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A periodically-forced mathematical model for the seasonal dynamics of malaria in mosquitoes. (English) Zbl 1237.92040
Summary: We describe and analyze a periodically-forced difference equation model for malaria in mosquitoes that captures the effects of seasonality and allows the mosquitoes to feed on a heterogeneous population of hosts. We numerically show the existence of a unique globally asymptotically stable periodic orbit and calculate periodic orbits of field-measurable quantities that measure malaria transmission. We integrate this model with an individual-based stochastic simulation model for malaria in humans to compare the effects of insecticide-treated nets (ITNs) and indoor residual spraying (IRS) in reducing malaria transmission, prevalence, and incidence. We show that ITNs are more effective than IRS in reducing transmission and prevalence though IRS would achieve its maximal effects within 2 years while ITNs would need two mass distribution campaigns over several years to do so. Furthermore, the combination of both interventions is more effective than either intervention alone. However, although these interventions reduce transmission and prevalence, they can lead to increased clinical malaria; and all three malaria indicators return to preintervention levels within 3 years after the interventions are withdrawn.

MSC:
92C60Medical epidemiology
39A60Applications of difference equations
65C20Models (numerical methods)
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References:
[1] Anderson, R. M., & May, R. M. (1991). Infectious diseases of humans: dynamics and control. Oxford: Oxford Unversity Press.
[2] Anderson, R. A., Knols, B. G. J., & Koella, J. C. (2000). Plasmodium falciparum sporozoites increase feeding-associated mortality of their mosquito hosts Anopheles gambiae s.l. Parasitology, 120, 329--333. · doi:10.1017/S0031182099005570
[3] Aron, J. L. (1988). Mathematical modeling of immunity to malaria. Math. Biosci., 90, 385--396. · Zbl 0651.92018 · doi:10.1016/0025-5564(88)90076-4
[4] Aron, J. L., & May, R. M. (1982). The population dynamics of malaria. In R. M. Anderson (Ed.), The population dynamics of infectious disease: theory and applications (pp. 139--179). London: Chapman and Hall.
[5] Charlwood, J. D., Smith, T., Billingsley, P. F., Takken, W., Lyimo, E. O. K., & Meuwissen, J. H. E. T. (1997). Survival and infection probabilities of anthropophagic anophelines from an area of high prevalence of Plasmodium falciparum in humans. Bull. Entomol. Res., 87, 445--453. · doi:10.1017/S0007485300041304
[6] Chitnis, N., Cushing, J. M., & Hyman, J. M. (2006). Bifurcation analysis of a mathematical model for malaria transmission. SIAM J. Appl. Math., 67, 24--45. · Zbl 1107.92047 · doi:10.1137/050638941
[7] Chitnis, N., Smith, T., & Steketee, R. (2008). A mathematical model for the dynamics of malaria in mosquitoes feeding on a heterogeneous host population. J. Biol. Dyn., 2(3), 259--285. · Zbl 1154.92030 · doi:10.1080/17513750701769857
[8] Chitnis, N., Schapira, A., Smith, T., & Steketee, R. (2010a). Comparing the effectiveness of malaria vector-control interventions through a mathematical model. Am. J. Trop. Med. Hyg., 83(2), 230--240. · doi:10.4269/ajtmh.2010.09-0179
[9] Chitnis, N., Schapira, A., Smith, D. L., Smith, T., Hay, S. I., & Steketee, R. W. (2010b). Mathematical modelling to support malaria control and elimination. In Progress & Impact Series (number 5). Geneva, Switzerland: Roll Back Malaria.
[10] Clements, A. N., & Paterson, G. D. (1981). The analysis of mortality and survival rates in wild populations of mosquitoes. J. Appl. Ecol., 18, 373--399. · doi:10.2307/2402401
[11] Cosner, C., Beier, J. C., Cantrell, R. S., Impoinvil, D., Kapitanski, I., Potts, M. D., Troyo, A., & Ruan, S. (2009). The effects of human movement on the persistence of vector-borne diseases. J. Theor. Biol., 258(4), 550--560. · doi:10.1016/j.jtbi.2009.02.016
[12] Cushing, J. M. (1998). Periodically forced nonlinear systems of difference equations. J. Differ. Equ. Appl., 3, 547--561. · Zbl 0905.39003 · doi:10.1080/10236199708808120
[13] Dietz, K., Molineaux, L., & Thomas, A. (1974). A malaria model tested in the African savannah. Bull. World Health Organ., 50, 347--357.
[14] Eckhoff, P. A. (2011). A malaria transmission-directed model of mosquito life cycle and ecology. Malar. J., 10(303).
[15] Gillies, M. T. (1988). Anopheline mosquitoes: vector behaviour and bionomics. In W. H. Wernsdorfer & I. McGregor (Eds.), Malaria: principles and practice of malariology (Vol. 1, pp. 453--485). Edinburgh: Churchill Livingstone.
[16] Griffin, J. T., Hollingsworth, T. D., Okell, L. C., Churcher, T. S., White, M., Hinsley, W., Bousema, T., Drakeley, C. J., Ferguson, N. M., Basáñez, M. G., & Ghani, A. C. (2010). Reducing Plasmodium falciparum malaria transmission in Africa: a model-based evaluation of intervention strategies. PLoS Med., 7(8), e1000324. · doi:10.1371/journal.pmed.1000324
[17] Hoshen, M. B., & Morse, A. P. (2004). A weather-driven model of malaria transmission. Malar. J., 3(32).
[18] Kilian, A., Byamukama, W., Pigeon, O., Atieli, F., Duchon, S., & Phan, C. (2008). Long-term field performance of a polyester-based long-lasting insecticidal mosquito net in rural Uganda. Malar. J., 7(49).
[19] Killeen, G. F., & Smith, T. A. (2007). Exploring the contributions of bed nets, cattle, insecticides and excitorepellency in malaria control: a deterministic model of mosquito host-seeking behaviour and mortality. Trans. R. Soc. Trop. Med. Hyg., 101, 867--880. · doi:10.1016/j.trstmh.2007.04.022
[20] Le Menach, A., Takala, S., McKenzie, F. E., Perisse, A., Harris, A., Flahault, A., & Smith, D. L. (2007). An elaborated feeding cycle model for reductions in vectorial capacity of night-biting mosquitoes by insecticide-treated nets. Malar. J., 6(10).
[21] Lindblade, K. A., Dotson, E., Hawley, W. A., Bayoh, N., Williamson, J., Mount, D., Olang, G., Vulule, J., Slutsker, L., & Gimnig, J. (2005). Evaluation of long-lasting insecticidal nets after 2 years of household use. Trop. Med. Int. Health, 10(11), 1141--1150. · doi:10.1111/j.1365-3156.2005.01501.x
[22] Lou, Y., & Zhao, X. Q. (2010). A climate-based malaria transmission model with structured vector population. SIAM J. Appl. Math., 70(6), 2023--2044. · Zbl 1221.34224 · doi:10.1137/080744438
[23] Macdonald, G. (1950). The analysis of malaria parasite rates in infants. Trop. Dis. Bull., 47, 915--938.
[24] Macdonald, G. (1952). The analysis of the sporozoite rate. Trop. Dis. Bull., 49, 569--585.
[25] Maire, N., Aponte, J. J., Ross, A., Thompson, R., Alonso, P., Utzinger, J., Tanner, M., & Smith, T. (2006). Modeling a field trial of the RTS,S/AS02A malaria vaccine. Am. J. Trop. Med. Hyg., 75(Suppl. 2), 104--110.
[26] McKenzie, F. E., Wong, R. C., & Bossert, W. H. (1998). Discrete-event simulation models of Plasmodium falciparum malaria. Simulation, 71(4), 250--261. · Zbl 02061303 · doi:10.1177/003754979807100405
[27] Ngwa, G. A., & Shu, W. S. (2000). A mathematical model for endemic malaria with variable human and mosquito populations. Math. Comput. Model., 32, 747--763. · Zbl 0998.92035 · doi:10.1016/S0895-7177(00)00169-2
[28] OpenMalaria (2011). http://code.google.com/p/openmalaria/ . Date accessed: 11 November 2011.
[29] Penny, M. A., Maire, N., Studer, A., Schapira, A., & Smith, T. A. (2008). What should vaccine developers ask? Simulation of the effectiveness of malaria vaccines. PLoS ONE, 3(9).
[30] Roca-Feltrer, A., Armstrong Schellenberg, J. R. M., Smith, L., & Carneiro, I. (2009). A simple method for defining malaria seasonality. Malar. J., 8(276).
[31] Roll Back Malaria Partnership (2008). The Global Malaria Action Plan. http://www.rollbackmalaria.org/gmap/ .
[32] Ross, R. (1905). The logical basis of the sanitary policy of mosquito reduction. Science, 22(570), 689--699. · doi:10.1126/science.22.570.689
[33] Ross, R. (1911). The prevention of malaria (2nd ed.). London: Murray.
[34] Ross, A., Maire, N., Molineaux, L., & Smith, T. (2006). An epidemiologic model of severe morbidity and mortality caused by Plasmodium falciparum. Am. J. Trop. Med. Hyg., 75(Suppl. 2), 63--73.
[35] Ross, A., Penny, M., Maire, N., Studer, A., Carneiro, I., Schellenberg, D., Greenwood, B., Tanner, M., & Smith, T. (2008). Modelling the epidemiological impact of intermittent preventive treatment against malaria in infants. PLoS ONE, 3(7).
[36] Ross, A., Maire, N., Sicuri, E., Smith, T., & Conteh, L. (2011). Determinants of the cost-effectiveness of intermittent preventive treatment for malaria in infants and children. PLoS ONE, 6(4).
[37] Sadasivaiah, S., Tozan, Y., & Breman, J. G. (2007). Dichlorodiphenyltrichloroethane (DDT) for indoor residual spraying in Africa: How can it be used for malaria control? Am. J. Trop. Med. Hyg., 77(Suppl. 6), 249--263.
[38] Saul, A. (2003). Zooprophylaxis or zoopotentiation: the outcome of introducing animals on vector transmission is highly dependent on the mosquito mortality while searching. Malar. J., 2(32).
[39] Saul, A. J., Graves, P. M., & Kay, B. H. (1990). A cyclical feeding model for pathogen transmission and its application to determine vector capacity from vector infection rates. J. Appl. Ecol., 27, 123--133. · doi:10.2307/2403572
[40] Smith, D. L., & McKenzie, F. E. (2004). Statics and dynamics of malaria infection in Anopheles mosquitoes. Malar. J., 3(13).
[41] Smith, T., Charlwood, J. D., Kihonda, J., Mwankusye, S., Billingsley, P., Meuwissen, J., Lyimo, E., Takken, W., Teuscher, T., & Tanner, M. (1993). Absence of seasonal variation in malaria parasitaemia in an area of intense seasonal transmission. Acta Trop., 54, 55--72. · doi:10.1016/0001-706X(93)90068-M
[42] Smith, T., Killeen, G. F., Maire, N., Ross, A., Molineaux, L., Tediosi, F., Hutton, G., Utzinger, J., Dietz, K., & Tanner, M. (2006). Mathematical modeling of the impact of malaria vaccines on the clinical epidemiology and natural history of Plasmodium falciparum malaria: overview. Am. J. Trop. Med. Hyg., 75(Suppl. 2), 1--10.
[43] Smith, T., Maire, N., Ross, A., Penny, M., Chitnis, N., Schapira, A., Studer, A., Genton, B., Lengeler, C., Tediosi, F., de Savigny, D., & Tanner, M. (2008). Towards a comprehensive simulation model of malaria epidemiology and control. Parasitology, 135, 1507--1516. · doi:10.1017/S0031182008000371
[44] Smith, T., Ross, A., Maire, N., Chitnis, N., Studer, A., Hardy, D., Brooks, A., Penny, M., & Tanner, M. (2012, in press). Ensemble modeling of the likely public health impact of the RTS,S malaria vaccine. PLoS Med. doi: 10.1371/journal.pmed.1001157 .
[45] The malERA Consultative Group on Modeling (2011). A research agenda for malaria eradication: modeling. PLoS Med., 8, e1000403. · doi:10.1371/journal.pmed.1000403
[46] White, M. T., Griffin, J. T., Churcher, T. S., Ferguson, N. M., Basáñez, M. G., & Ghani, A. C. (2011). Modelling the impact of vector control interventions on Anopheles gambiae population dynamics. Parasites Vectors, 4(153).
[47] World Health Organization (2009). World Malaria Report 2009. http://www.who.int/malaria/publications/atoz/9789241563901/en/index.html .