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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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Campo VN, Palacios JL, Nagahashi H, Oh H, Rychtář J, Taylor D. A game-theoretic model of rabies in domestic dogs with multiple voluntary preventive measures. J Math Biol 2022; 85:57. [PMID: 36264390 PMCID: PMC9583067 DOI: 10.1007/s00285-022-01826-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2022] [Revised: 08/14/2022] [Accepted: 10/02/2022] [Indexed: 11/26/2022]
Abstract
Game theory is now routinely applied to quantitatively model the decision making of individuals presented with various voluntary actions that can prevent a given disease. Most models consider only a single preventive strategy and the case where multiple preventative actions are available is severely understudied. In our paper, we consider a very simple SI compartmental model of rabies in the domestic dog population. We study two choices of the dog owners: to vaccinate their dogs or to restrict the movements of unvaccinated dogs. We analyze the relatively rich patterns of Nash equilibria (NE). We show that there is always at least one NE at which the owners utilize only one form of prevention. However, there can be up to three different NEs at the same time: two NEs at which the owners use exclusively only the vaccination or movement restriction, and the third NE when the owners use both forms of prevention simultaneously. However, we also show that, unlike the first two types of NEs, the third kind of NE is not convergent stable.
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Affiliation(s)
- Vince N. Campo
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85281 USA
| | - John Lawrence Palacios
- Division of Mathematics and Computer Science, University of Guam, Mangilao, GU 96913 USA
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284 USA
| | - Hideo Nagahashi
- Division of Mathematics and Computer Science, University of Guam, Mangilao, GU 96913 USA
| | - Hyunju Oh
- Division of Mathematics and Computer Science, University of Guam, Mangilao, GU 96913 USA
| | - Jan Rychtář
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284 USA
| | - Dewey Taylor
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284 USA
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Rychtář J, Taylor D. A game-theoretic model of lymphatic filariasis prevention. PLoS Negl Trop Dis 2022; 16:e0010765. [PMID: 36137005 PMCID: PMC9498957 DOI: 10.1371/journal.pntd.0010765] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2022] [Accepted: 08/23/2022] [Indexed: 11/18/2022] Open
Abstract
Lymphatic filariasis (LF) is a mosquito-borne parasitic neglected tropical disease. In 2000, WHO launched the Global Programme to Eliminate Lymphatic Filariasis (GPELF) as a public health problem. In 2020, new goals for 2030 were set which includes a reduction to 0 of the total population requiring Mass Drug Administrations (MDA), a primary tool of GPELF. We develop a mathematical model to study what can happen at the end of MDA. We use a game-theoretic approach to assess the voluntary use of insect repellents in the prevention of the spread of LF through vector bites. Our results show that when individuals use what they perceive as optimal levels of protection, the LF incidence rates will become high. This is in striking difference to other vector-borne NTDs such as Chagas or zika. We conclude that the voluntary use of the protection alone will not be enough to keep LF eliminated as a public health problem and a more coordinated effort will be needed at the end of MDA.
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Affiliation(s)
- Jan Rychtář
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, Virginia, United States of America
- * E-mail:
| | - Dewey Taylor
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, Virginia, United States of America
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