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Davis C, Javor ER, Rebarber SI, Rychtář J, Taylor D. A mathematical model of visceral leishmaniasis transmission and control: Impact of ITNs on VL prevention and elimination in the Indian subcontinent. PLoS One 2024; 19:e0311314. [PMID: 39365771 PMCID: PMC11452004 DOI: 10.1371/journal.pone.0311314] [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: 08/26/2023] [Accepted: 09/17/2024] [Indexed: 10/06/2024] Open
Abstract
Visceral Leishmaniasis (VL) is a deadly, vector-borne, parasitic, neglected tropical disease, particularly prevalent on the Indian subcontinent. Sleeping under the long-lasting insecticide-treated nets (ITNs) was considered an effective VL prevention and control measures, until KalaNet, a large trial in Nepal and India, did not show enough supporting evidence. In this paper, we adapt a biologically accurate, yet relatively simple compartmental ordinary differential equations (ODE) model of VL transmission and explicitly model the use of ITNs and their role in VL prevention and elimination. We also include a game-theoretic analysis in order to determine an optimal use of ITNs from the individuals' perspective. In agreement with the previous more detailed and complex model, we show that the ITNs coverage amongst the susceptible population has to be unrealistically high (over 96%) in order for VL to be eliminated. However, we also show that if the whole population, including symptomatic and asymptomatic VL cases adopt about 90% ITN usage, then VL can be eliminated. Our model also suggests that ITN usage should be accompanied with other interventions such as vector control.
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Affiliation(s)
- Cameron Davis
- Department of Mathematics, Fitchburg State University, Fitchburg, MA, United States of America
| | - Elizabeth R. Javor
- Department of Mathematics, Rochester Institute of Technology, Rochester, NY, United States of America
| | - Sonja I. Rebarber
- Department of Mathematics and Statistics, Swarthmore College, Swarthmore, PA, United States of America
| | - Jan Rychtář
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, United States of America
| | - Dewey Taylor
- Department of Mathematics, Rochester Institute of Technology, Rochester, NY, United States of America
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2
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Dias LKS, Sanhueza-Sanzana C, Pinheiro FML, Martins AF, Correia FGS, de Aguiar IWO, Ferreira NC, Stolow J, Rutherford G, Teixeira MG, Pires RDJ, de Almeida RLF, Coelho ICB, Frota CC, Kendall C, Kerr LRFS. Use of insect repellent as personal protection among women of childbearing age in an arbovirus endemic area in Northeastern Brazil. REVISTA BRASILEIRA DE EPIDEMIOLOGIA 2024; 27:e240025. [PMID: 38747743 PMCID: PMC11093518 DOI: 10.1590/1980-549720240025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2023] [Revised: 01/11/2024] [Accepted: 01/30/2024] [Indexed: 05/19/2024] Open
Abstract
OBJECTIVE To analyze the factors associated with the individual use of insect repellent by women of childbearing age living in area endemic for arboviruses in Fortaleza, Brazil. METHODS This is a cohort study carried out between 2018 and 2019 with women aged between 15 and 39 years in Fortaleza, state of Ceará, Brazil. A total of 1,173 women users of one of the four selected primary health care units participated in the study. The outcome was divided into: continued use, discontinued use, and nonuse of insect repellent. Crude and adjusted multinominal logistic regression analysis was carried out guided by a hierarchical model, with presentation of the respective odds ratio (OR) and 95% confidence intervals (95%CI). The independent variables include: socioeconomic and demographic data, environmental and sanitary characteristics, knowledge of the insect repellent, and behavioral and pregnancy-related aspects. RESULTS Only 28% of the participants reported using insect repellent during the two waves of the cohort. Women with higher education (OR=2.55; 95%CI 1.44-4.51); who are employed (OR=1.51; 95%CI 1.12-2.03); who received guidance from healthcare professionals (OR=1.74; 95%CI 1.28-2.36) and the media (OR=1.43; 95%CI 1.01-2.02); who intensified precautions against mosquitoes during the epidemic (OR=3.64; 95%CI 2.29-5.78); and who were pregnant between 2016 and 2019 (OR=2.80; 95%CI 1.83-4.30) had increased odds for continued use of insect repellent. CONCLUSION The use of insect repellent among women of childbearing age was associated with a higher level of education, employment, guidance on insect repellent provided by healthcare professionals and the media, behavioral changes to protect against mosquitoes during the Zika virus epidemic, and pregnancy when occurring as of the beginning of the epidemic period.
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Affiliation(s)
- Livia Karla Sales Dias
- Universidade Federal do Ceará, School of Medicine, Department of Community Health – Fortaleza (CE), Brazil
| | - Carlos Sanhueza-Sanzana
- Universidade Federal do Ceará, School of Medicine, Department of Community Health – Fortaleza (CE), Brazil
| | | | - Adriano Ferreira Martins
- Universidade Federal do Ceará, School of Medicine, Department of Community Health – Fortaleza (CE), Brazil
| | | | | | - Nayane Cavalcante Ferreira
- Universidade Federal do Ceará, School of Medicine, Department of Community Health – Fortaleza (CE), Brazil
| | - Jeni Stolow
- Tulane University, Tulane School of Public Health and Tropical Medicine, Department of Social Behavior and Population Science – New Orleans (LA), USA
| | - George Rutherford
- University of California, Department of Epidemiology and Biostatistics – San Francisco, California (CA), USA
| | - Maria Gloria Teixeira
- Universidade Federal da Bahia, Institute of Collective Health – Salvador (BA), Brazil
| | - Roberto da Justa Pires
- Universidade Federal do Ceará, School of Medicine, Department of Community Health – Fortaleza (CE), Brazil
| | | | - Ivo Castelo Branco Coelho
- Universidade Federal do Ceará, School of Medicine, Department of Pathology and Legal Medicine – Fortaleza (CE), Brazil
| | - Cristiane Cunha Frota
- Universidade Federal do Ceará, School of Medicine, Department of Pathology and Legal Medicine – Fortaleza (CE), Brazil
| | - Carl Kendall
- Universidade Federal do Ceará, School of Medicine, Department of Community Health – Fortaleza (CE), Brazil
- Tulane University, Tulane School of Public Health and Tropical Medicine, Department of Social Behavior and Population Science – New Orleans (LA), USA
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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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Behavioral and game-theoretic modeling of dengue epidemic: Comment on "Mathematical models for dengue fever epidemiology: A 10-year systematic review" by M. Aguiar et al. Phys Life Rev 2022; 43:20-22. [PMID: 36029602 PMCID: PMC9712585 DOI: 10.1016/j.plrev.2022.07.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2022] [Accepted: 07/28/2022] [Indexed: 12/15/2022]
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5
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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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6
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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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7
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Angina J, Bachhu A, Talati E, Talati R, Rychtář J, Taylor D. Game-Theoretical Model of the Voluntary Use of Insect Repellents to Prevent Zika Fever. DYNAMIC GAMES AND APPLICATIONS 2022; 12:133-146. [PMID: 35127230 PMCID: PMC8800840 DOI: 10.1007/s13235-021-00418-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 12/10/2021] [Indexed: 05/14/2023]
Abstract
Zika fever is an emerging mosquito-borne disease. While it often causes no or only mild symptoms that are similar to dengue fever, Zika virus can spread from a pregnant woman to her baby and cause severe birth defects. There is no specific treatment or vaccine, but the disease can be mitigated by using several control strategies, generally focusing on the reduction in mosquitoes or mosquito bites. In this paper, we model Zika virus transmission and incorporate a game-theoretical approach to study a repeated population game of DEET usage to prevent insect bites. We show that the optimal use effectively leads to disease elimination. This result is robust and not significantly dependent on the cost of the insect repellents.
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Affiliation(s)
- Jabili Angina
- Department of Biology, Virginia Commonwealth University, Richmond, VA 23284-2012 USA
| | - Anish Bachhu
- Department of Biology, Virginia Commonwealth University, Richmond, VA 23284-2012 USA
| | - Eesha Talati
- Department of Biology, Virginia Commonwealth University, Richmond, VA 23284-2012 USA
| | - Rishi Talati
- Department of Biology, Virginia Commonwealth University, Richmond, VA 23284-2012 USA
| | - Jan Rychtář
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014 USA
| | - Dewey Taylor
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014 USA
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8
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Optimal Voluntary Vaccination of Adults and Adolescents Can Help Eradicate Hepatitis B in China. GAMES 2021. [DOI: 10.3390/g12040082] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
Hepatitis B (HBV) is one of the most common infectious diseases, with a worldwide annual incidence of over 250 million people. About one-third of the cases are in China. While China made significant efforts to implement a nationwide HBV vaccination program for newborns, a significant number of susceptible adults and teens remain. In this paper, we analyze a game-theoretical model of HBV dynamics that incorporates government-provided vaccination at birth coupled with voluntary vaccinations of susceptible adults and teens. We show that the optimal voluntary vaccination brings the disease incidence to very low levels. This result is robust and, in particular, due to a high HBV treatment cost, essentially independent from the vaccine cost.
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9
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Fortunato AK, Glasser CP, Watson JA, Lu Y, Rychtář J, Taylor D. Mathematical modelling of the use of insecticide-treated nets for elimination of visceral leishmaniasis in Bihar, India. ROYAL SOCIETY OPEN SCIENCE 2021; 8:201960. [PMID: 34234949 PMCID: PMC8242840 DOI: 10.1098/rsos.201960] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2020] [Accepted: 05/24/2021] [Indexed: 05/27/2023]
Abstract
Visceral leishmaniasis (VL) is a deadly neglected tropical disease caused by a parasite Leishmania donovani and spread by female sand flies Phlebotomus argentipes. There is conflicting evidence regarding the role of insecticide-treated nets (ITNs) on the prevention of VL. Numerous studies demonstrated the effectiveness of ITNs. However, KalaNet, a large trial in Nepal and India did not support those findings. The purpose of this paper is to gain insight into the situation by mathematical modelling. We expand a mathematical model of VL transmission based on the KalaNet trial and incorporate the use of ITNs explicitly into the model. One of the major contributions of this work is that we calibrate the model based on the available epidemiological data, generally independent of the KalaNet trial. We validate the model on data collected during the KalaNet trial. We conclude that in order to eliminate VL, the ITN usage would have to stay above 96%. This is higher than the 91% ITNs use at the end of the trial which may explain why the trial did not show a positive effect from ITNs. At the same time, our model indicates that asymptomatic individuals play a crucial role in VL transmission.
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Affiliation(s)
- Anna K. Fortunato
- Department of Mathematics, University of Richmond, Richmond, VA 23173, USA
| | - Casey P. Glasser
- Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-1026, USA
| | - Joy A. Watson
- Department of Mathematics and Economics, Virginia State University, Petersburg, VA 23806, USA
| | - Yongjin Lu
- Department of Mathematics and Economics, Virginia State University, Petersburg, VA 23806, USA
| | - Jan Rychtář
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA
| | - Dewey Taylor
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA
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10
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Xue L, Ren X, Magpantay F, Sun W, Zhu H. Optimal Control of Mitigation Strategies for Dengue Virus Transmission. Bull Math Biol 2021; 83:8. [PMID: 33404917 DOI: 10.1007/s11538-020-00839-3] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2019] [Accepted: 11/21/2020] [Indexed: 11/30/2022]
Abstract
Dengue virus is transmitted by Aedes mosquitoes, posing threat to people's health and leading to great economic cost in many tropical and subtropical regions. We develop an ordinary differential equation model taking into account multiple strains of dengue virus. Using the model, we assess the effectiveness of human vaccination considering its waning and failure. We derive the lower bound and upper bound for the final size of the epidemic. Sensitivity analysis quantifies the impact of parameters on the basic reproduction number. Different scenarios of vaccinating humans show that it is better to vaccinate humans at early stages. We find that the cumulative number of infected humans is small when the vaccination rate is high or the waning rate is low for previously infected humans. We analyze the necessary conditions for implementing optimal control and derive the corresponding optimal solutions for mitigation dengue virus transmission by applying Pontryagin's Maximum Principle. Our findings may provide guidance for the public health authorities to implement human vaccination and other mitigation strategies.
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Affiliation(s)
- Ling Xue
- College of Automation, Harbin Engineering University, Harbin, 150001, China.,College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, China
| | - Xue Ren
- College of Automation, Harbin Engineering University, Harbin, 150001, China.,College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, China
| | - Felicia Magpantay
- Department of Mathematics and Statistics, Queen's University, Kingston, K7L 3N6, Canada
| | - Wei Sun
- College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, China.
| | - Huaiping Zhu
- Department of Mathematics and Statistics, York University, Toronto, M3J 1P3, Canada
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Klein SRM, Foster AO, Feagins DA, Rowell JT, Erovenko IV. Optimal voluntary and mandatory insect repellent usage and emigration strategies to control the chikungunya outbreak on Reunion Island. PeerJ 2020; 8:e10151. [PMID: 33362952 PMCID: PMC7750003 DOI: 10.7717/peerj.10151] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2019] [Accepted: 09/21/2020] [Indexed: 12/18/2022] Open
Abstract
In 2005, a chikungunya virus outbreak devastated the tropical island of Reunion, infecting a third of the total population. Motivated by the Reunion Island case study, we investigate the theoretic potential for two intervention measures under both voluntary and mandatory protocols to control a vector-borne disease when there is risk of the disease becoming endemic. The first measure uses insect repellent to prevent mosquito bites, while the second involves emigrating to the neighboring Mauritius Island to avoid infection. There is a threshold on the cost of using repellent above which both voluntary and mandatory regimes find it optimal to forgo usage. Below that threshold, mandatory usage protocols will eradicate the disease; however, voluntary adoption leaves the disease at a small endemic level. Emigrating from the island to avoid infection results in a tragedy-of-the-commons effect: while being potentially beneficial to specific susceptible individuals, the remaining islanders paradoxically face a higher risk of infection. Mandated relocation of susceptible individuals away from the epidemic is viable only if the cost of this relocation is several magnitudes lower than the cost of infection. Since this assumption is unlikely to hold for chikungunya, it is optimal to discourage such emigration for the benefit of the entire population. An underlying assumption about the conservation of human-vector encounter rates in mosquito biting behavior informs our conclusions and may warrant additional experimental verification.
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Affiliation(s)
- Sylvia R M Klein
- Department of Mathematics, St. Mary's College of Maryland, St. Mary's City, MD, USA
| | - Alex O Foster
- Department of Mathematics and Statistics, Coastal Carolina University, Conway, SC, USA
| | - David A Feagins
- Department of Mathematics, St. Mary's University, San Antonio, TX, USA
| | - Jonathan T Rowell
- Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC, USA
| | - Igor V Erovenko
- Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC, USA
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12
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Han CY, Issa H, Rychtář J, Taylor D, Umana N. A voluntary use of insecticide treated nets can stop the vector transmission of Chagas disease. PLoS Negl Trop Dis 2020; 14:e0008833. [PMID: 33141850 PMCID: PMC7671556 DOI: 10.1371/journal.pntd.0008833] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2020] [Revised: 11/17/2020] [Accepted: 09/24/2020] [Indexed: 11/19/2022] Open
Abstract
One of the stated goals of the London Declaration on Neglected Tropical Diseases is the interruption of domiciliary transmissions of Chagas disease in the region of the Americas. We used a game-theoretic approach to assess the voluntary use of insecticide treated nets (ITNs) in the prevention of the spread of infection through vector bites. Our results show that individuals behave rationally and weigh the risks of insect bites against the cost of the ITNs. The optimal voluntary use of ITNs results in predicted incidence rates that closely track the real incidence rates in Latin America. This means that ITNs are effective and could be used to control the spread of the disease by relying on individual decisions rather than centralized policies. Our model shows that to completely eradicate the vector transmission through the voluntary individual use of ITNs, the cost of ITNs should be as low as possible.
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Affiliation(s)
- Cheol Yong Han
- Department of Mechanical and Nuclear Engineering, Virginia Commonwealth University, Richmond, Virginia, USA
| | - Habeeb Issa
- Department of Biology, Virginia Commonwealth University, Richmond, Virginia, USA
| | - Jan Rychtář
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, Virginia, USA
| | - Dewey Taylor
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, Virginia, USA
| | - Nancy Umana
- Department of Biology, Virginia Commonwealth University, Richmond, Virginia, USA
- Department of Psychology, Virginia Commonwealth University, Richmond, Virginia, USA
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13
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Acosta-Alonzo CB, Erovenko IV, Lancaster A, Oh H, Rychtář J, Taylor D. High endemic levels of typhoid fever in rural areas of Ghana may stem from optimal voluntary vaccination behaviour. Proc Math Phys Eng Sci 2020; 476:20200354. [PMID: 33071586 PMCID: PMC7544331 DOI: 10.1098/rspa.2020.0354] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 08/04/2020] [Indexed: 01/24/2023] Open
Abstract
Typhoid fever has long established itself endemically in rural Ghana despite the availability of cheap and effective vaccines. We used a game-theoretic model to investigate whether the low vaccination coverage in Ghana could be attributed to rational human behaviour. We adopted a version of an epidemiological model of typhoid fever dynamics, which accounted not only for chronic life-long carriers but also for a short-cycle transmission in the immediate environment and a long-cycle transmission via contamination of the water supply. We calibrated the model parameters based on the known incidence data. We found that unless the (perceived) cost of vaccination is negligible, the individually optimal population vaccination rate falls significantly short of the societally optimal population vaccination rate needed to reach herd immunity. We expressed both the herd immunity and the optimal equilibrium vaccination rates in terms of only a few observable parameters such as the incidence rate, demographics, vaccine waning rate and the perceived cost of vaccination relative to the cost of infection. This allowed us not to rely on other uncertain epidemiological model parameters and, in particular, to bypass uncertainties about the role of the carriers in the transmission.
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Affiliation(s)
| | - Igor V. Erovenko
- Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27402, USA
| | - Aaleah Lancaster
- Department of Mathematics and Computer Science, Bennett College, Greensboro, NC 27401, USA
| | - Hyunju Oh
- Division of Mathematics and Computer Science, University of Guam, Mangilao, Guam 96923, USA
| | - Jan Rychtář
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA
| | - Dewey Taylor
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA
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Chouhan A, Maiwand S, Ngo M, Putalapattu V, Rychtář J, Taylor D. Game-Theoretical Model of Retroactive Hepatitis B Vaccination in China. Bull Math Biol 2020; 82:80. [PMID: 32542575 DOI: 10.1007/s11538-020-00748-5] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2020] [Accepted: 05/14/2020] [Indexed: 02/08/2023]
Abstract
Hepatitis B (HepB) is one of the most common infectious diseases affecting over two billion people worldwide. About one third of all HepB cases are in China. In recent years, China made significant efforts to implement a nationwide HepB vaccination program and reduced the number of unvaccinated infants from 30 to 10%. However, many individuals still remain unprotected, particularly those born before 2003. Consequently, a catch-up retroactive vaccination is an important and potentially cost-effective way to reduce HepB prevalence. In this paper, we analyze a game theoretical model of HepB dynamics that incorporates government-provided vaccination at birth coupled with voluntary retroactive vaccinations. Given the uncertainty about the long-term efficacy of the HepB vaccinations, we study several scenarios. When the waning rate is relatively high, we show that this retroactive vaccination should be a necessary component of any HepB eradication effort. When the vaccine offers long-lasting protection, the voluntary retroactive vaccination brings the disease incidence to sufficiently low levels. Also, we find that the optimal vaccination rates are almost independent of the vaccination coverage at birth. Moreover, it is in an individual's self-interest to vaccinate (and potentially re-vaccinate) at a rate just slightly above the vaccine waning rate.
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Affiliation(s)
- Ali Chouhan
- Department of Biology, Virginia Commonwealth University, Richmond, VA, 23284-2012, USA
| | - Sohail Maiwand
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, 23284-2014, USA
| | - Matthew Ngo
- Department of Biology, Virginia Commonwealth University, Richmond, VA, 23284-2012, USA
| | - Vooha Putalapattu
- Department of Psychology, Virginia Commonwealth University, Richmond, VA, 23284-2018, USA
| | - Jan Rychtář
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, 23284-2014, USA.
| | - Dewey Taylor
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, 23284-2014, USA
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15
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Cheng E, Gambhirrao N, Patel R, Zhowandai A, Rychtář J, Taylor D. A game-theoretical analysis of poliomyelitis vaccination. J Theor Biol 2020; 499:110298. [PMID: 32371008 DOI: 10.1016/j.jtbi.2020.110298] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2019] [Revised: 04/21/2020] [Accepted: 04/26/2020] [Indexed: 12/15/2022]
Abstract
Poliomyelitis is a worldwide disease that has nearly been eradicated thanks to the Global Polio Eradication Initiative. Nevertheless, the disease is currently still endemic in three countries. In this paper, we incorporate the vaccination in a two age-class model of polio dynamics. Our main objective is to see whether mandatory vaccination policy is needed or if polio could be almost eradicated by a voluntary vaccination. We perform game theoretical analysis and compare the herd immunity vaccination levels with the Nash equilibrium vaccination levels. We show that the gap between two vaccination levels is too large. We conclude that the mandatory vaccination policy is therefore needed to achieve a complete eradication.
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Affiliation(s)
- Emily Cheng
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, VA 23284-3068, USA.
| | - Neeha Gambhirrao
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, VA 23284-3068, USA.
| | - Rohani Patel
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, VA 23284-3068, USA.
| | - Aufia Zhowandai
- Department of Biology, Virginia Commonwealth University, Richmond, VA 23284-2012, USA.
| | - Jan Rychtář
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA.
| | - Dewey Taylor
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA.
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16
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Kobe J, Pritchard N, Short Z, Erovenko IV, Rychtář J, Rowell JT. A Game-Theoretic Model of Cholera with Optimal Personal Protection Strategies. Bull Math Biol 2018; 80:2580-2599. [PMID: 30203140 DOI: 10.1007/s11538-018-0476-5] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2016] [Accepted: 07/23/2018] [Indexed: 11/27/2022]
Abstract
Cholera is an acute gastro-intestinal infection that affects millions of people throughout the world each year, primarily but not exclusively in developing countries. Because of its public health ramifications, considerable mathematical attention has been paid to the disease. Here we consider one neglected aspect of combating cholera: personal participation in anti-cholera interventions. We construct a game-theoretic model of cholera in which individuals choose whether to participate in either vaccination or clean water consumption programs under assumed costs. We find that relying upon individual compliance significantly lowers the incidence of the disease as long as the cost of intervention is sufficiently low, but does not eliminate it. The relative costs of the measures determined whether a population preferentially adopts a single preventative measure or employs the measure with the strongest early adoption.
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Affiliation(s)
- Julia Kobe
- Department of Applied Mathematics, Wentworth Institute of Technology, Boston, MA, 02115, USA
| | - Neil Pritchard
- Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC, 27402, USA
| | - Ziaqueria Short
- Department of Biological Sciences, Winston-Salem State University, Winston-Salem, NC, 27110, USA
| | - Igor V Erovenko
- Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC, 27402, USA.
| | - Jan Rychtář
- Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC, 27402, USA
| | - Jonathan T Rowell
- Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC, 27402, USA
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17
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Brettin A, Rossi–Goldthorpe R, Weishaar K, Erovenko IV. Ebola could be eradicated through voluntary vaccination. ROYAL SOCIETY OPEN SCIENCE 2018; 5:171591. [PMID: 29410863 PMCID: PMC5792940 DOI: 10.1098/rsos.171591] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2017] [Accepted: 12/11/2017] [Indexed: 05/04/2023]
Abstract
Ebola virus disease (EVD) is a severe infection with an extremely high fatality rate spread through direct contact with body fluids. A promising Ebola vaccine (rVSV-ZEBOV) may soon become universally available. We constructed a game-theoretic model of Ebola incorporating individual decisions to vaccinate. We found that if a population adopts selfishly optimal vaccination strategies, then the population vaccination coverage falls negligibly short of the herd immunity level. We concluded that eradication of Ebola is feasible if voluntary vaccination programmes are coupled with focused public education efforts. We conducted uncertainty and sensitivity analysis to demonstrate that our findings do not depend on the choice of the epidemiological model parameters.
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Affiliation(s)
- Andrew Brettin
- Department of Mathematics, University of Minnesota—Twin Cities, Minneapolis, MN 55455, USA
| | | | - Kyle Weishaar
- Department of Mathematics, Regis University, Denver, CO 80221, USA
| | - Igor V. Erovenko
- Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27402, USA
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