Modelling the impact of climatic variables on malaria transmission

Abstract

Malaria is one of the most severe disease in the world. The projected climate change will probably alter the region and transmission potential of malaria in Africa. In this study, a climate-based mathematical model to investigate the impact of temperature and rainfall on malaria transmission is developed and analysed. The basic reproduction number (R0) is derived along with stability analysis. The effect of the larval death rate on the reproduction number is also investigated. The model is validated on observed malaria transmission in Limpopo Province, South Africa, giving a reasonable fit and in particular, detecting accurately all the spikes in malaria prevalence. The model provides a numerical basis for further refinement towards prediction of the impact of climate variability on malaria transmission.

Keywords

• Malaria,climate,temperature,rainfall,basic reproduction number,disease-free equilibrium,endemic equilibrium

References

1. Abiodun, G.J., Marcus, N., Okosun, K.O. and Witbooi, P.J. A model for control of HIV/AIDS with parental care, International Journal of Biomathematics 6 (02), 1350006, 2013.
2. Abiodun, G.J., Maharaj, R., Witbooi, P. and Okosun, K.O. Modelling the influence of temperature and rainfall on the population dynamics of Anopheles arabiensis, Malaria Journal 15 (1), 364, 2016.
3. Abiodun, G.J., Witbooi, P. and Okosun, K.O. Modeling and analyzing the impact of temperature and rainfall on mosquito population dynamics over Kwazulu- Natal province, South Africa, International Journal of Biomathematics 2016. DOI: http://dx.doi.org/10.1142/S1793524517500553.
4. Alonso, D., Bouma, M.J. and Pascual, M. Epidemic malaria and warmer temperatures in recent decades in an East African highland, Proceedings of the Royal Society of London B: Biological Sciences 278 (1712), 1661-1669, 2011.
5. Anderson, R.M., May, R.M. and Anderson, B. Infectious diseases of humans: dynamics and control (Vol. 28). Oxford: Oxford university press, 1992.
6. Gerritsen, A.A., Kruger, P., van der Loeff, M.F.S. and Grobusch, M.P. Malaria incidence in Limpopo Province, South Africa, 1998–2007, Malaria journal 7 (1), 162, 2008.
7. Briere, J.F., Pracros, P., Le Roux, A.Y. and Pierre, J.S. A novel rate model of temperaturedependent development for arthropods, Environmental Entomology 28 (1), 22-29, 1999.
8. Chitnis, N., Hyman, J.M. and Cushing, J.M. Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bulletin of mathematical biology 70 (5), 1272, 2008.

9. Chiyaka, C., Tchuenche, J.M., Garira, W. and Dube, S. A mathematical analysis of the effects of control strategies on the transmission dynamics of malaria, Applied Mathematics and Computation 195 (2), 641-662, 2008.
10. Craig, M.H., Kleinschmidt, I., Nawn, J.B., Le Sueur, D. and Sharp, B.L. Exploring 30 years of malaria case data in KwaZulu-Natal, South Africa: part I. The impact of climatic factors, Tropical Medicine & International Health 9 (12), 1247-1257, 2004.
11. Craig, M.H., Snow, R.W. and Le Sueur, D. A climate-based distribution model of malaria transmission in sub-Saharan Africa, Parasitology today 15 (3), 105-111, 1999.
12. Depinay, J.M.O., Mbogo, C.M., Killeen, G., Knols, B., Beier, J., Carlson, J., Dushoff, J., Billingsley, P., Mwambi, H., Githure, J. and Toure, A.M. A simulation model of African Anopheles ecology and population dynamics for the analysis of malaria transmission, Malaria journal 3 (1), 29, 2004.
13. Diekmann, O., Heesterbeek, J.A.P. and Roberts, M.G. The construction of next-generation matrices for compartmental epidemic models, Journal of the Royal Society Interface, p.rsif20090386, 2009.
14. Eckhoff, P.A. A malaria transmission-directed model of mosquito life cycle and ecology, Malaria journal, 10 (1), 303, 2011.
15. Ermert, V., Fink, A.H., Jones, A.E. and Morse, A.P. Development of a new version of the Liverpool Malaria Model. I. Refining the parameter settings and mathematical formulation of basic processes based on a literature review, Malaria journal 10 (1), 35, 2011.
16. Ermert, V., Fink, A.H., Jones, A.E. and Morse, A.P. Development of a new version of the Liverpool Malaria Model. II. Calibration and validation for West Africa, Malaria journal 10 (1), 62, 2011.
17. Rubel, F. and Brugger, K. Dynamics of infectious diseases according to climate change: the Usutu virus epidemics in Vienna, In Game meat hygiene in focus 173-198, 2011.
18. Hethcote, H.W. The mathematics of infectious diseases, SIAM review 42 (4), 599-653, 2000.
19. Hoshen, M.B. and Morse, A.P. A weather-driven model of malaria transmission, Malaria Journal 3 (1), 32, 2004.
20. Yang, H.M. Malaria transmission model for different levels of acquired immunity and temperature-dependent parameters (vector), Revista de saude publica 34 (3), 223-231, 2000.
21. Jepson, W.F., Moutia, A. and Courtois, C. The malaria problem in Mauritius: the bionomics of Mauritian anophelines, Bulletin of entomological research 38 (01), 177-208, 1947.
22. Li, J., A malaria model with partial immunity in humans, Mathematical biosciences and engineering 5 (4), 789-801, 2008.
23. Joshi, H.R. Optimal control of an HIV immunology model, Optimal control applications and methods 23 (4), 199-213, 2002.
24. Jones, A.E. and Morse, A.P. Application and validation of a seasonal ensemble prediction system using a dynamic malaria model, Journal of Climate 23 (15), 4202-4215, 2010.
25. Jones, A.E. and Morse, A.P. Skill of ENSEMBLES seasonal re-forecasts for malaria prediction in West Africa, Geophysical Research Letters 39 (23), 2012.
26. Koella, J.C. On the use of mathematical models of malaria transmission, Acta tropica 49 (1), 1-25, 1991.
27. Lafferty, K.D. The ecology of climate change and infectious diseases, Ecology 90 (4), 888- 900, 2009.
28. Limpopo Province, South Africa. SouthAfrica.info. http://www.southafrica.info/about/ geography/limpopo.htm.UxHXN85j-18 (Feb 2014).
29. Maharaj, R. Life table characteristics of Anopheles arabiensis (Diptera: Culicidae) under simulated seasonal conditions, Journal of medical entomology 40 (6), 737-742, 2003.
30. Macdonald, G. The epidemiology and control of malaria, 1957, London, New York, and Toronto: Oxford University Press Google Scholar.
31. MacDonald, G., Cuellar, C.B. and Foll, C.V. The dynamics of malaria, Bulletin of the World Health Organization 38 (5), 743, 1968.
32. Makinde, O.D. and Okosun, K.O. Impact of chemo-therapy on optimal control of malaria disease with infected immigrants, BioSystems 104 (1), 32-41, 2011.
33. Martens, W.J., Niessen, L.W., Rotmans, J., Jetten, T.H. and McMichael, A.J. Potential impact of global climate change on malaria risk Environmental health perspectives 103 (5), 458, 1995.
34. McKenzie, F.E. Why model malaria?, Parasitology Today 16 (12), 511-516, 2000.
35. Moghadas, S.M. and Gumel, A.B. Global stability of a two-stage epidemic model with generalized non-linear incidence, Mathematics and computers in simulation 60 (1), 107-118, 2002.
36. Mordecai, E.A., Paaijmans, K.P., Johnson, L.R., Balzer, C., Ben-Horin, T., Moor, E., McNally, A., Pawar, S., Ryan, S.J., Smith, T.C. and Lafferty, K.D. Optimal temperature for malaria transmission is dramatically lower than previously predicted, Ecology letters 16 (1), 22-30, 2013.
37. Nakazawa, M., Ohmae, H., Ishii, A. and Leafasia, J. Malaria infection and human behavioral factors: A stochastic model analysis for direct observation data in the Solomon Islands, American journal of human biology, 10 (6), 781-789, 1998.
38. Ngarakana-Gwasira, E.T., Bhunu, C.P. and Mashonjowa, E. Assessing the impact of temperature on malaria transmission dynamics, Afrika Matematika 25 (4), 1095-1112, 2014.
39. Okosun, K.O. and Makinde, O.D. Modelling the impact of drug resistance in malaria transmission and its optimal control analysis, International Journal of Physical Sciences 6 (28), 6479-6487, 2011.
40. Ozair, M., Lashari, A.A., Jung, I.H. and Okosun, K.O. Stability analysis and optimal control of a vector-borne disease with nonlinear incidence, Discrete Dynamics in Nature and Society, 2012.
41. Paaijmans, K.P., Cator, L.J. and Thomas, M.B. Temperature-dependent pre-bloodmeal period and temperature-driven asynchrony between parasite development and mosquito biting rate reduce malaria transmission intensity PLOS one 8 (1), e55777, 2013.
42. Paaijmans, K.P., Wandago, M.O., Githeko, A.K. and Takken, W. Unexpected high losses of Anopheles gambiae larvae due to rainfall, PLoS One 2 (11), e1146, 2007.
43. Parham, P.E. and Michael, E. Modelling climate change and malaria transmission, Modelling Parasite Transmission and Control 184-199, 2010.
44. Reisen, W.K. Effect of temperature on Culex tarsalis (Diptera: Culicidae) from the Coachella and San Joaquin valleys of California, Journal of medical entomology 32 (5), 636-645, 1995.
45. Rausher, M.D. Larval habitat suitability and oviposition preference in three related butterflies, Ecology 60 (3), 503-511, 1979.
46. South African National Census of 2001. http://www.statssa.gov.za/census01/html/.
47. Silal, S.P., Barnes, K.I., Kok, G., Mabuza, A. and Little, F. Exploring the seasonality of reported treated malaria cases in Mpumalanga, South Africa, PloS one 8 (10), e76640, 2013.
48. Sheffield, J., Goteti, G. and Wood, E.F. Development of a 50-year high-resolution global dataset of meteorological forcings for land surface modeling, Journal of Climate 19 (13), 3088-3111, 2006.
49. Ruan, S., Xiao, D. and Beier, J.C. On the delayed Ross-Macdonald model for malaria transmission, Bulletin of mathematical biology 70 (4), 1098-1114, 2008.
50. le Sueur, D. and Sharp, B.L. The breeding requirements of three members of the Anopheles gambiae Giles complex (Diptera: Culicidae) in the endemic malaria area of Natal, South Africa, Bulletin of entomological research 78 (04), 549-560, 1988.
51. Smith, T.A. Estimation of heterogeneity in malaria transmission by stochastic modelling of apparent deviations from mass action kinetics, Malaria journal 7 (1), 12, 2008.
52. Thomson, M.C., Doblas-Reyes, F.J., Mason, S.J., Hagedorn, R., Connor, S.J., Phindela, T., Morse, A.P. and Palmer, T.N. Malaria early warnings based on seasonal climate forecasts from multi-model ensembles, Nature 439 (7076), 576-579, 2006.
53. Tompkins, A.M. and Ermert, V. A regional-scale, high resolution dynamical malaria model that accounts for population density, climate and surface hydrology, Malaria journal 12 (1), 65, 2013.
54. Van den Driessche, P. and Watmough, J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical biosciences 180 (1), 29-48, 2002.
55. Wang, Y., Gilbreath III, T.M., Kukutla, P., Yan, G. and Xu, J. Dynamic gut microbiome across life history of the malaria mosquito Anopheles gambiae in Kenya, PloS one 6 (9), e24767, 2011.
56. World Health Organization. World Malaria Report 2008. http://www.who.int/malaria/publications/world-malaria-report-2008/report/en/
57. World Health Organization. World Malaria Report 2015. http://www.who.int/malaria/publications/world-malaria-report-2015/report/en/
58. Yazoume, Y., Hoshen, M., Kyobutungi, C., Louis, V.R. and Sauerborn, R. Local scale prediction of Plasmodium falciparum malaria transmission in an endemic region using temperature and rainfall, Global Health Action 2, 2009.
59. Lou, Y. and Zhao, X.Q. A climate-based malaria transmission model with structured vector population, SIAM Journal on Applied Mathematics 70 (6), 2023-2044, 2010.