Analysis of a temperature- and rainfall-dependent model for malaria transmission dynamics

Mathematical Biosciences

Volumn 287, Issue , 2017, Pages 72-92

  Okuneye, Kamaldeen ^a   Gumel, Abba B ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Age structure; Malaria; Non autonomous model; Reproduction ratio; Stability

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DYNAMICS; MALARIA CONTROL; NUMERICAL MODELS; PROBLEM SOLVING; RAIN; RECOVERY; SENSITIVITY ANALYSIS; UNCERTAINTY ANALYSIS;

AGE STRUCTURES; GLOBALLY ASYMPTOTICALLY STABLE; MALARIA; NONAUTONOMOUS; POSITIVE PERIODIC SOLUTION; REPRODUCTION RATIO; TRANSMISSION PROBABILITIES; UNCERTAINTY AND SENSITIVITY ANALYSIS;

DISEASES;

AGE STRUCTURE; AIR TEMPERATURE; DISEASE TRANSMISSION; MALARIA; NUMERICAL MODEL; RAINFALL;

AGE; ARTICLE; ASYMPTOMATIC INFECTION; DISEASE TRANSMISSION; ENVIRONMENTAL IMPACT; ENVIRONMENTAL TEMPERATURE; HOST PARASITE INTERACTION; HUMAN; INFECTION CONTROL; INFECTION SENSITIVITY; MALARIA; MALARIA CONTROL; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MORTALITY; MOSQUITO; NONHUMAN; PARASITE TRANSMISSION; POPULATION DYNAMICS; PROBABILITY; REPRODUCTION; RURAL AREA; SENSITIVITY ANALYSIS; SIMULATION; TEMPERATURE MEASUREMENT; TEMPERATURE SENSITIVITY; ANIMAL; MOSQUITO VECTOR; SOUTH AFRICA; TEMPERATURE; THEORETICAL MODEL; TRANSMISSION;

KWAZULU-NATAL; SOUTH AFRICA;

RAIN;

ANIMALS; HUMANS; MALARIA; MODELS, THEORETICAL; MOSQUITO VECTORS; RAIN; SOUTH AFRICA; TEMPERATURE;

EID: 84964744540     PISSN: 00255564     EISSN: 18793134     Source Type: Journal    
DOI: 10.1016/j.mbs.2016.03.013     Document Type: Article

References (79)

1. [1] Agusto, F.B., Gumel, A.B., Parham, P.E., Qualitative assessment of the role of temperature variations on malaria transmission dynamics. J. Biol. Syst. 23:4 (2015), 1–34.
2. [2] Alonso, D., Bouma, M.J., Pascual, M., Epidemic malaria and warmer temperatures in recent decades in an east african highland. Proc. R. Soc. B 278 (2011), 1661–1669, 10.1098/rspb.2010.2020.
3. [3] Baeza, A., Bouma, M.J., Dhiman, R., Pascual, M., Malaria control under unstable dynamics: reactive vs. climate-based strategies. Acta Trop. 129 (2014), 42–51, 10.1016/j.actatropica.2013.04.001.
4. [4] Beck-Johnson, L.M., Nelson, W.A., Paaijmans, K.P., Read, A.F., Thomas, M.B., Bjornstad, O.N., The effect of temperature on anopheles mosquito population dynamics and the potential for malaria transmission. PLOS ONE, 8, 2013, 11 E79276.
5. [5] Blanford, J.I., Blanford, S., Crane, R.G., Mann, M.E., Paaijmans, K.P., Schreiber, K.V., Thomas, M.B., Implications of temperature variation for malaria parasite development across africa. Sci. Rep., 1300, 2013, 10.1038/srep01300.
6. [6] Blower, S.M., Dowlatabadi, H., Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example. Int. Stat. Rev. 2 (1994), 229–243.
7. [7] Bouma, M.J., Baeza, A., terVeen, A., Pascual, M., Global malaria maps and climate change: a focus on east african highlands. Trends Parasitol. 27 (2011), 421–422.
8. [8] Bowman, C., Gumel, A.B., Van den Driessche, P., Wu, J., Zhu, H., A mathematical model for assessing control strategies against west nile virus. Bull. Math. Biol. 67 (2005), 1107–1133.
9. [9] Boyd, M.F., Epidemiology of Malaria: Factors Related to the Definitive Host. In Malariology: A Comprehensive Survey of all Aspects of this Group of Diseases from a Global Standpoint (ed. MF Boyd), 1949, PA: W.B. Saunders Company, Philadelphia, 608–697.
10. [10] Cash, B., Rodó, X., Ballester, J., Bouma, M.J., Baeza, A., Dhiman, R.C., Pascual, M., Malaria epidemics highlight the influence of the tropical south atlantic on the indian monsoons. Nat. Clim. Chang., 3, 2013, 10.1038/nclimate1834 502–207.
11. [11] Castillo-Chavez, C.C., Song, B., Dynamical models of tuberculosis and their applications. Math. Biosci. Eng. 1 (2004), 361–404.
12. [12] Chitnis, N., Cushing, J.M., Hyman, J.M., Bifurcation analysis of a mathematical model for malaria transmission. SIAM J. Appl. Math. 67 (2006), 24–45.
13. [13] Craig, M.H., Snow, R.W., Le Sueur, D., Scholarly articles for a climate-based distribution model of malaria transmission in sub-saharan africa. Parasitol. Today 15 (2005), 149–158.
14. [14] Dentinova, T.S., Age-grouping methods in diptera of medical importance, 1962, World Health Organisation, Geneva, Switzerland.
15. 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28 (1990), 365–382.
16. [16] Dumont, Y., Chiroleu, F., Vector control for the chikungunya disease. Math. Biosci. Eng. 7 (2010), 105–111.
17. [17] Durban Monthly Climate Average, South Africa. http://www.worldweatheronline.com/Durban-weather-averages/Kwazulu-Natal/ZA.aspx. Accessed: June 2015.
18. [18] Edwin, M., Robert, C., Modeling parasite transmission and control. Adv. Exp. Med. Biol., 673, 2010.
19. [19] Egbendewe-Mondzozo, A., Musumba, M., McCarl, B.A., Wu, X., Climate change and vector-borne diseases: an economic impact analysis of malaria in africa. Int. J. Environ. Res. Public Health 8 (2011), 913–930 2011.
20. [20] Elbasha, E.H., Gumel, A.B., Theoretical assessment of public health impact of imperfect prophylactic HIV-1 vaccines with therapeutic benefits. Bull. Math. Biol. 7 (2006), 577–614.
21. [21] Faye, O., Gaye, O., Fontenille, D., Hébrard, G., Konate, L., Sy, N., Herve, J.P., Toure, Y.T., Diallo, S., Molez, J.F., Malaria decrease and drought in the niayes area of senegal. Sante 5 (1995), 299–305.
22. [22] Forouzannia, F., Gumel, A.B., Mathematical analysis of an age-structured model for malaria transmission dynamics. Math. Biosci. 247 (2014), 80–94.
23. [23] Garba, S.M., Gumel, A.B., Abu Bakar, M.R., Backward bifurcations in dengue transmission dynamics. Math. Biosci. 215 (2008), 11–25.
24. [24] Garms, R., Walsh, J.F., Davies, J.B., Studies on the reinvasion of the onchocerciasis control programme in the volta river basin by simulium damnosum s.i. with emphasis on the south-western areas. Tropenmedizin Parasitol. 30 (1979), 345–362.
25. [25] Githeko, A.K., Lindsay, S.W., Confalonieri, U.E., Patz, J.A., Climate change and vector-borne diseases: a regional analysis. Bull. World Health Organ., 78, 2000, 9.
26. [26] Health and Environment Linkages Initiative - HELI. World Health Organization. http://www.who.int/heli/risks/vectors/vector/en/. Accessed: June 2015.
27. [27] Horsfall, W.R., Mosquitoes: their bionomics and relation to disease, 1955, Hafner Publishing Company, New York.
28. [28] Hoshen, M.B., Morse, A.P., A weather-driven model of malaria transmission. Malar. J., 3, 2004, 32, 10.1186/1475-2875-3-32.
29. [29] Imbahale, S.S., Paaijmans, K.P., Mukabana, W.R., van Lammeren, R., Githeko, A.K., Takken, W., A longitudinal study on anopheles mosquito larval abundance in distinct geographical and environmental settings in western kenya. Malar. J., 10, 2011, 81.
30. [30] Jepson, W.F., Moutia, A., Courtois, C., The malaria problem in mauritius: the bionomics of mauritian anophelines. Bull. Entomol. 38 (1947), 177–208.
31. [31] Lafferty, K.D., The ecology of climate change and infectious diseases. Ecology 90 (2009), 888–900, 10.1890/08-0079.1.
32. [32] J.P. LaSalle, The stability of dynamical systems, Regional Conference Series in Applied Mathematics. SIAM Philadephia (1976).
33. [33] V. Lakshmikantham, S. Leela, Differential and Integral Inequalities: Theory and Applications, Academic Press, New York.
34. [34] Laperriere, V., Brugger, K., Rubel, F., Simulation of the seasonal cycles of bird, equine and human west nile virus cases. Prev. Vet. Med. 88 (2011), 99–110.
35. [35] Lou, Y., Zhao, X.-Q., A climate-based malaria transmission model with structured vector population. SIAM J. Appl. Math. 70 (2010), 2023–2044.
36. [36] Lunde, T.M., Bayoh, M.N., Lindtjorn, B., How malaria models relate temperature to malaria transmission. Parasites Vectors, 6, 2013, 20 http://www.parasitesandvectors.com/content/6/1/20.
37. [37] Macdonald, G., The Epidemiology and Control of Malaria, 1957, Oxford University Press, London, UK.
38. [38] Magal, P., Zhao, X.-Q., Global attractors and steady states for uniformly persistent dynamical systems. SIAM J. Math. Anal. 37 (2005), 251–275.
39. [39] MARA/ARMA. towards an atlas of malaria risk in africa. albany print ltd. durban, south africa, 1998, 1–31.
40. [40] Marino, S., Hogue, I.B., Ray, C.J., Kirschner, D.E., A methodology for performing global uncertainty and sensitivity analysis in systems biology. J. Theor. Biol. 254 (2008), 178–196.
41. [41] Martens, W.J., Health impacts of climate change and ozone depletion: an ecoepidemiologic modeling approach. Environ. Health Perspect. 106 (1998), 241–251, 10.1289/ehp.98106s1241 (Suppl. 1).
42. [42] Mckay, M.D., Beckman, R.J., Conover, W.J., Comparison of 3 methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21 (1979), 239–245.
43. [43] McLeod, R.G., Brewster, J.F., Gumel, A.B., Slonowsky, D.A., Sensitivity and uncertainty analyses for a SARS model with time-varying inputs and outputs. Math. Biosci. Eng. 2 (2006), 527–544.
44. [44] Mordecai, E.A., Optimal temperature for malaria transmission is dramatically lower than previously predicted. Ecol. Lett. 16 (2013), 22–30.
45. [45] Murdock, C.C., Paaijmans, K.P., Bell, A.S., King, J.G., Hillyer, J.F., Read, A.F., Thomas, M.B., Complex effects of temperature on mosquito immune function. Proc. Biol. Sci./R. Soc. 279 (2012), 3357–3366, 10.1098/rspb.2012.0638.
46. [46] Murdock, C.C., Paaijmans, K.P., Cox-Foster, D., Read, A.F., Thomas, M.B., Rethinking vector immunology: the role of environmental temperature in shaping resistance. Nat. Rev. Microbiol. 10 (2012), 869–876, 10.1038/nrmicro2900.
47. [47] Niger, A.M., Gumel, A.B., Mathematical analysis of the role of repeated exposure on malaria transmission dynamics. Differ. Equ. Dyn. Syst. 16 (2008), 251–287.
48. [48] Paaijmans, K.P., Imbahale, S.S., Thomas, M.B., Takken, W., Relevant microclimate for determining the development rate of malaria mosquitoes and possible implications of climate change. Malar. J., 9, 2010, 196, 10.1186/1475-2875-9-196.
49. [49] Paaijmans, K.P., Wandago, M.O., Githeko, A.K., Takken, W., Unexpected high losses of anopheles gambiae larvae due to rainfall. PLOS One, 2, 2007.
50. [50] Parham, P.E., Michael, E., Modelling climate change and malaria transmission. Adv. Exp. Med. Biol. 673 (2010), 184–199, 10.1007/978-1-4419-6064-1_13.
51. [51] Parham, P.E., Michael, E., Modeling the effects of weather and climate change on malaria transmission. Environ. Health Perspect. 118 (2010), 620–626, 10.1289/ehp.0901256.
52. [52] Parham, P.E., Pople, D., Christiansen-Jucht, C., Lindsay, S., Hinsley, W., Michael, E., Modeling the role of environmental variables on the population dynamics of the malaria vector anopheles gambiae sensu stricto. Malar. J., 11, 2012, 271.
53. [53] Parham, P.E., Waldock, J., Christophides, K.G., Hemming, D., Agusto, F., Evans, J.K., Fefferman, N., Gaff, H., Gumel, A.B., LaDeau, S., Lenhart, S., Mickens, R.E., Naumova, E., Ostfeld, R., Ready, P., Thomas, M., Velasco-Hernandez, J., Michael, E., Climate, environmental, and socioeconomic change - weighing up the balance in vector-borne disease transmission. Philos. Trans. R. Soc. B, 370, 2015, 20130551 http://dx.doi.org/10.1098/rstb.2013.0551.
54. [54] J.M. Pilgrim, X. Fang, H.G. Stefan, Correlations of minnesota stream water temperatures with air temperatures. Project report 382, prepared for national agricultural water quality laboratory agricultural research service u. s. department of agriculture durant, oklahoma, 1995.
55. [55] E.B. Preud'homme, H.G. Stefan, Relationship between water temperatures and air temperatures for central u. s. streams. Project report no. 333, prepared for environmental research laboratory u.s. environmental protection agency duluth, minnesota, 1992.
56. [56] Rodó, X., Climate change and infectious diseases: can we meet the needs for better prediction?. Clim. Chang. 118 (2013), 625–640, 10.1007/s10584-013-0744-1.
57. [57] Rogers, D.J., Randolph, S.E., The global spread of malaria in a future, warmer world. Science 289 (2000), 1763–1767.
58. [58] Rohr, J.R., Dobson, A.P., Johnson, P.T., Kilpatrick, A.M., Paull, S.H., Raffel, T.R., Ruiz-Moreno, D., Thomas, M.B., Frontiers in climate change disease research. Trends Ecol. Evol. 26 (2011), 270–277.
59. [59] Rubel, F., Brugger, K., Hantel, M., Chvala-Mannsberger, S., Bakonyi, T., Weissenbock, H., Nowotny, N., Explaining usutu virus dynamics in austria: model development and calibration. Prev. Vet. Med. 85 (2008), 166–186.
60. [60] Safi, M.A., Imran, M., Gumel, A.B., Threshold dynamics of a non-autonomous SEIRS model with quarantine and isolation. Theory Biosci. 131 (2012), 19–30.
61. [61] Sinka, M.E., The dominant anopheles vectors of human malaria in africa, europe and the middle east: occurrence data, distribution maps and bionomic precis. Parasites Vectors, 3, 2010, 10.1186/1756-3305-3-117.
62. [62] Smith, H.L., Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. Am. Math. Soc., 41, 1995.
63. [63] South Africa's Population. Statistics South Africa. http://www.southafrica.info/about/people/population.htm. Accessed: June 2015.
64. [64] Sutherst, R.W., Global change and human vulnerability to vector-borne diseases. Clin. Microbiol. Rev. 17 (2004), 136–173.
65. [65] Suwanchaichinda, C., Paskewitz, S.M., 1998 effects of larval nutrition, adult body size, and adult temperature on the ability of anopheles gambiae (diptera: Culicidae) to melanize sephadex beads. J. Med. Entomol. 35 (1998), 157–161.
66. [66] Tabachnick, W.J., Challenges in predicting climate and environmental effects on vector-borne disease episystems in a changing world. J. Exp. Biol. 213 (2010), 946–954.
67. [67] Thieme, H.R., Convergence results and a poincaré-Bendixson trichotomy for asymptotically autonomous differential equations. J. Math. Biol. 30 (1992), 755–763.
68. [68] Thieme, H.R., Persistence under relaxed point dissipativity (with application to an endemic model). SIAM J. Math. Anal. 24 (1993), 407–411.
69. [69] United Nations, Department of Economic and Social Affairs, Population Division. World Population Prospects: The 2010 Revision. 2011. http://www.un.org/en/. Accessed: July 2015.
70. [70] Van den Driessche, P., Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180 (2002), 29–48.
71. [71] Wang, W., Zhao, X.-Q., Threshold dynamics for compartmental epidemic models in periodic environments. J. Dyn. Differ. Equ. 20 (2008), 699–717.
72. [72] World Health Organization. World Malaria Report (2008). http://www.who.int/malaria/publications/atoz/9789241563697/en/. Accessed: June 2015.
73. [73] Yang, H.M., Macoris, M.L., Galvani, K.C., Andrighetti, M.T., Wanderley, D.M., Assessing the effects of temperature on dengue transmission. Epidemiol. Infect. 137 (2009), 1179–1187, 10.1017/S0950268809002052.
74. [74] Yang, H.M., Macoris, M.L., Galvani, K.C., Andrighetti, M.T., Wanderley, D.M., Assessing the effects of temperature on the population of aedes aegypti, the vector of dengue. Epidemiol. Infect. 137 (2009), 1188–1202, 10.1017/S0950268809002040.
75. [75] Zhang, F., Zhao, X.-Q., A periodic epidemic model in a patchy environment. J. Math. Anal. Appl. 325 (2007), 496–516.
76. [76] Zhang, Z., Ding, T.W., Huang, T., Dong, Z., Qualitative theory of differential equations. Am. Math. Soc., 101, 2006, 461.
77. [77] Zhao, X.-Q., Uniform persistence and periodic coexistence states in infinite-dimensional periodic semiflows with applications. Can. Appl. Math. Q. 3 (1995), 473–495.
78. [78] Zhao, X.-Q., Dynamical systems in population biology. 2003, Springer, New York.
79. [79] Zhao, X.-Q., Permanence implies the existence of interior periodic solutions for FDEs. Int. J. Qual. Theory Differ. Equ. Appl. 2 (2008), 125–137.