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Aguiar M, Anam V, Blyuss KB, Estadilla CDS, Guerrero BV, Knopoff D, Kooi BW, Mateus L, Srivastav AK, Steindorf V, Stollenwerk N. Prescriptive, descriptive or predictive models: What approach should be taken when empirical data is limited? Reply to comments on "Mathematical models for Dengue fever epidemiology: A 10-year systematic review". Phys Life Rev 2023; 46:56-64. [PMID: 37245453 DOI: 10.1016/j.plrev.2023.05.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2023] [Accepted: 05/07/2023] [Indexed: 05/30/2023]
Affiliation(s)
- Maíra Aguiar
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain; Ikerbasque, Basque Foundation for Science, Bilbao, Spain.
| | - Vizda Anam
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
| | | | - Carlo Delfin S Estadilla
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain; Preventive Medicine and Public Health Department, University of the Basque Country (UPV/EHU), Leioa, Basque Country Spain
| | - Bruno V Guerrero
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
| | - Damián Knopoff
- Centro de Investigaciones y Estudios de Matemática CIEM, CONICET, Córdoba, Argentina; Intelligent Biodata SL, San Sebastián, Spain
| | - Bob W Kooi
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain; VU University, Faculty of Science, De Boelelaan 1085, NL 1081, HV Amsterdam, the Netherlands
| | - Luís Mateus
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
| | - Akhil Kumar Srivastav
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
| | - Vanessa Steindorf
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
| | - Nico Stollenwerk
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
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Mathematical Modelling of Dengue Transmission with Intervention Strategies Using Fractional Derivatives. Bull Math Biol 2022; 84:138. [DOI: 10.1007/s11538-022-01096-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2022] [Accepted: 10/10/2022] [Indexed: 11/02/2022]
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Wang X, Wang S, Wang J, Rong L. A Multiscale Model of COVID-19 Dynamics. Bull Math Biol 2022; 84:99. [PMID: 35943625 PMCID: PMC9360740 DOI: 10.1007/s11538-022-01058-8] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2021] [Accepted: 07/12/2022] [Indexed: 12/19/2022]
Abstract
COVID-19, caused by the infection of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has been a global pandemic and created unprecedented public health challenges throughout the world. Despite significant progresses in understanding the disease pathogenesis and progression, the epidemiological triad of pathogen, host, and environment remains unclear. In this paper, we develop a multiscale model to study the coupled within-host and between-host dynamics of COVID-19. The model includes multiple transmission routes (both human-to-human and environment-to-human) and connects multiple scales (both the population and individual levels). A detailed analysis on the local and global dynamics of the fast system, slow system and full system shows that rich dynamics, including both forward and backward bifurcations, emerge with the coupling of viral infection and epidemiological models. Model fitting to both virological and epidemiological data facilitates the evaluation of the influence of a few infection characteristics and antiviral treatment on the spread of the disease. Our work underlines the potential role that the environment can play in the transmission of COVID-19. Antiviral treatment of infected individuals can delay but cannot prevent the emergence of disease outbreaks. These results highlight the implementation of comprehensive intervention measures such as social distancing and wearing masks that aim to stop airborne transmission, combined with surface disinfection and hand hygiene that can prevent environmental transmission. The model also provides a multiscale modeling framework to study other infectious diseases when the environment can serve as a reservoir of pathogens.
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Affiliation(s)
- Xueying Wang
- Department of Mathematics and Statistics, Washington State University, Pullman, WA, 99163, USA.
| | - Sunpeng Wang
- Zhengxin Yuguang Group Co. Ltd, 1 Haitang New Street, Chongqing, 400000, China
| | - Jin Wang
- Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, USA
| | - Libin Rong
- Department of Mathematics, University of Florida, Gainesville, FL, 32611, USA
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Aguiar M, Anam V, Blyuss KB, Estadilla CDS, Guerrero BV, Knopoff D, Kooi BW, Srivastav AK, Steindorf V, Stollenwerk N. Mathematical models for dengue fever epidemiology: A 10-year systematic review. Phys Life Rev 2022; 40:65-92. [PMID: 35219611 PMCID: PMC8845267 DOI: 10.1016/j.plrev.2022.02.001] [Citation(s) in RCA: 25] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Accepted: 02/08/2022] [Indexed: 01/11/2023]
Abstract
Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. Mathematical models describing dengue fever epidemiological dynamics are found back from 1970. Dengue fever is a viral mosquito-borne infection caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4). With 2.5 billion people at risk of acquiring the infection, it is a major international public health concern. Although most of the cases are asymptomatic or mild, the disease immunological response is complex, with severe disease linked to the antibody-dependent enhancement (ADE) - a disease augmentation phenomenon where pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection. Here, we present a 10-year systematic review on mathematical models for dengue fever epidemiology. Specifically, we review multi-strain frameworks describing host-to-host and vector-host transmission models and within-host models describing viral replication and the respective immune response. Following a detailed literature search in standard scientific databases, different mathematical models in terms of their scope, analytical approach and structural form, including model validation and parameter estimation using empirical data, are described and analyzed. Aiming to identify a consensus on infectious diseases modeling aspects that can contribute to public health authorities for disease control, we revise the current understanding of epidemiological and immunological factors influencing the transmission dynamics of dengue. This review provide insights on general features to be considered to model aspects of real-world public health problems, such as the current epidemiological scenario we are living in.
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Affiliation(s)
- Maíra Aguiar
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain; Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14, Povo, Trento, 38123, Italy; Ikerbasque, Basque Foundation for Science, Bilbao, Spain.
| | - Vizda Anam
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
| | - Konstantin B Blyuss
- VU University, Faculty of Science, De Boelelaan 1085, NL 1081, HV Amsterdam, the Netherlands
| | - Carlo Delfin S Estadilla
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
| | - Bruno V Guerrero
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
| | - Damián Knopoff
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain; Centro de Investigaciones y Estudios de Matemática CIEM, CONICET, Medina Allende s/n, Córdoba, 5000, Argentina
| | - Bob W Kooi
- University of Sussex, Department of Mathematics, Falmer, Brighton, UK
| | - Akhil Kumar Srivastav
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
| | - Vanessa Steindorf
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
| | - Nico Stollenwerk
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain; Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14, Povo, Trento, 38123, Italy
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Forde JE, Ciupe SM. Modeling the Influence of Vaccine Administration on COVID-19 Testing Strategies. Viruses 2021; 13:2546. [PMID: 34960814 PMCID: PMC8708841 DOI: 10.3390/v13122546] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2021] [Revised: 12/13/2021] [Accepted: 12/15/2021] [Indexed: 01/01/2023] Open
Abstract
Vaccination is considered the best strategy for limiting and eliminating the COVID-19 pandemic. The success of this strategy relies on the rate of vaccine deployment and acceptance across the globe. As these efforts are being conducted, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is continuously mutating, which leads to the emergence of variants with increased transmissibility, virulence, and resistance to vaccines. One important question is whether surveillance testing is still needed in order to limit SARS-CoV-2 transmission in a vaccinated population. In this study, we developed a multi-scale mathematical model of SARS-CoV-2 transmission in a vaccinated population and used it to predict the role of testing in an outbreak with variants of increased transmissibility. We found that, for low transmissibility variants, testing was most effective when vaccination levels were low to moderate and its impact was diminished when vaccination levels were high. For high transmissibility variants, widespread vaccination was necessary in order for testing to have a significant impact on preventing outbreaks, with the impact of testing having maximum effects when focused on the non-vaccinated population.
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Affiliation(s)
- Jonathan E. Forde
- Department of Mathematics and Computer Sciences, Hobart and William Smith Colleges, Geneva, NY 14456, USA
| | - Stanca M. Ciupe
- Department of Mathematics, Virginia Tech, Blacksburg, VA 24060, USA;
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Thibodeaux JJ, Nuñez D, Rivera A. A generalized within-host model of dengue infection with a non-constant monocyte production rate. JOURNAL OF BIOLOGICAL DYNAMICS 2020; 14:143-161. [PMID: 32122254 DOI: 10.1080/17513758.2020.1733678] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2019] [Accepted: 02/04/2020] [Indexed: 06/10/2023]
Abstract
In this paper, we generalize a previous model of within-host dengue infection with a nonconstant monocyte production rate. We establish the existence of three equilibria and give some local stability results. We then estimate three parameters in the model from clinical data for dengue virus serotype 2. It is then shown that the model can exhibit behaviours that are not possible under the assumption of constant monocyte production. Lastly, we perform a sensitivity analysis of the model in two contexts, antiviral treatment and immunostimulatory treatment. The results predict that antiviral treatments that reduce the viral replication rate in infected monocytes are the most effective, while immunostimulatory treatments that increase the rate at which infected monocytes are removed are best.
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Affiliation(s)
- Jeremy J Thibodeaux
- Department of Mathematics and Computer Science, Loyola University New Orleans, New Orleans, LA, USA
| | - Daniel Nuñez
- Department of Natural Sciences and Mathematics, Javeriana University Cali, Cali, Colombia
| | - Andres Rivera
- Department of Natural Sciences and Mathematics, Javeriana University Cali, Cali, Colombia
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Gulbudak H, Browne CJ. Infection severity across scales in multi-strain immuno-epidemiological Dengue model structured by host antibody level. J Math Biol 2020; 80:1803-1843. [PMID: 32157381 DOI: 10.1007/s00285-020-01480-3] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2019] [Revised: 01/19/2020] [Indexed: 01/08/2023]
Abstract
Infection by distinct Dengue virus serotypes and host immunity are intricately linked. In particular, certain levels of cross-reactive antibodies in the host may actually enhance infection severity leading to Dengue hemorrhagic fever (DHF). The coupled immunological and epidemiological dynamics of Dengue calls for a multi-scale modeling approach. In this work, we formulate a within-host model which mechanistically recapitulates characteristics of antibody dependent enhancement in Dengue infection. The within-host scale is then linked to epidemiological spread by a vector-host partial differential equation model structured by host antibody level. The coupling allows for dynamic population-wide antibody levels to be tracked through primary and secondary infections by distinct Dengue strains, along with waning of cross-protective immunity after primary infection. Analysis of both the within-host and between-host systems are conducted. Stability results in the epidemic model are formulated via basic and invasion reproduction numbers as a function of immunological variables. Additionally, we develop numerical methods in order to simulate the multi-scale model and assess the influence of parameters on disease spread and DHF prevalence in the population.
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Affiliation(s)
- Hayriye Gulbudak
- Mathematics Department, University of Louisiana at Lafayette, Lafayette, LA, USA.
| | - Cameron J Browne
- Mathematics Department, University of Louisiana at Lafayette, Lafayette, LA, USA
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