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Pepiot A, Supervie V, Breban R. Impact of voluntary testing on infectious disease epidemiology: A game theoretic approach. PLoS One 2023; 18:e0293968. [PMID: 37934734 PMCID: PMC10629633 DOI: 10.1371/journal.pone.0293968] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2023] [Accepted: 10/23/2023] [Indexed: 11/09/2023] Open
Abstract
The World Health Organization recommends test-and-treat interventions to curb and even eliminate epidemics of HIV, viral hepatitis, and sexually transmitted infections (e.g., chlamydia, gonorrhea, syphilis and trichomoniasis). Epidemic models show these goals are achievable, provided the participation of individuals in test-and-treat interventions is sufficiently high. We combine epidemic models and game theoretic models to describe individual's decisions to get tested for infectious diseases within certain epidemiological contexts, and, implicitly, their voluntary participation to test-and-treat interventions. We develop three hybrid models, to discuss interventions against HIV, HCV, and sexually transmitted infections, and the potential behavioral response from the target population. Our findings are similar across diseases. Particularly, individuals use three distinct behavioral patterns relative to testing, based on their perceived costs for testing, besides the payoff for discovering their disease status. Firstly, if the cost of testing is too high, then individuals refrain from voluntary testing and get tested only if they are symptomatic. Secondly, if the cost is moderate, some individuals will test voluntarily, starting treatment if needed. Hence, the spread of the disease declines and the disease epidemiology is mitigated. Thirdly, the most beneficial testing behavior takes place as individuals perceive a per-test payoff that surpasses a certain threshold, every time they get tested. Consequently, individuals achieve high voluntary testing rates, which may result in the elimination of the epidemic, albeit on temporary basis. Trials and studies have attained different levels of participation and testing rates. To increase testing rates, they should provide each eligible individual with a payoff, above a given threshold, each time the individual tests voluntarily.
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Affiliation(s)
- Amandine Pepiot
- Institut Pierre Louis d’Epidémiologie et de Santé Publique (IPLESP), Sorbonne Université, INSERM, Paris, France
| | - Virginie Supervie
- Institut Pierre Louis d’Epidémiologie et de Santé Publique (IPLESP), Sorbonne Université, INSERM, Paris, France
| | - Romulus Breban
- Institut Pasteur, Unité d’Epidémiologie des Maladies Emergentes, Paris, France
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2
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Augsburger IB, Galanthay GK, Tarosky JH, Rychtář J, Taylor D. Imperfect vaccine can yield multiple Nash equilibria in vaccination games. Math Biosci 2023; 356:108967. [PMID: 36649795 DOI: 10.1016/j.mbs.2023.108967] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2022] [Revised: 12/13/2022] [Accepted: 01/07/2023] [Indexed: 01/15/2023]
Abstract
As infectious diseases continue to threaten communities across the globe, people are faced with a choice to vaccinate, or not. Many factors influence this decision, such as the cost of the disease, the chance of contracting the disease, the population vaccination coverage, and the efficacy of the vaccine. While the vaccination games in which individuals decide whether to vaccinate or not based on their own interests are gaining in popularity in recent years, the vaccine imperfection has been an overlooked aspect so far. In this paper we investigate the effects of an imperfect vaccine on the outcomes of a vaccination game. We use a simple SIR compartmental model for the underlying model of disease transmission. We model the vaccine imperfection by adding vaccination at birth and maintain a possibility for the vaccinated individual to become infected. We derive explicit conditions for the existence of different Nash equilibria, the solutions of the vaccination game. The outcomes of the game depend on the complex interplay between disease transmission dynamics (the basic reproduction number), the relative cost of the infection, and the vaccine efficacy. We show that for diseases with relatively low basic reproduction numbers (smaller than about 2.62), there is a little difference between outcomes for perfect or imperfect vaccines and thus the simpler models assuming perfect vaccines are good enough. However, when the basic reproduction number is above 2.62, then, unlike in the case of a perfect vaccine, there can be multiple equilibria. Moreover, unless there is a mandatory vaccination policy in place that would push the vaccination coverage above the value of unstable Nash equilibrium, the population could eventually slip to the "do not vaccinate" state. Thus, for diseases that have relatively high basic reproduction numbers, the potential for the vaccine not being perfect should be explicitly considered in the models.
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Affiliation(s)
- Ian B Augsburger
- Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Grace K Galanthay
- Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA 01610, USA.
| | - Jacob H Tarosky
- Department of Mathematical Sciences, High Point University, High Point, NC 27268, 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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3
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Allaire M, Bruix J, Korenjak M, Manes S, Maravic Z, Reeves H, Salem R, Sangro B, Sherman M. What to do about hepatocellular carcinoma: Recommendations for health authorities from the International Liver Cancer Association. JHEP Rep 2022; 4:100578. [PMID: 36352896 PMCID: PMC9638834 DOI: 10.1016/j.jhepr.2022.100578] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 07/24/2022] [Revised: 08/26/2022] [Accepted: 08/29/2022] [Indexed: 12/02/2022] Open
Abstract
Hepatocellular carcinoma (HCC) is a major public health problem worldwide for which the incidence and mortality are similar, pointing to the lack of effective treatment options. Knowing the different issues involved in the management of HCC, from risk factors to screening and management, is essential to improve the prognosis and quality of life of affected individuals. This document summarises the current state of knowledge and the unmet needs for all the different stakeholders in the care of liver cancer, meaning patients, relatives, physicians, regulatory agencies and health authorities so that optimal care can be delivered to patients. The document was commissioned by the International Liver Cancer Association and was reviewed by senior members, including two ex-presidents of the Association. This document lays out the recommended approaches to the societal management of HCC based on the economic status of a given region.
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Key Words
- AASLD, American Association for the Study of Liver Disease
- AFP, alpha-fetoprotein
- ALT, alanine aminotransferase
- APRI, aspartate aminotransferase-to-platelet ratio index
- Alcohol consumption
- BCLC, Barcelona clinic liver cancer
- DCP, des-gammacarboxy prothrombin
- DEB-TACE, TACE with drug-eluting beads
- EASL, European Association for the study of the Liver
- EBRT, external beam radiation therapy
- ELF, enhanced liver fibrosis
- GGT, gamma-glutamyltransferase
- HCC, hepatocellular carcinoma
- Hepatocellular carcinoma
- Hepatocellular carcinoma surveillance
- Hepatocellular carcinoma treatment
- Li-RADS, Liver Imaging Reporting and Data System
- NAFLD, non-alcoholic fatty liver disease
- Obesity
- RFA, radiofrequency ablation
- TACE, transarterial chemoembolisation
- TARE, transarterial radioembolisation
- TKI, tyrosine kinase inhibitor
- Viral hepatitis
- cTACE, conventional TACE
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Affiliation(s)
- Manon Allaire
- AP-HP Sorbonne Université, Hôpital Universitaire Pitié-Salpêtrière, Service d’Hépato-gastroentérologie, Paris, France
| | - Jordi Bruix
- University Hospital Clinic IDIBAPS, Barcelona, Spain
| | - Marko Korenjak
- European Liver Patients' Association (ELPA), Brussels, Belgium
| | - Sarah Manes
- Global Liver Institute Washington District of Columbia, USA
| | | | - Helen Reeves
- The Newcastle University Centre for Cancer, Newcastle University, Newcastle upon Tyne, UK
| | - Riad Salem
- Department of Radiology, Section of Interventional Radiology, Department of Radiology, Northwestern Memorial Hospital, Chicago, IL 60611, USA
| | - Bruno Sangro
- Liver Unit and HPB Oncology Area, Clinica Universidad de Navarra and CIBEREHD, Pamplona, Spain
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4
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Augsburger IB, Galanthay GK, Tarosky JH, Rychtář J, Taylor D. Voluntary vaccination may not stop monkeypox outbreak: A game-theoretic model. PLoS Negl Trop Dis 2022; 16:e0010970. [PMID: 36516113 DOI: 10.1371/journal.pntd.0010970] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2022] [Accepted: 11/21/2022] [Indexed: 12/15/2022] Open
Abstract
Monkeypox (MPX) is a viral zoonotic disease that was endemic to Central and West Africa. However, during the first half of 2022, MPX spread to almost 60 countries all over the world. Smallpox vaccines are about 85% effective in preventing MPX infections. Our objective is to determine whether the vaccines should be mandated or whether voluntary use of the vaccine could be enough to stop the MPX outbreak. We incorporate a standard SVEIR compartmental model of MPX transmission into a game-theoretical framework. We study a vaccination game in which individuals decide whether or not to vaccinate by assessing their benefits and costs. We solve the game for Nash equilibria, i.e., the vaccination rates the individuals would likely adopt without any outside intervention. We show that, without vaccination, MPX can become endemic in previously non-endemic regions, including the United States. We also show that to "not vaccinate" is often an optimal solution from the individual's perspective. Moreover, we demonstrate that, for some parameter values, there are multiple equilibria of the vaccination game, and they exhibit a backward bifurcation. Thus, without centrally mandated minimal vaccination rates, the population could easily revert to no vaccination scenario.
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Affiliation(s)
- Ian B Augsburger
- Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, Maryland, United States of America
| | - Grace K Galanthay
- Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, Massachusetts, United States of America
| | - Jacob H Tarosky
- Department of Mathematical Sciences, High Point University, High Point, North Carolina, United States of America
| | - Jan Rychtář
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, Virginia, United States of America
| | - Dewey Taylor
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, Virginia, United States of America
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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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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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11
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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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12
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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 DOI: 10.1098/rspa.2020.0354] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [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)
- Carmen B Acosta-Alonzo
- Department of Mathematics and Computer Science, Bennett College, Greensboro, NC 27401, USA
| | - 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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13
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Bankuru SV, Kossol S, Hou W, Mahmoudi P, Rychtář J, Taylor D. A game-theoretic model of Monkeypox to assess vaccination strategies. PeerJ 2020; 8:e9272. [PMID: 32607280 PMCID: PMC7316080 DOI: 10.7717/peerj.9272] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2020] [Accepted: 05/11/2020] [Indexed: 01/05/2023] Open
Abstract
Monkeypox (MPX) is a zoonotic disease similar to smallpox. Its fatality rate is about 11% and it is endemic to the Central and West African countries. In this paper, we analyze a compartmental model of MPX dynamics. Our goal is to see whether MPX can be controlled and eradicated by voluntary vaccinations. We show that there are three equilibria—disease free, fully endemic and previously neglected semi-endemic (with disease existing only among humans). The existence of semi-endemic equilibrium has severe implications should the MPX virus mutate to increased viral fitness in humans. We find that MPX is controllable and can be eradicated in a semi-endemic equilibrium by vaccination. However, in a fully endemic equilibrium, MPX cannot be eradicated by vaccination alone.
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Affiliation(s)
- Sri Vibhaav Bankuru
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, VA, United States of America
| | - Samuel Kossol
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, VA, United States of America
| | - William Hou
- Department of Kinesiology and Health Sciences, Virginia Commonwealth University, Richmond, VA, United States of America
| | - Parsa Mahmoudi
- Department of Biology, Virginia Commonwealth University, Richmond, VA, 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 and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, United States of America
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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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