Game-theoretical model of the voluntary use of insect repellents to prevent Zika fever. (English) Zbl 1489.92136
Summary: 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.
References:
| [1] | 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 behavior, Proc R Soc A, 476, 20200354 (2020) · Zbl 1472.92192 |
| [2] | Agusto, FB; Bewick, S.; Fagan, W., Mathematical model of Zika virus with vertical transmission, Infect Dis Model, 2, 2, 244-267 (2017) |
| [3] | Agusto, FB; Bewick, S.; Fagan, WF, Mathematical model for Zika virus dynamics with sexual transmission route, Ecol Complex, 29, 61-81 (2017) |
| [4] | Andraud, M.; Hens, N.; Marais, C.; Beutels, P., Dynamic epidemiological models for dengue transmission: a systematic review of structural approaches, PLoS ONE, 7, 11, e49085 (2012) |
| [5] | Arefin, MR; Kabir, KA; Tanimoto, J., A mean-field vaccination game scheme to analyze the effect of a single vaccination strategy on a two-strain epidemic spreading, J Stat Mech Theory Exp, 2020, 3, 033501 (2020) · Zbl 1456.92131 |
| [6] | Arefin, MR; Masaki, T.; Kabir, KA; Tanimoto, J., Interplay between cost and effectiveness in influenza vaccine uptake: a vaccination game approach, Proc R Soc A, 475, 2232, 20190608 (2019) · Zbl 1472.92196 |
| [7] | Arriola L, Hyman JM (2009) Sensitivity analysis for uncertainty quantification in mathematical models. In: Mathematical and statistical estimation approaches in epidemiology. Springer, pp 195-247 · Zbl 1345.92001 |
| [8] | Bankuru, SV; Kossol, S.; Hou, W.; Mahmoudi, P.; Rychtář, J.; Taylor, D., A game-theoretic model of Monkeypox to assess vaccination strategies, PeerJ, 8, e9272 (2020) |
| [9] | Basso, C.; da Rosa, EG; Lairihoy, R.; Caffera, RM; Roche, I.; González, C.; da Rosa, R.; Gularte, A.; Alfonso-Sierra, E.; Petzold, M., Scaling up of an innovative intervention to reduce risk of dengue, chikungunya, and zika transmission in Uruguay in the framework of an intersectoral approach with and without community participation, Am J Trop Med Hyg, 97, 5, 1428-1436 (2017) |
| [10] | Bauch, CT; Earn, DJ, Vaccination and the theory of games, Proc Natl Acad Sci, 101, 36, 13391-13394 (2004) · Zbl 1064.91029 |
| [11] | Bonyah, E.; Khan, MA; Okosun, KO; Gómez-Aguilar, J., On the co-infection of dengue fever and Zika virus, Optim Control Appl Methods, 40, 3, 394-421 (2019) · Zbl 1425.92179 |
| [12] | Bonyah, E.; Okosun, KO, Mathematical modeling of Zika virus, Asian Pacific J Trop Dis, 6, 9, 673-679 (2016) |
| [13] | Brettin, A.; Rossi-Goldthorpe, R.; Weishaar, K.; Erovenko, IV, Ebola could be eradicated through voluntary vaccination, R Soc Open Sci, 5, 1, 171591 (2018) |
| [14] | Brooks, JT; Friedman, A.; Kachur, RE; LaFlam, M.; Peters, PJ; Jamieson, DJ, Update: interim guidance for prevention of sexual transmission of Zika virus—United States, July 2016, Morb Mortal Wkly Report, 65, 29, 745-747 (2016) |
| [15] | Broom M, Rychtář J, Spears-Gill T (2016) The game-theoretical model of using insecticide-treated bed-nets to fight malaria. Appl Math 7(09):852-860 |
| [16] | Bruno L (2016) Mosquito repellant sales boom in Brazil amid Zika scare. https://www.reuters.com/article/health-zika-repellant/mosquito-repellant-sales-boom-in-brazil-amid-zika-scare-idUSL8N15I52T. Accessed 10 Nov 2020 |
| [17] | Carran, S.; Ferrari, M.; Reluga, T., Unintended consequences and the paradox of control: management of emerging pathogens with age-specific virulence, PLoS Negl Trop Dis, 12, 4, e0005997 (2018) |
| [18] | Chang, SL; Piraveenan, M.; Pattison, P.; Prokopenko, M., Game theoretic modelling of infectious disease dynamics and intervention methods: a review, J Biol Dyn, 14, 1, 57-89 (2020) · Zbl 1447.92405 |
| [19] | Cheng, E.; Gambhirrao, N.; Patel, R.; Zhowandai, A.; Rychtář, J.; Taylor, D., A game-theoretical analysis of Poliomyelitis vaccination, J Theor Biol, 499, 110298 (2020) · Zbl 1455.92083 |
| [20] | Choi, W.; Shim, E., Optimal strategies for vaccination and social distancing in a game-theoretic epidemiologic model, J Theor Biol, 505, 110422 (2020) · Zbl 1455.92084 |
| [21] | 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, 82, 80 (2020) · Zbl 1453.92186 |
| [22] | Chubb, MC; Jacobsen, KH, Mathematical modeling and the epidemiological research process, Eur J Epidemiol, 25, 1, 13-19 (2010) |
| [23] | CIA (2020) The world factbook—birth rate. https://www.cia.gov/library/publications/the-world-factbook/fields/345.html. Accessed 13 Apr 2020 |
| [24] | Crawford, K.; Lancaster, A.; Oh, H.; Rychtář, J., A voluntary use of insecticide-treated cattle can eliminate African sleeping sickness, Lett Biomath, 2, 1, 91-101 (2015) |
| [25] | Dantas, E.; Tosin, M.; Cunha, A. Jr, Calibration of a SEIR-SEI epidemic model to describe the Zika virus outbreak in Brazil, Appl Math Comput, 338, 249-259 (2018) · Zbl 1427.92086 |
| [26] | Ding C, Tao N, Zhu Y (2016) A mathematical model of Zika virus and its optimal control. In: 2016 35th Chinese control conference (CCC). IEEE, pp 2642-2645 |
| [27] | Dorsett, C.; Oh, H.; Paulemond, ML; Rychtář, J., Optimal repellent usage to combat dengue fever, Bull Math Biol, 78, 5, 916-922 (2016) · Zbl 1348.92150 |
| [28] | EPA (2020) US Environmental Protection Agency: find the repellent that is right for you. https://www.epa.gov/insect-repellents/find-repellent-right-you. Accessed 10 Nov 2020 |
| [29] | Fauci, AS; Morens, DM, Zika virus in the Americas-yet another arbovirus threat, N Engl J Med, 374, 7, 601-604 (2016) |
| [30] | Ferguson, NM; Cucunubá, ZM; Dorigatti, I.; Nedjati-Gilani, GL; Donnelly, CA; Basáñez, M-G; Nouvellet, P.; Lessler, J., Countering the Zika epidemic in Latin America, Science, 353, 6297, 353-354 (2016) |
| [31] | 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, R Soc Open Sci, 8, 6, 201960 (2021) |
| [32] | Foy, BD; Kobylinski, KC; Foy, JLC; Blitvich, BJ; da Rosa, AT; Haddow, AD; Lanciotti, RS; Tesh, RB, Probable non-vector-borne transmission of Zika virus, Colorado, USA, Emerg Infect Dis, 17, 5, 880 (2011) |
| [33] | Gao, D.; Lou, Y.; He, D.; Porco, TC; Kuang, Y.; Chowell, G.; Ruan, S., Prevention and control of Zika as a mosquito-borne and sexually transmitted disease: a mathematical modeling analysis, Sci Rep, 6, 28070 (2016) |
| [34] | Hamel, R.; Dejarnac, O.; Wichit, S.; Ekchariyawat, P.; Neyret, A.; Luplertlop, N.; Perera-Lecoin, M.; Surasombatpattana, P.; Talignani, L.; Thomas, F., Biology of Zika virus infection in human skin cells, J Virol, 89, 17, 8880-8896 (2015) |
| [35] | 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, 14, 11, e0008833 (2020) |
| [36] | Hennessey, M.; Fischer, M.; Staples, JE, Zika virus spreads to new areas—region of the Americas, May 2015-January 2016, Am J Transplant, 16, 3, 1031-1034 (2016) |
| [37] | Honein, MA; Dawson, AL; Petersen, EE; Jones, AM; Lee, EH; Yazdy, MM; Ahmad, N.; Macdonald, J.; Evert, N.; Bingham, A., Birth defects among fetuses and infants of US women with evidence of possible Zika virus infection during pregnancy, JAMA, 317, 1, 59-68 (2017) |
| [38] | Ibuka, Y.; Li, M.; Vietri, J.; Chapman, GB; Galvani, AP, Free-riding behavior in vaccination decisions: an experimental study, PLoS ONE, 9, 1, e87164 (2014) |
| [39] | Kabir, KA; Jusup, M.; Tanimoto, J., Behavioral incentives in a vaccination-dilemma setting with optional treatment, Phys Rev E, 100, 6, 062402 (2019) |
| [40] | 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, 8, e10151 (2020) |
| [41] | 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, 80, 10, 2580-2599 (2018) · Zbl 1400.92506 |
| [42] | Kroeger, A.; Lenhart, A.; Ochoa, M.; Villegas, E.; Levy, M.; Alexander, N.; McCall, P., Effective control of dengue vectors with curtains and water container covers treated with insecticide in Mexico and Venezuela: cluster randomised trials, BMJ, 332, 7552, 1247-1252 (2006) |
| [43] | Kucharski, AJ; Funk, S.; Eggo, RM; Mallet, H-P; Edmunds, WJ; Nilles, EJ, Transmission dynamics of Zika virus in island populations: a modelling analysis of the 2013-14 French Polynesia outbreak, PLoS Negl Trop Dis, 10, 5, e0004726 (2016) |
| [44] | Kuga, K.; Tanimoto, J.; Jusup, M., To vaccinate or not to vaccinate: a comprehensive study of vaccination-subsidizing policies with multi-agent simulations and mean-field modeling, J Theor Biol, 469, 107-126 (2019) · Zbl 1411.92174 |
| [45] | Lee, BY; Alfaro-Murillo, JA; Parpia, AS; Asti, L.; Wedlock, PT; Hotez, PJ; Galvani, AP, The potential economic burden of Zika in the continental United States, PLoS Negl Trop Dis, 11, 4, e0005531 (2017) |
| [46] | Lessler, J.; Ott, CT; Carcelen, AC; Konikoff, JM; Williamson, J.; Bi, Q.; Kucirka, LM; Cummings, DA; Reich, NG; Chaisson, LH, Times to key events in Zika virus infection and implications for blood donation: a systematic review, Bull World Health Organ, 94, 11, 841 (2016) |
| [47] | Li, Y.; Liu, X., Modeling and control of mosquito-borne diseases with Wolbachia and insecticides, Theor Popul Biol, 132, 82-91 (2020) · Zbl 1516.92126 |
| [48] | Lowe, R.; Barcellos, C.; Brasil, P.; Cruz, OG; Honório, NA; Kuper, H.; Carvalho, MS, The zika virus epidemic in Brazil: from discovery to future implications, Int J Environ Res Public Health, 15, 1, 96 (2018) |
| [49] | Maciel-De-Freitas, R.; Codeco, CT; Lourenco-De-Oliveira, R., Daily survival rates and dispersal of Aedes aegypti females in Rio de Janeiro, Brazil, Am J Trop Med Hyg, 76, 4, 659-665 (2007) |
| [50] | Martinez A, Machado J, Sanchez E, Erovenko I (2019) Optimal vaccination strategies to reduce endemic levels of meningitis in Africa. Preprint |
| [51] | Maskin, E., Nash equilibrium and welfare optimality, Rev Econ Stud, 66, 1, 23-38 (1999) · Zbl 0956.91034 |
| [52] | Maxian, O.; Neufeld, A.; Talis, EJ; Childs, LM; Blackwood, JC, Zika virus dynamics: when does sexual transmission matter?, Epidemics, 21, 48-55 (2017) |
| [53] | Melo, VD; Silva, JS; La Corte, R., Use of mosquito repellents to protect against Zika virus infection among pregnant women in Brazil, Public Health, 171, 89-96 (2019) |
| [54] | Miller, P., Avoiding the bite: update on DEET: safe and effective against West Nile virus when properly used, Can Pharm J/Rev Pharm Can, 137, 5, 44-47 (2004) |
| [55] | Ministério da Saúde Brasília (2017) Secretaria de vigilância em saúde-ministério da saúde monitoramento dos casos de dengue, febre de chikungunya e febre pelo vírus zika até a semana epidemiológica 52, 2016. Bol Epidemiol 48(3):1-11 |
| [56] | Momoh, AA; Fügenschuh, A., Optimal control of intervention strategies and cost effectiveness analysis for a Zika virus model, Oper Res Health Care, 18, 99-111 (2018) |
| [57] | Nahlen BL, Clark JP, Alnwick D (2003) Insecticide-treated bed nets. Am J Trop Med Hyg \(68(4_-\) suppl):1-2 |
| [58] | Nelson, MJ, Aedes aegypti: biology and ecology (1986), Washington: Pan American Health Organization, Washington |
| [59] | Oduyebo, T.; Petersen, EE; Rasmussen, SA; Mead, PS; Meaney-Delman, D.; Renquist, CM; Ellington, SR; Fischer, M.; Staples, JE; Powers, AM, Update: interim guidelines for health care providers caring for pregnant women and women of reproductive age with possible Zika virus exposure—United States, 2016, Morb Mortal wkly Rep, 65, 5, 122-127 (2016) |
| [60] | Otero, M.; Solari, HG; Schweigmann, N., A stochastic population dynamics model for Aedes aegypti: formulation and application to a city with temperate climate, Bull Math Biol, 68, 8, 1945-1974 (2006) · Zbl 1296.92215 |
| [61] | Padmanabhan, P.; Seshaiyer, P.; Castillo-Chavez, C., Mathematical modeling, analysis and simulation of the spread of Zika with influence of sexual transmission and preventive measures, Lett Biomath, 4, 1, 148-166 (2017) |
| [62] | Petersen, LR; Jamieson, DJ; Powers, AM; Honein, MA, Zika virus, N Engl J Med, 374, 16, 1552-1563 (2016) |
| [63] | Quintana-Domeque, C.; Carvalho, JR; de Oliveira, VH, Zika virus incidence, preventive and reproductive behaviors: correlates from new survey data, Econ Hum Biol, 30, 14-23 (2018) |
| [64] | Robert, MA; Christofferson, RC; Silva, NJ; Vasquez, C.; Mores, CN; Wearing, HJ, Modeling mosquito-borne disease spread in US urbanized areas: the case of dengue in Miami, PLoS ONE, 11, 8, e0161365 (2016) |
| [65] | Robert, MA; Christofferson, RC; Weber, PD; Wearing, HJ, Temperature impacts on dengue emergence in the United States: investigating the role of seasonality and climate change, Epidemics, 28, 100344 (2019) |
| [66] | Robert, MA; Stewart-Ibarra, AM; Estallo, EL, Climate change and viral emergence: evidence from Aedes-borne arboviruses, Curr Opin Virol, 40, 41-47 (2020) |
| [67] | Scheckelhoff K, Ejaz A, Erovenko IV (2019) A game-theoretic model of optimal clean equipment usage to prevent hepatitis C among injecting drug users. Preprint |
| [68] | Scheckelhoff, K.; Ejaz, A.; Erovenko, IV; Rychtář, J.; Taylor, D., Optimal voluntary vaccination of adults and adolescents can help eradicate hepatitis B in China, Games, 12, 4, 82 (2021) · Zbl 1484.92062 |
| [69] | Serpell, L.; Green, J., Parental decision-making in childhood vaccination, Vaccine, 24, 19, 4041-4046 (2006) |
| [70] | Sykes, D.; Rychtář, J., A game-theoretic approach to valuating toxoplasmosis vaccination strategies, Theor Popul Biol, 105, 33-38 (2015) · Zbl 1342.92284 |
| [71] | Tang, B.; Xiao, Y.; Wu, J., Implication of vaccination against dengue for Zika outbreak, Sci Rep, 6, 35623 (2016) |
| [72] | Taylor, D., Mathematical model of Zika virus transmission and control measures, N C J Math Stat, 7, 1-12 (2021) |
| [73] | Turelli, M.; Barton, NH, Deploying dengue-suppressing Wolbachia: robust models predict slow but effective spatial spread in Aedes aegypti, Theor Popul Biol, 115, 45-60 (2017) · Zbl 1381.92099 |
| [74] | Valega-Mackenzie, W.; Ríos-Soto, KR, Can vaccination save a Zika virus epidemic?, Bull Math Biol, 80, 3, 598-625 (2018) · Zbl 1391.92056 |
| [75] | Verelst, F.; Willem, L.; Beutels, P., Behavioural change models for infectious disease transmission: a systematic review (2010-2015), J R Soc Interface, 13, 125, 20160820 (2016) |
| [76] | Wei, H-M; Li, X-Z; Martcheva, M., An epidemic model of a vector-borne disease with direct transmission and time delay, J Math Anal Appl, 342, 2, 895-908 (2008) · Zbl 1146.34059 |
| [77] | World Bank (2020) Life expectancy at birth. https://data.worldbank.org/indicator/SP.DYN.LE00.IN?cid=GPD_10. Accessed 13 Apr 2020 |
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