Year 2018,
Volume: 47 Issue: 2, 219 - 235, 01.04.2018
Gbenga J. Abiodun
P. Witbooi
Kazeem O. Okosun
References
- 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.
- 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.
- 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.
- 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.
- Anderson, R.M., May, R.M. and Anderson, B. Infectious diseases of humans: dynamics and
control (Vol. 28). Oxford: Oxford university press, 1992.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Eckhoff, P.A. A malaria transmission-directed model of mosquito life cycle and ecology,
Malaria journal, 10 (1), 303, 2011.
- 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.
- 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.
- 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.
- Hethcote, H.W. The mathematics of infectious diseases, SIAM review 42 (4), 599-653, 2000.
- Hoshen, M.B. and Morse, A.P. A weather-driven model of malaria transmission, Malaria
Journal 3 (1), 32, 2004.
- 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.
- 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.
- Li, J., A malaria model with partial immunity in humans, Mathematical biosciences and
engineering 5 (4), 789-801, 2008.
- Joshi, H.R. Optimal control of an HIV immunology model, Optimal control applications
and methods 23 (4), 199-213, 2002.
- 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.
- 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.
- Koella, J.C. On the use of mathematical models of malaria transmission, Acta tropica 49
(1), 1-25, 1991.
- Lafferty, K.D. The ecology of climate change and infectious diseases, Ecology 90 (4), 888-
900, 2009.
- Limpopo Province, South Africa. SouthAfrica.info. http://www.southafrica.info/about/
geography/limpopo.htm.UxHXN85j-18 (Feb 2014).
- Maharaj, R. Life table characteristics of Anopheles arabiensis (Diptera: Culicidae) under
simulated seasonal conditions, Journal of medical entomology 40 (6), 737-742, 2003.
- Macdonald, G. The epidemiology and control of malaria, 1957, London, New York, and
Toronto: Oxford University Press Google Scholar.
- MacDonald, G., Cuellar, C.B. and Foll, C.V. The dynamics of malaria, Bulletin of the
World Health Organization 38 (5), 743, 1968.
- 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.
- 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.
- McKenzie, F.E. Why model malaria?, Parasitology Today 16 (12), 511-516, 2000.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Parham, P.E. and Michael, E. Modelling climate change and malaria transmission, Modelling
Parasite Transmission and Control 184-199, 2010.
- 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.
- Rausher, M.D. Larval habitat suitability and oviposition preference in three related butterflies,
Ecology 60 (3), 503-511, 1979.
- South African National Census of 2001. http://www.statssa.gov.za/census01/html/.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- World Health Organization. World Malaria Report 2008.
http://www.who.int/malaria/publications/world-malaria-report-2008/report/en/
- World Health Organization. World Malaria Report 2015.
http://www.who.int/malaria/publications/world-malaria-report-2015/report/en/
- 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.
- 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.
Modelling the impact of climatic variables on malaria transmission
Year 2018,
Volume: 47 Issue: 2, 219 - 235, 01.04.2018
Gbenga J. Abiodun
P. Witbooi
Kazeem O. Okosun
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.
References
- 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.
- 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.
- 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.
- 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.
- Anderson, R.M., May, R.M. and Anderson, B. Infectious diseases of humans: dynamics and
control (Vol. 28). Oxford: Oxford university press, 1992.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Eckhoff, P.A. A malaria transmission-directed model of mosquito life cycle and ecology,
Malaria journal, 10 (1), 303, 2011.
- 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.
- 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.
- 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.
- Hethcote, H.W. The mathematics of infectious diseases, SIAM review 42 (4), 599-653, 2000.
- Hoshen, M.B. and Morse, A.P. A weather-driven model of malaria transmission, Malaria
Journal 3 (1), 32, 2004.
- 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.
- 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.
- Li, J., A malaria model with partial immunity in humans, Mathematical biosciences and
engineering 5 (4), 789-801, 2008.
- Joshi, H.R. Optimal control of an HIV immunology model, Optimal control applications
and methods 23 (4), 199-213, 2002.
- 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.
- 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.
- Koella, J.C. On the use of mathematical models of malaria transmission, Acta tropica 49
(1), 1-25, 1991.
- Lafferty, K.D. The ecology of climate change and infectious diseases, Ecology 90 (4), 888-
900, 2009.
- Limpopo Province, South Africa. SouthAfrica.info. http://www.southafrica.info/about/
geography/limpopo.htm.UxHXN85j-18 (Feb 2014).
- Maharaj, R. Life table characteristics of Anopheles arabiensis (Diptera: Culicidae) under
simulated seasonal conditions, Journal of medical entomology 40 (6), 737-742, 2003.
- Macdonald, G. The epidemiology and control of malaria, 1957, London, New York, and
Toronto: Oxford University Press Google Scholar.
- MacDonald, G., Cuellar, C.B. and Foll, C.V. The dynamics of malaria, Bulletin of the
World Health Organization 38 (5), 743, 1968.
- 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.
- 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.
- McKenzie, F.E. Why model malaria?, Parasitology Today 16 (12), 511-516, 2000.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Parham, P.E. and Michael, E. Modelling climate change and malaria transmission, Modelling
Parasite Transmission and Control 184-199, 2010.
- 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.
- Rausher, M.D. Larval habitat suitability and oviposition preference in three related butterflies,
Ecology 60 (3), 503-511, 1979.
- South African National Census of 2001. http://www.statssa.gov.za/census01/html/.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- World Health Organization. World Malaria Report 2008.
http://www.who.int/malaria/publications/world-malaria-report-2008/report/en/
- World Health Organization. World Malaria Report 2015.
http://www.who.int/malaria/publications/world-malaria-report-2015/report/en/
- 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.
- 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.