A Mathematical Model for Malaria Disease Dynamics with Relapse Parameter
Article Sidebar
Page Numbers:
126-140
Digital Object Identifier:
10.58578/mjms.v3i1.4985
Viewed: 229 times
Downloaded: 194 times
LYAS Publisher cordially invites qualified professionals to serve as Editors or Reviewers. Your expertise will make an important contribution to maintaining and strengthening the academic quality of our publications. Interested applicants are kindly requested to complete the application form at the following link: Editors & Reviewers
Please feel free to contact us if you need any further information about the submission process or if you have any additional questions.
Authors:
Adamu A. K1*, Williams B2, Bulus S. M3 
Copyright :
Authors retain copyright and grant the journal right of first publication.
Main Article Content
Abstract
Malaria is one of the oldest diseases that has been extensively researched from multiple perspectives. Although many infectious diseases, including malaria, are preventable, they remain widespread in numerous communities due to insufficient, delayed, or ineffective control measures. Effective disease control involves rapidly reducing the infected population when a cure is available and minimizing susceptibility through vaccination when possible. Since malaria vaccines are still under development, vaccination offers a potential strategy for reducing the number of susceptible individuals. In this paper, we have analyzed and modified the SPITR mathematical model by Adamu et al. (2017) to study the transmission and control of malaria. Our modifications include the incorporation of a relapse parameter, and we have determined the basic reproduction number for the revised model. We demonstrated that the disease-free equilibrium (DFE) is locally asymptotically stable when the reproduction number is less than one and becomes unstable when it exceeds one. This finding suggests that with a combination of effective treatment, malaria relapse rate can be reduced and malaria in general can be effectively controlled in the population if the reproduction number is kept below unity.
Citation Metrics:
Downloads
Article Details
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
References
Adamu et al. (2017). Local Stability Analysis of a Susceptible Protected Infected Treated Recovered (SPITR) Mathematical Model for Malaria Disease Dynamics
Anderson RM & May RM. (1991). Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford.
Aron JL & May RM 1982. The population dynamics of malaria, in: R.M. Anderson (Ed.), The population Dynamics of Infectious Diseases: The Theory and Applications, Chapman and Hall, London. 139–179
Ashley, E. A., Dhorda, M., Fairhurst, R. M., et al. (2014). Spread of artemisinin resistance in Plasmodium falciparum malaria. New England Journal of Medicine, 371(5), 411-423.
Baird, J. K. (2013). Evidence and implications of mortality associated with acute Plasmodium vivax malaria. Clinical Microbiology Reviews, 26(1), 36-57.
Bennett, J. W., Pybus, B. S., Yadava, A., et al. (2013). Plasmodium vivax relapse: classical and contemporary studies. The American Journal of Tropical Medicine and Hygiene, 89(5), 850- 861
Chitnis N, J.M. Cushing, and J.M. Hyman. (2006). Bifurcation Analysis of Mathematical model for malaria transmission,” SIAM Journal on Applied Mathematics, 67(1) 24-45, 2006
Chitnis N. (2005). Using mathematical models in controlling the spread of malaria. PhD thesis. University of Arizona, Program in Applied Mathematics.
Fekadu TK, Purnachandra R.K. (2015). Controlling the spread of Malaria Disease using intervention strategies, Journal of Multidisciplinary Engineering Science and Technology (JMEST), 2(5): 1068-1074
Howes, R. E., Piel, F. B., Patil, A. P., et al. (2012). G6PD deficiency prevalence and estimates of affected populations in malaria-endemic countries. PLOS Medicine, 9(5), e1001339
Hethcote HW. (2000). The Mathematics of Infectious Disease. SIAM review. 42(4): 599-653
Kakkilaya BS. (2003). Rapid diagnosis of malaria, lab medicine, 8(34), 602-608
Imwong, M., Pukrittayakamee, S., Pongtavornpinyo, W., et al. (2012). Relapses of Plasmodium vivax infection usually result from activation of heterologous hypnozoites. The Journal of Infectious Diseases, 195(7), 927-933.
Llanos-Cuentas, A., Lacerda, M. V. G., Rueangweerayut, R., et al. (2019). Tafenoquine versus primaquine to prevent relapse of Plasmodium vivax malaria. New England Journal of Medicine, 380(3), 229-241.
Li et al. (1999). An intuitive formulation for the reproduction number for the spread of diseases in heterogeneous populations, Journal of Mathematical Biosciences. Elsevier 167 (2000) 65-86
Macdonald G. (1957). The Epidemiology and Control of Malaria, Oxford university press, Oxford.
Marsh K. (1998). Malaria disaster in Africa, Lancet, 352(9132):924
N. Chitnis, J.M. Cushing, and J.M. Hyman. (2006). Bifurcation Analysis of Mathematical model for malaria transmission. SIAM Journal on Applied Mathematics, 67(1) 24-45, 2006
Ngwa and Shu. (2000). A mathematical Model for endermic malaria with variable human and mosquito populations. Mathematical and computer modeling. 32:747-767
Price, R. N., Commons, R. J., Battle, K. E., et al. (2020). Prevention of Plasmodium vivax malaria relapses by tafenoquine. The New England Journal of Medicine, 383(12), 1080-1082.
Recht, J., Ashley, E. A., White, N. J. (2018). Use of primaquine and tafenoquine in Plasmodium vivax malaria. The Lancet Infectious Diseases, 18(2), e25-e30.
Ross R. (1911). The prevention of malaria. London: John Murray.
Wells, T. N. C., Burrows, J. N., & Baird, J. K. (2010). Targeting the hypnozoite reservoir in Plasmodium vivax: the hidden obstacle to malaria elimination. Trends in Parasitology, 26(3), 145-151.
White, N. J. (2011). The parasite clearance curve. Malaria Journal, 10(1), 278.
World Health Organization (WHO) and WHO Global Malaria Programme. http://www.who.int/topics/malaria/en/