Malaria infection is a major problem in many countries. The use of the Insecticide-Treated Bed-Nets (ITNs) has been shown to significantly reduce the number of malaria infections; however, the effectiveness is often jeopardized by improper handling or human behavior such as inconsistent usage. In this paper, we present a game-theoretical model for ITN usage in communities with malaria infections. We show that it is in the individual’s self interest to use the ITNs as long as the malaria is present in the community. Such an optimal ITN usage will significantly decrease the malaria prevalence and under some conditions may even lead to complete eradication of the disease.
KeywordsGame TheoryMalaria PreventionOptimal StrategyEpidemic ModellingSIS Model
WHO (2005) World Malaria Report.
Raghavendra, K., Barik, T.K., Niranjan Reddy, B.P., Sharma, P. and Dash, A.P. (2011) Malaria Vector Control: From Past to Future. Parasitology Research, 108, 757-779. http://dx.doi.org/10.1007/s00436-010-2232-0
Lengeler, C. (2004) Insecticide-Treated Bed Nets and Curtains for Preventing Malaria. Cochrane Database of Systematic Reviews, 2, Article ID: CD000363. http://dx.doi.org/10.1002/14651858.cd000363.pub2
Goodman, C.A. and Mills, A.J. (1999) The Evidence Base on the Cost-Effectiveness of Malaria Control Measures in Africa. Health Policy and Planning, 14, 301-312. http://dx.doi.org/10.1093/heapol/14.4.301
Goodman, C.A., Coleman, P.G. and Mills, A.J. (1999) Cost-Effectiveness of Malaria Control in Sub-Saharan Africa. The Lancet, 354, 378-385. http://dx.doi.org/10.1016/S0140-6736(99)02141-8
White, M.T., Conteh, L., Cibulskis, R. and Ghani, A.C. (2011) Costs and Cost-Effectiveness of Malaria Control Interventions—A Systematic Review. Malaria Journal, 10, 1475-2875. http://dx.doi.org/10.1186/1475-2875-10-337
Miller, J.M., Korenromp, E.L., Nahlen, B.L. and Steketee, R.W. (2007) Estimating the Number of Insecticide-Treated Nets Required by African Households to Reach Continent-Wide Malaria Coverage Targets. JAMA, 297, 2241-2250. http://dx.doi.org/10.1001/jama.297.20.2241
White, L.J., Maude, R.J., Pongtavornpinyo, W., Saralamba, S., Aguas, R., Van Effelterre, T., Day, N.P.J. and White, N.J. (2009) The Role of Simple Mathematical Models in Malaria Elimination Strategy Design. Malaria Journal, 8, 212. http://dx.doi.org/10.1186/1475-2875-8-212
Chitnis, N., Schapira, A., Smith, T. and Steketee, R. (2010) Comparing the Effectiveness of Malaria Vector-Control Interventions through a Mathematical Model. The American Journal of Tropical Medicine and Hygiene, 83, 230. http://dx.doi.org/10.4269/ajtmh.2010.09-0179
Agusto, F.B., Del Valle, S.Y., Blayneh, K.W., Ngonghala, C.N., Goncalves, M.J., Li, N.P., Zhao, R.J. and Gong, H.F. (2013) The Impact of Bed-Net Use on Malaria Prevalence. Journal of Theoretical Biology, 320, 58-65. http://dx.doi.org/10.1016/j.jtbi.2012.12.007
Von Neumann, J. and Morgenstern, O. (2007) Theory of Games and Economic Behavior (Commemorative Edition). Princeton University Press.
Smith, J.M. and Price, G.R. (1973) The Logic of Animal Conflict. Nature, 246, 15-18. http://dx.doi.org/10.1038/246015a0
Broom, M. and Rychtá?, J. (2013) Game-Theoretical Models in Biology. CRC Press.
Bauch, C.T. and Earn, D.J.D. (2004) Vaccination and the Theory of Games. Proceedings of the National Academy of Sciences of the United States of America, 101, 13391-13394. http://dx.doi.org/10.1073/pnas.0403823101
Bauch, C.T., Galvani, A.P. and Earn, D.J.D. (2003) Group Interest versus Self-Interest in Smallpox Vaccination Policy. Proceedings of the National Academy of Sciences of the United States of America, 100, 10564-10567. http://dx.doi.org/10.1073/pnas.1731324100
Bauch, C.T. (2005) Imitation Dynamics Predict Vaccinating Behaviour. Proceedings of the Royal Society B: Biological Sciences, 272, 1669-1675. http://dx.doi.org/10.1098/rspb.2005.3153
Galvani, A.P., Reluga, T.C. and Chapman, G.B. (2007) Long-Standing Influenza Vaccination Policy Is in Accord with Individual Self-Interest but Not with the Utilitarian Optimum. Proceedings of the National Academy of Sciences, 104, 5692-5697. http://dx.doi.org/10.1073/pnas.0606774104
Shim, E., Kochin, B. and Galvani, A. (2009) Insights from Epidemiological Game Theory into Gender-Specific Vaccination against Rubella. Mathematical Biosciences and Engineering: MBE, 6, 839-854. http://dx.doi.org/10.3934/mbe.2009.6.839
Shim, E., Grefenstette, J.J., Albert, S.M., Cakouros, B.E. and Burke, D.S. (2012) A Game Dynamic Model for Vaccine Skeptics and Vaccine Believers: Measles as an Example. Journal of Theoretical Biology, 295, 194-203. http://dx.doi.org/10.1016/j.jtbi.2011.11.005
Crawford, K., Lancaster, A., Oh, H. and Rychtá?, J. (2015) A Voluntary Use of Insecticide-Treated Cattle Can Eliminate African Sleeping Sickness. Letters in Biomathematics, 2, 91-101. http://dx.doi.org/10.1080/23737867.2015.1111777
Sykes, D. and Rychtá?, J. (2015) A Game-Theoretic Approach to Valuating Toxoplasmosis Vaccination Strategies. Theoretical Population Biology, 105, 33-38. http://dx.doi.org/10.1016/j.tpb.2015.08.003
Shim, E., Chapman, G.B., Townsend, J.P. and Galvani, A.P. (2012) The Influence of Altruism on Influenza Vaccination Decisions. Journal of the Royal Society Interface, 9, 2234-2243.
Geoffard, P.-Y. and Philipson, T. (1997) Disease Eradication: Private versus Public Vaccination. The American Economic Review, 87, 222-230.
Teboh-Ewungkem, M.I., Podder, C.N. and Gumel, A.B. (2010) Mathematical Study of the Role of Gametocytes and an Imperfect Vaccine on Malaria Transmission Dynamics. Bulletin of Mathematical Biology, 72, 63-93. http://dx.doi.org/10.1007/s11538-009-9437-3
Bowman, C., Gumel, A.B., van den Driessche, P., Wu, J. and Zhu, H. (2005) A Mathematical Model for Assessing Control Strategies against West Nile Virus. Bulletin of Mathematical Biology, 67, 1107-1133. http://dx.doi.org/10.1016/j.bulm.2005.01.002
Guyatt, H.L., Kinnear, J., Burini, M. and Snow, R.W. (2002) A Comparative Cost Analysis of Insecticide-Treated Nets and Indoor Residual Spraying in Highland Kenya. Health Policy and Planning, 17, 144-153. http://dx.doi.org/10.1093/heapol/17.2.144
Mulligan, J.-A., Yukich, J. and Hanson, K. (2008) Costs and Effects of the Tanzanian National Voucher Scheme for Insecticide-Treated Nets. Malaria Journal, 7, 32. http://dx.doi.org/10.1186/1475-2875-7-32
Asenso-Okyere, W.K. and Dzator, J.A. (1997) Household Cost of Seeking Malaria Care. A Retrospective Study of Two Districts in Ghana. Social Science & Medicine, 45, 659-667. http://dx.doi.org/10.1016/S0277-9536(96)00383-8
Akazili, J., Aikins, M. and Binka, F.N. (2008) Malaria Treatment in Northern Ghana: What Is the Treatment Cost per Case to Households? African Journal of Health Sciences, 14, 70-79. http://dx.doi.org/10.4314/ajhs.v14i1.30849
Mutabingwa, T.K. (2005) Artemisinin-Based Combination Therapies (ACTs): Best Hope for Malaria Treatment but Inaccessible to the Needy! Acta Tropica, 95, 305-315. http://dx.doi.org/10.1016/j.actatropica.2005.06.009
Whitty, C.J.M., Chandler, C., Ansah, E., Leslie, T. and Staedke, S.G. (2008) Deployment of ACT Antimalarials for Treatment of Malaria: Challenges and Opportunities. Malaria Journal, 7, S7. http://dx.doi.org/10.1186/1475-2875-7-S1-S7
Lubell, Y., Reyburn, H., Mbakilwa, H., Mwangi, R., Chonya, S., Whitty, C.J.M. and Mills, A. (2008) The Impact of Response to the Results of Diagnostic Tests for Malaria: Cost-Benefit Analysis. BMJ, 336, 202-205. http://dx.doi.org/10.1136/bmj.39395.696065.47
Killeen, G.F., Kihonda, J., Lyimo, E., Oketch, F.R., Kotas, M.E., Mathenge, E., Schellenberg, J.A., Lengeler, C., Smith, T.A. and Drakeley, C.J. (2006) Quantifying Behavioural Interactions between Humans and Mosquitoes: Evaluating the Protective Efficacy of Insecticidal Nets against Malaria Transmission in Rural Tanzania. BMC Infectious Diseases, 6, 161. http://dx.doi.org/10.1186/1471-2334-6-161