A climate-based malaria transmission model with structured vector population

SIAM Journal on Applied Mathematics

Volumn 70, Issue 6, 2010, Pages 2023-2044

  Lou, Yijun ^a   Zhao, Xiao Qiang ^a  

^a MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

Author keywords

Basic reproduction ratio; Malaria transmission; Sensitivity analysis; Uniform persistence; Vector borne diseases

Indexed keywords

AGE STRUCTURES; BASIC REPRODUCTION RATIO; BIRTH RATES; KWAZULU-NATAL PROVINCE , SOUTH AFRICA; MALARIA TRANSMISSION; PERIODIC STATE; POTENTIAL IMPACTS; UNIFORM PERSISTENCE; VECTOR-BORNE DISEASE;

CLIMATE CHANGE; CLIMATE MODELS; PERIODIC STRUCTURES; POPULATION STATISTICS; VECTORS;

SENSITIVITY ANALYSIS;

EID: 77951198377     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/080744438     Document Type: Article

References (51)

1. M. F. BOYD, Epidemiology: Factors related to the definitive host, in Malariology, Vol.1, M. F. Boyd, ed., W. B. Saunders, Philadelphia, 1949, pp.608-697.
2. N. CHITNIS, J. M. CUSHING, AND J. M. HYMAN, Bifurcation analysis of a mathematical model for malaria transmission, SIAM J. Appl. Math., 67 (2006), pp.24-45.
3. N. CHITNIS, J. M. HYMAN, AND J. M. CUSHING, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol., 70 (2008), pp.1272-1296.
4. C. CHIYAKA, J. M. Tc HUENOHE, W. GARIRA, AND S. DUBE, A mathematical analysis of the effects of control strategies on the transmission dynamics of malaria, Appl. Math. Comput., 195 (2008), pp.641-662.
5. CLIMATE ENVIRONMENTAL PROTECTION AGENCY, http://yosemite.epa.gov/.
6. K. COOKE, P. VAN DEN DRIESSCHE, AND X. ZOU, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol., 39 (1999), pp.332-352.
7. M. H. CRAIG, I. KLEINSCHMIDT, J. B. NAWN, D. LE SUEUR, AND B. L. SHARP, Exploring 30 years of malaria case data in Kwa Zulu-Natal, South Africa: Part I. The impact of climatic factors, Tropical Medicine & International Health, 9 (2004), pp.1247-1257.
8. O. DIEKMANN, J. A. P. HEESTERBEEK, AND J. A. J. METZ, On the definition and the computation of the basic reproduction ratio Ro in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), pp.365-382.
9. DEPARTMENT OF HEALTH, South Africa, http://www.doh.gov.za.
10. A. M. GERRITSEN, P. KRUGER, M. F. S. VAN DER LOEFF, AND M. P. GROBUSCH, Malaria incidence in Limpopo Province, South Africa, 1998-2007, Malar. J., 7 (2008), article 162.
11. H. M. GILES AND D. A. WARREL, Bruce-Chwatt's Essential Malariology, 3rd ed., Heinemann Medical Books, Portsmouth, NH, 1993.
12. S. A. GOURLEY, R. LIU, AND J. WU, Some vector borne diseases with structured host populations: Extinction and spatial spread, SIAM J. Appl. Math., 67 (2007), pp.408-433.
13. B. GREENWOOD, The microepidemiology of malaria and its importance to malaria control, Trans. R. Soc. Trop. Med. Hyg., 83 (1989), pp.25-29.
14. M. B. HOSHEN AND A. P. MORSE, A weather-driven model of malaria transmission, Malar. J., 3 (2004), article 32.
15. M. HULME, J. MITCHELL, W. J. INGRAM, J. E. LOWE, T. C. JOHNS, M. NEW, AND D. VINER, Climate change scenarios for global impacts studies, Global Environ. Change, 9 (1999), pp.3-20.
16. T. KATO, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, Heidelberg, 1976.
17. G. F. Kl LLEEN, F. E. MCKENZIE, B. D. FOY, C. SCHIEFFELIN, P. F. Bl LLINGSLEY, AND J. C. BEIER, A simplified model for predicting malaria entomologic inoculation rates based on entomologic and parasitologic parameters relevant to control, Am. J. Trop. Med. Hyg., 62 (2000), pp.535-544.
18. G. F. KILLEEN, F. E. MCKENZIE, B. D. FOY, C. SCHIEFFELIN, P. F. BILLINGSLEY, AND J. C. BEIER, The potential impact of integrated malaria transmission control on entomologic inoculation rate in highly endemic areas, Am. J. Trop. Med. Hyg., 62 (2000), pp.545-551.
19. F. LARDEux, R. TEJERINA, V. QUISPE, AND T. CHAVEZ, A physiological time analysis of the duration of the gonotrophic cycle of Anopheles pseu dopunctipennis and its implications for malaria transmission in Bolivia, Malar. J., 7 (2008), article 141.
20. J. Li, A malaria model with partial immunity in humans, Math. Biosci. Eng., 5 (2008), pp.789-801.
21. J. Li AND F. BRAUER, Continuous-time age-structured models in population dynamics and epidemiology, in Mathematical Epidemiology, F. Brauer, P. van den Driessche, and J. Wu, eds., Springer-Verlag, Berlin, 2008, pp.205-227.
22. Y. Lou AND X.-Q. ZHAO, Threshold dynamics in a time-delayed periodic SIS epidemic model, Discrete Contin. Dyn. Syst. Ser. B, 1 (2009), pp.169-186.
23. G. MACDONALD, The Epidemiology and Control of Malaria, Oxford University Press, Oxford, UK, 1957.
24. P. MAGAL AND X.-Q. ZHAO, Global attractors and steady states for uniformly persistent dynamical systems, SIAM J. Math. Anal., 37 (2005), pp.251-275.
25. W. J. M. MARTENS, Health Impacts of Climate Change and Ozone Depletion: An Eco-epidemiological Modelling Approach, Ph. D.thesis, Maastricht University, Maastricht, The Netherlands, 1997.
26. W. J. M. MARTENS, Health impacts of climate change and ozone depletion: An eco-epidemiological modelling approach, Environ. Health Perspectives, 106 (1998), pp.241-251.
27. D. A. Mui R, Anopheline mosquitoes: Vector reproduction, life-cycle and biotope, in Malaria: Principles and Practice of Malariology, Vol.1, W. H. Wernsdorfer and I. Mc Gregor, eds., Churchill Livingstone, Edinburgh, 1988, pp.431-451.
28. NATIONAL CLIMATE DATA CENTER, http://www.ncdc.noaa.gov/oa/ncdc.html.
29. G. A. NGWA, Modelling the dynamics of endemic malaria in growing populations, Discrete Contin. Dyn. Syst. Ser. B, 4 (2004), pp.1173-1202.
30. G. A. NGWA AND W. S. SHU, A mathematical model for endemic malaria with variable human and mosquito populations, Math. Comput. Modelling, 32 (2000), pp.747-763.
31. P. REITER, Climate change and mosquito-borne disease, Envir. Hlth. Perspect., 109 (2001), pp.141-161.
32. R. ROSS, The Prevention of Malaria, 2nd ed., Murray, London, 1911.
33. S. Ru AN, D. XIAO, AND J. C. BEIER, On the delayed Ross-Macdonald model for malaria transmission, Bull. Math. Biol., 70 (2008), pp.1098-1114.
34. L. M. Ru EDA, K. J. PATEL, R. C. Ax TELL, AND R. E. STINNER, Temperature-dependent development and survival rates of Culex quinquefasciatus and Aedes aegypti (Diptera: Culici-dae), J. Med. Entomol., 27 (1990), pp.892-898.
35. M. W. SERVICE, Mosquito Ecology. Field Sampling Methods, 2nd ed., Elsevier, London, 1993.
36. D. L. SMITH, F. E. MCKENZIE, R. W. SNOW, AND S. I. H AY, Revisiting the basic reproductive number for malaria and its implications for malaria control, PLo S Biol., 5 (2007), pp.531-542.
37. H. L. SMITH, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Math. Surveys Monogr.41, AMS, Providence, RI, 1995.
38. H. L. SMITH AND P. WALTMAN, Perturbation of a globally stable steady state, Proc. Amer. Math. Soc., 127 (1999), pp.447-453.
39. R. J. SMITH AND S. D. HOVE-MUSEKWA, Determining effective spraying periods to control malaria via indoor residual spraying in sub-Saharan Africa, J. Appl. Math. Decis. Sci., (2008), article 745463.
40. K. B. TAN, H. L. KOH, A. I. MD ISMAIL, AND S. Y. TEH, Modeling mosquito population with temperature effects, in Proceedings of the International Conference on Environmental Research and Technology (ICERT 2008), Penang, Ma laysia, 2008, pp.536-540.
41. P. VAN DEN DRIESSCHE AND J. WATMOUGH, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease, Math. Biosci., 180 (2002), pp.525-540.
42. W. WANG AND X.-Q. ZHAO, An age-structured epidemic model in a patchy environment, SIAM J. Appl. Math., 65 (2005), pp.1597-1614.
43. W. WANG AND X.-Q. ZHAO, Threshold dynamics for compartmental epidemic models in peri-odic environments, J. Dynam. Differential Equations, 20 (2008), pp.699-717.
44. M. J. WONHAM, M. A. LEWIS, J. RENCAWOWICZ, AND P. VAN DEN DRIESSCHE, Transmission assumptions generate conflicting predictions in host-vector disease models: A case study in West Nile virus, Ecol. Lett., 9 (2006), pp.706-725.
45. THE WORLD HEALTH REPORT (2002), http://www.who.int/whr/2002/en/.
46. THE WORLD HEALTH REPORT (2008), http://www.who.int/malaria/wmr2008/.
47. D. XU AND X.-Q. ZHAO, Dynamics in a periodic competitive model with stage structure, J. Math. Anal. Appl., 311 (2005), pp.417-438.
48. F. ZHANG AND X.-Q. ZHAO, A periodic epidemic model in a patchy environment, J. Math. Anal. Appl., 325 (2007), pp.496-516.
49. X.-Q. ZHAO, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003.
50. X.-Q. ZHAO, Permanence implies the existence of interior periodic solutions for FDEs, Inter-nat. J. Qualitative Theory Differential Equations Appl., 2 (2008), pp.125-137.
51. G. ZHOU, N. MINAKAWA, A. K. GITHEKO, AND G. YAN, Association between climate variability and malaria epidemics in the east African highlands, Proc. Natl. Acad. Sci. USA, 101 (2004), pp.2375-2380.