Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

A reaction-diffusion system modeling the spread of resistance to an antimalarial drug

1. Institut de Recherche pour le Développement (I.R.D.), 32 avenue Henri Varagnat, 93143 Bondy cedex
2. Laboratoire de Paludologie, Institut de Recherche pour le Développement, B.P. 1386, Dakar

A mathematical model representing the diffusion of resistance to an antimalarial drug is developed. Resistance can spread only when the basic reproduction number of the resistant parasites is bigger than the basic reproduction number of the sensitive parasites (which depends on the fraction of infected people treated with the antimalarial drug). Based on a linearization study and on numerical simulations, an expression for the speed at which resistance spreads is conjectured. It depends on the ratio of the two basic reproduction numbers, on a coefficient representing the diffusion of mosquitoes, on the death rate of mosquitoes infected by resistant parasites, and on the recovery rate of nonimmune humans infected by resistant parasites.
  Article Metrics

Keywords propagation speed.; malaria; reaction-diffusion; resistance

Citation: Nicolas Bacaër, Cheikh Sokhna. A reaction-diffusion system modeling the spread of resistance to an antimalarial drug. Mathematical Biosciences and Engineering, 2005, 2(2): 227-238. doi: 10.3934/mbe.2005.2.227


This article has been cited by

  • 1. A. Ducrot, S. B. Sirima, B. Somé, P. Zongo, A mathematical model for malaria involving differential susceptibility, exposedness and infectivity of human host, Journal of Biological Dynamics, 2009, 3, 6, 574, 10.1080/17513750902829393
  • 2. Le Thi Thanh An, Willi Jäger, A quantitative model of population dynamics in malaria with drug treatment, Journal of Mathematical Biology, 2014, 69, 3, 659, 10.1007/s00285-013-0716-0
  • 3. Maoxing Liu, Guiquan Sun, Zhen Jin, Tao Zhou, An analysis of transmission dynamics of drug-resistant disease on scale-free networks, Applied Mathematics and Computation, 2013, 222, 177, 10.1016/j.amc.2013.07.023
  • 4. Lourdes Esteva, Abba B. Gumel, Cruz Vargas de León, Qualitative study of transmission dynamics of drug-resistant malaria, Mathematical and Computer Modelling, 2009, 50, 3-4, 611, 10.1016/j.mcm.2009.02.012
  • 5. Aleisha Brock, Carole Gibbs, Joshua Ross, Adrian Esterman, The Impact of Antimalarial Use on the Emergence and Transmission of Plasmodium falciparum Resistance: A Scoping Review of Mathematical Models, Tropical Medicine and Infectious Disease, 2017, 2, 4, 54, 10.3390/tropicalmed2040054
  • 6. Nakul Chitnis, J. M. Cushing, J. M. Hyman, Bifurcation Analysis of a Mathematical Model for Malaria Transmission, SIAM Journal on Applied Mathematics, 2006, 67, 1, 24, 10.1137/050638941
  • 7. C. Chiyaka, J.M. Tchuenche, W. Garira, S. Dube, A mathematical analysis of the effects of control strategies on the transmission dynamics of malaria, Applied Mathematics and Computation, 2008, 195, 2, 641, 10.1016/j.amc.2007.05.016
  • 8. F. B. AGUSTO, A. B. GUMEL, P. E. PARHAM, QUALITATIVE ASSESSMENT OF THE ROLE OF TEMPERATURE VARIATIONS ON MALARIA TRANSMISSION DYNAMICS, Journal of Biological Systems, 2015, 23, 04, 1550030, 10.1142/S0218339015500308
  • 9. E.Y. Klein, Antimalarial drug resistance: a review of the biology and strategies to delay emergence and spread, International Journal of Antimicrobial Agents, 2013, 41, 4, 311, 10.1016/j.ijantimicag.2012.12.007
  • 10. Geoffrey R. Hosack, Philippe A. Rossignol, P. van den Driessche, The control of vector-borne disease epidemics, Journal of Theoretical Biology, 2008, 255, 1, 16, 10.1016/j.jtbi.2008.07.033
  • 11. Rashad Abdul-Ghani, Hoda F. Farag, Amal F. Allam, Ahmed A. Azazy, Measuring resistant-genotype transmission of malaria parasites: challenges and prospects, Parasitology Research, 2014, 113, 4, 1481, 10.1007/s00436-014-3789-9
  • 12. Daozhou Gao, Shigui Ruan, , Analyzing and Modeling Spatial and Temporal Dynamics of Infectious Diseases, 2015, 109, 10.1002/9781118630013.ch6
  • 13. Aleisha R. Brock, Joshua V. Ross, Sunil Parikh, Adrian Esterman, The role of antimalarial quality in the emergence and transmission of resistance, Medical Hypotheses, 2018, 111, 49, 10.1016/j.mehy.2017.12.018
  • 14. Christinah Chiyaka, Winston Garira, Shadreck Dube, Effects of treatment and drug resistance on the transmission dynamics of malaria in endemic areas, Theoretical Population Biology, 2009, 75, 1, 14, 10.1016/j.tpb.2008.10.002
  • 15. Farinaz Forouzannia, A. Gumel, Dynamics of an age-structured two-strain model for malaria transmission, Applied Mathematics and Computation, 2015, 250, 860, 10.1016/j.amc.2014.09.117
  • 16. Sebastian Aniţa, Vincenzo Capasso, Stabilization of a reaction-diffusion system modelling malaria transmission, Discrete and Continuous Dynamical Systems - Series B, 2012, 17, 6, 1673, 10.3934/dcdsb.2012.17.1673
  • 17. F. B. Agusto, Malaria Drug Resistance: The Impact of Human Movement and Spatial Heterogeneity, Bulletin of Mathematical Biology, 2014, 76, 7, 1607, 10.1007/s11538-014-9970-6
  • 18. Sebastian Aniţa, Vincenzo Capasso, Gabriel Dimitriu, Regional control for a spatially structured malaria model, Mathematical Methods in the Applied Sciences, 2019, 10.1002/mma.5560
  • 19. Saminu Bala, Bello Gimba, Global Sensitivity Analysis to Study the Impacts of Bed-Nets, Drug Treatment, and Their Efficacies on a Two-Strain Malaria Model, Mathematical and Computational Applications, 2019, 24, 1, 32, 10.3390/mca24010032
  • 20. Sebastian Aniţa, Vincenzo Capasso, Regional Control for Spatially Structured Mosquito Borne Epidemics, Vietnam Journal of Mathematics, 2020, 10.1007/s10013-020-00395-2

Reader Comments

your name: *   your email: *  

Copyright Info: 2005, Nicolas Bacaër, et al., 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)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved