated the time-varying disease transmission rate from the reported influenza cases and the time-varying antigenic change rate of the viruses from the changes in amino acid sequences. By incorporating the time-varying antigenic change rate into the transmission models, we found that the models could capture the evolutionary transmission dynamics of influenza viruses in the United States. Our modeling results also showed that the antigenic change of the virus plays an essential role in seasonal influenza dynamics.
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Affiliation(s)
- Chaiwat Wilasang
- Biophysics Group, Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
| | - Pikkanet Suttirat
- Biophysics Group, Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
| | - Sudarat Chadsuthi
- Department of Physics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
| | - Anuwat Wiratsudakul
- Department of Clinical Sciences and Public Health, and the Monitoring and Surveillance Center for Zoonotic Diseases in Wildlife and Exotic Animals, Faculty of Veterinary Science, Mahidol University, Nakhon Pathom 73170, Thailand
| | - Charin Modchang
- Biophysics Group, Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand; Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand; Thailand Center of Excellence in Physics, Ministry of Higher Education, Science, Research and Innovation, 328 Si Ayutthaya Road, Bangkok 10400, Thailand.
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Furuse Y. [Comprehensive understanding of viral diseases by field, molecular, and theoretical studies]. Uirusu 2022; 72:87-92. [PMID: 37899235 DOI: 10.2222/jsv.72.87] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/31/2023]
Abstract
Viral diseases are responsible for substantial morbidity and mortality and continue to be of great concern. To ensure better control of viral infections, I have been tackling the issue as a medical doctor, an academic researcher, and a public health officer. Especially, I have studied respiratory viruses, such as the influenza virus, from the perspectives of molecular virology, theoretical modeling, and field epidemiology. RNA biology and its involvement with viral life-cycle and pathogenicity are central topics of molecular study, while mathematical models of transmission dynamics and phylogenetics are major components of theoretical research. As a field epidemiologist, I work with public health authorities during viral disease outbreaks. I was deployed to West Africa for viral hemorrhagic fever outbreak responses as a WHO consultant, and I have served the Japanese Government as an advisor for COVID-19 countermeasures. I would like to integrate various approaches from clinical medicine to epidemiology, theoretical modeling, evolutionary biology, genetics, and molecular biology in my research. In that way, we could gain a more comprehensive understanding of viral diseases. I hope these findings will help ease the disease burden of viral infections around the world.
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Affiliation(s)
- Yuki Furuse
- Nagasaki University Graduate School of Biomedical Sciences/Nagasaki University Hospital Medical Education Development Center
- Institute for Frontier Life and Medical Sciences/Hakubi Center for Advanced Research, Kyoto University
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Tuygun N, Karacan CD, Göktuğ A, Çağlar AA, Tekeli A, Bodur İ, Öztürk B, Güngör A, Güneylioğlu MM, Yaradılmış RM, Akelma Z. Evaluation of changes in pediatric emergency department utilization during COVID-19 pandemic: Changes during COVID-19 pandemic. Arch Pediatr 2021; 28:677-682. [PMID: 34702623 PMCID: PMC8492613 DOI: 10.1016/j.arcped.2021.09.014] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Revised: 05/24/2021] [Accepted: 09/28/2021] [Indexed: 11/10/2022]
Abstract
Background During the coronavirus disease 2019 (COVID-19) pandemic period, the use of emergency services with pediatric non-COVID patients has decreased considerably. We aimed to examine whether there was a change in the demographic data, triage profile, causes, management, and cost of pediatric emergency department (PED) visits of non-COVID patients during the pandemic period. Methods This study was a retrospective, single-center, observational comparative study that was conducted at the PED. Patient records were examined during “the pandemic spring” and the same period of the previous year. Patient demographics, waiting time, and outcome of the PED visit were analyzed in the entire population of children admitted to the PED during the study period, whereas more precise data such as the reason for PED use, duration of symptoms, urgency levels according to the Emergency Severity Index (ESI), final diagnosis, management, and cost of patient care were analyzed in a sample of admitted patients. We used the chi-square test, Fisher's exact test, and Mann–Whitney U test for statistical analyses. Results A total of 62,593 PED visits occurred. During the pandemic period, PED visits showed a decrease of 55.8% compared to the previous year. Patients included in the sampling study group were selected using a systematic random sampling method. The median waiting time during the pandemic period was significantly shorter than the previous year (median 14 min [IQR: 5–32] vs. median 5 min [IQR: 2–16]; p<0.001). The median duration of symptoms was 1 day (1–2) in both groups. Emergency Severity Index (ESI) levels I, II, and III showed a significant increase (27.7% vs. 37.3%) in triage scoring compared to levels IV and V (72.3% vs. 62.7%) during the pandemic period (p<0.001). The median cost per patient during the pandemic period was statistically higher compared to the previous year ($19.57 [19.57–40.50] vs. $25.34 [31.50–52.01]; p<0.001). Overall costs during the pandemic period had a 1.6-fold decline. Conclusion We highlighted the changes in an ordinary PED profile during an extraordinary period. A shift in ESI levels in a more emergent direction was observed. While the number of nonurgent patients, especially those with infections, decreased, the rates of surgical cases, acute neurological and heart diseases, home accidents, and poisoning increased relative to the pre-pandemic period.
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Affiliation(s)
- Nilden Tuygun
- Department of Pediatric Emergency Medicine, Dr. Sami Ulus Maternity and Child Health and Diseases Training and Research Hospital, Ankara, Turkey..
| | - Can Demir Karacan
- Department of Pediatric Emergency Medicine, Dr. Sami Ulus Maternity and Child Health and Diseases Training and Research Hospital, Ankara, Turkey
| | - Aytaç Göktuğ
- Department of Pediatric Emergency Medicine, Dr. Sami Ulus Maternity and Child Health and Diseases Training and Research Hospital, Ankara, Turkey
| | - Ayla Akca Çağlar
- Department of Pediatric Emergency Medicine, Dr. Sami Ulus Maternity and Child Health and Diseases Training and Research Hospital, Ankara, Turkey
| | - Aysun Tekeli
- Department of Pediatric Emergency Medicine, Dr. Sami Ulus Maternity and Child Health and Diseases Training and Research Hospital, Ankara, Turkey
| | - İlknur Bodur
- Department of Pediatric Emergency Medicine, Dr. Sami Ulus Maternity and Child Health and Diseases Training and Research Hospital, Ankara, Turkey
| | - Betül Öztürk
- Department of Pediatric Emergency Medicine, Dr. Sami Ulus Maternity and Child Health and Diseases Training and Research Hospital, Ankara, Turkey
| | - Ali Güngör
- Department of Pediatric Emergency Medicine, Dr. Sami Ulus Maternity and Child Health and Diseases Training and Research Hospital, Ankara, Turkey
| | - Muhammed Mustafa Güneylioğlu
- Department of Pediatric Emergency Medicine, Dr. Sami Ulus Maternity and Child Health and Diseases Training and Research Hospital, Ankara, Turkey
| | - Raziye Merve Yaradılmış
- Department of Pediatric Emergency Medicine, Dr. Sami Ulus Maternity and Child Health and Diseases Training and Research Hospital, Ankara, Turkey
| | - Zülfikar Akelma
- Department of Pediatric Emergency Medicine, Dr. Sami Ulus Maternity and Child Health and Diseases Training and Research Hospital, Ankara, Turkey
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Furuse Y, Oshitani H. Viruses That Can and Cannot Coexist With Humans and the Future of SARS-CoV-2. Front Microbiol 2020; 11:583252. [PMID: 33042101 PMCID: PMC7530166 DOI: 10.3389/fmicb.2020.583252] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2020] [Accepted: 08/19/2020] [Indexed: 12/14/2022] Open
Abstract
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has become a worldwide pandemic. Many projections concerning the outbreak, such as the estimated number of cases and deaths in upcoming months, have been made available. However, what happens to the virus after the pandemic subsides has not been fully explored. In this article, we discuss the ways that past and present human viruses have emerged via zoonotic transmission, the mechanisms that they have acquired the ability for effective transmission among humans, the process to sustain a chain of transmission to coexist with humans, and the factors important for complete containment leading to eradication of viruses. These aspects of viral disease may provide clues for the future path that SARS-CoV-2 might take in relation to human infection.
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Affiliation(s)
- Yuki Furuse
- Institute for Frontier Life and Medical Sciences, Kyoto University, Kyoto, Japan
- Hakubi Center for Advanced Research, Kyoto University, Kyoto, Japan
| | - Hitoshi Oshitani
- Department of Virology, Tohoku University Graduate School of Medicine, Sendai, Japan
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Arden KE, Greer RM, Wang CYT, Mackay IM. Genotypic diversity, circulation patterns and co-detections among rhinoviruses in Queensland, 2001. Access Microbiol 2019; 2:acmi000075. [PMID: 33062934 PMCID: PMC7525053 DOI: 10.1099/acmi.0.000075] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2019] [Accepted: 10/07/2019] [Indexed: 12/13/2022] Open
Abstract
Purpose Rhinoviruses (RVs) occur more frequently than other viruses and more often in people displaying symptoms than in those without. We sought to estimate the spectrum of RV diversity, RV species seasonality and to analyse RV involvement in respiratory virus co-detections. Methodology A convenience collection of 1179 airway sample extracts from patients with suspected respiratory infections, collected during 2001, was subjected to comprehensive molecular testing. Results RVs were the most common virus detected. We were able to genotype ~90 % of RV detections, identifying 70 distinct RVs, spanning all three species. RV-Bs were under-represented. We found RV species co-circulated at times, although one species usually dominated. Each species displayed a bimodal distribution. Conclusion Notably, RVs and influenza A viruses (IFAV) seldom co-occurred, supporting their roles as primary pathogens of the airway among acutely ill infants. Whether RV circulation has a moderating or controlling effect on the IFAV season or is controlled by it cannot be determined from these data. Despite the frequent perception that RVs commonly co-occur with another virus, our findings indicated this was not always the case. Nearly 80 % of RV detections occurred alone. Understanding more about population-level interference between viruses may allow us to harness aspects of it to generate a non-specific antiviral intervention that mimics a putative protective effect. For routine respiratory virus screening to best serve the patient, RV testing should be a principal component of any acute respiratory illness testing algorithm throughout the year.
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Affiliation(s)
- Katherine E Arden
- Child Health Research Centre, The University of Queensland, Brisbane, Queensland, Australia
| | - Ristan M Greer
- Faculty of Medicine, The University of Queensland, Brisbane, Queensland, Australia
| | - Claire Y T Wang
- Child Health Research Centre, The University of Queensland, Brisbane, Queensland, Australia.,Centre for Children's Health Research, Children's Health Queensland South Brisbane, Queensland, 4101, Australia
| | - Ian M Mackay
- Child Health Research Centre, The University of Queensland, Brisbane, Queensland, Australia
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