
Mathematical Biosciences and Engineering, 2019, 16(3): 14141444. doi: 10.3934/mbe.2019069
Research article Special Issues
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Mathematical assessment of the impact of different microclimate conditions on malaria transmission dynamics
Department of Mathematics, University of Benin, Benin City, Nigeria
Received: , Accepted: , Published:
Special Issues: Mathematical Modeling of MosquitoBorne Diseases
References
1. G. J. Abiodun, R. Maharaj, P. Witbooi, et al., Modelling the influence of temperature and rainfall on the population dynamics of anopheles arabiensis, Malaria J., 15 (2016), 364.
2. Y. A. Afrane, B.W. Lawson, A. K. Githeko, et al., Effects of microclimatic changes caused by land use and land cover on duration of gonotrophic cycles of anopheles gambiae (Diptera: Culicidae) in western Kenya highlands, J. Med. Entomol., 42 (2005), 974–980.
3. F. B. Agusto, A. B. Gumel and P. E. Parham, Qualitative assessment of the role of temperature variation on malaria transmission dynamics, J. Biol. Syst., 24 (2015), 1–34.
4. N. Bacaer, Approximation of the basic reproduction number Ro for vectorborne diseases with a periodic vector population, B. Math. Biol., 69 (2007), 1067–1091.
5. L. M. BeckJohnson, W. A. Nelson, K. P. Paaijmans, et al., The importance of temperature fluctuations in understanding mosquito population dynamics and malaria risk, Roy. Soc. Open Sci., 4 (2017). Available from :http://dx.doi.org/10.1098/rsos.160969.
6. J. I. Blanford, S. Blanford, R. G. Crane, et al., Implications of temperature variation for malaria parasite development across Africa, Sci. Rep., 3 (2013), 1300.
7. P. Cailly, A. Tran, T. Balenghien, et al., A climatedriven abundance model to assess mosquito control strategies, Ecol. Model., 227 (2012), 7–17.
8. C. ChristiansenJucht, K. Erguler, C. Y. Shek, et al., Modelling anopheles gambiae s.s. population dynamics with temperature and agedependent survival, Int. J. Env. Res. Pub. He., 12 (2015), 5975–6005.
9. O. Diekmann, J. Heesterbeek and J. Metz, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365–382.
10. Y. Dumont and F. Chiroleu, Vector control for the chikungunya disease, Math. Biosci. Eng., 7 (2010), 105–111.
11. A. EgbendeweMondzozo, M. Musumba, B. A. McCarl, et al., Climate change and vectorborne diseases: an economic impact analysis of malaria in Africa, Int. J. Env. Res. Pub. He., 8 (2011), 913–930.
12. S. M. Garba, A. B. Gumel and M. R. A. Bakar, Backward bifurcations in dengue transmission dynamics, Math. Biosci., 215 (2008), 11–25.
13. A. B. Gumel, Causes of backward bifurcation in some epidemiological models, J. Math. Anal. Appl., 395 (2012), 355–365.
14. V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications, Academic Press, New York, 1969.
15. J. La Salle and S. Lefschetz, The stability of dynamical systems, SIAM, Philadephia, 1976.
16. Y. Lou and X. Q. Zhao, A climatebased malaria transmission model with structured vector population, SIAM J. Appl. Math., 70 (2010), 2023–2044.
17. P. Magal and X. Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM J. Math. Anal., 37 (2005), 251–275.
18. E. A. Mordecai, Optimal temperature for malaria transmission is dramatically lower than previously predicted, Ecol. Lett., 16 (2013), 22–30.
19. E. T. NgarakanaGwasira, C. P. Bhunu, M. Masocha, et al., Assessing the role of climate change in malaria transmission in Africa, Malaria Res. Treat., 1 (2016), 1–7.
20. C. N. Ngonghala, S. Y. Del Valle, R. Zhao, et al., Quantifying the impact of decay in bednet efficacy on malaria transmission, J. Theor. Biol., 363 (2014), 247–261.
21. H. S. Ngowo, E. W. Kaindoa, J. Matthiopoulos, et al., Variations in household microclimate affect outdoorbiting behaviour of malaria vectors, Wellcome Open Research, 2 (2017).
22. A. M. Niger and A. B. Gumel, Mathematical analysis of the role of repeated exposure on malaria transmission dynamics, Diff. Equa. Dyn. Syst., 16 (2008), 251–287.
23. K. Okuneye and A. B. Gumel, Analysis of a temperature and rainfalldependent model for malaria transmission dynamics, Math. Biosci., 287 (2017), 72–92.
24. K. P. Paaijmans, A. F. Read and M. B. Thomas, Understanding the link between malaria risk and climate, P. Natl. Acad. Sci. USA, 106 (2009), 13844–13849.
25. K. P. Paaijmans, S. Blanford, A. S. Bell, et al., Influence of climate on malaria transmission depends on daily temperature variation, P. Natl. Acad. Sci. USA, 107 (2010), 15135–15139.
26. K. P. Paaijmans, S. S. Imbahale, M. B. Thomas, et al., Relevant microclimate for determining thedevelopment rate of malaria mosquitoes and possible implications of climate change, Malaria J., 9 (2010), 196.
27. K. P. Paaijmans and M. B. Thomas, The influence of mosquito resting behaviour and associated microclimate for malaria risk, Malaria J., 10 (2011), 183.
28. K. P. Paaijmans and M. B. Thomas, Relevant temperatures in mosquito and malaria biology, In: Ecology of parasitevector interactions, Wageningen Academic Publishers, 2013.
29. P. E. Parham and E. Michael, Modeling the effects of weather and climate change on malaria transmission, Environ. Health Persp., 118 (2010), 620–626.
30. D. J. Rogers and S. E. Randolph, Advances in Parasitology, Elsevier Academic Inc, San Diego, 2006.
31. M. A. Safi, M. Imran and A. B. Gumel, Threshold dynamics of a nonautonomous SEIRS model with quarantine and isolation, Theor. Biosci., 131 (2012), 19–30.
32. L. L. M. Shapiro, S. A. Whitehead and M. B. Thomas, Quantifying the effects of temperature on mosquito and parasite traits that determine the transmission potential of human malaria, PLoS Biol., 15 (2017), e2003489.
33. P. Singh, Y. Yadav, S. Saraswat, et al., Intricacies of using temperature of different niches for assessing impact on malaria transmission, Indian J. Med. Res., 144 (2016), 67–75.
34. H. L. Smith, Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, Am. Math. Soc., 41, 1995.
35. S. Thomas, S. Ravishankaran, N. A. J. Amala Justin, et al., Microclimate variables of the ambient environment deliver the actual estimates of the extrinsic incubation period of plasmodium vivax and plasmodium falciparum: a study from a malaria endemic urban setting, Chennai in India, Malaria J., 17 (2018), 201.
36. P. Van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48.
37. W. Wang and X. Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, J. Dyn. Differ. Equations, 20 (2008), 699–717.
38. Malaria Report, from World Health Organization, 2010. Available from: www.who.int/ mediacenter/factsheets/fs094/en/.
39. World Malaria Day, Report of the World Health Organisation (WHO), 2018. Available from: www.who.int/malaria/media/worldmalariaday2018/en/.
40. H. Zhang, P. Georgescu and A. S. Hassan, Mathematical insights and integrated strategies for the control of Aedes aegypti mosquito, Appl. Math. Comput., 273 (2016), 1059–1089.
41. F. Zhang and X. Q. Zhao, A periodic epidemic model in a patchy environment, J. Math. Anal. Appl., 325 (2007), 496–516.
42. X. Q. Zhao, Dynamical systems in population biology, Springer, New York, 2003.
43. X. Q. Zhao, Uniform persistence and periodic coexistence states in infinitedimensional periodic semiflows with applications, Can. Appl. Math. Q., 3 (1995), 473–495.
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)