Assessing The Impact of Medical Treatment and Fumigation on The Superinfection of Malaria: A Study of Sensitivity Analysis
DOI:
https://doi.org/10.5614/cbms.2023.6.1.5Keywords:
Malaria, superinfection, host-vector, basic and invasive reproduction number, sensitivity analysisAbstract
Malaria is a disease caused by the parasite Plasmodium, transmitted by the bite of an infected female Anopheles. In general, five species of Plasmodium that can cause malaria. Of the five species, Plasmodium falciparum and Plasmodium vivax are two species of Plasmodium that can allow malaria superinfection in the human body. Typically, the popular intervention for malaria eradication is the use of fumigation to control the vector population and provide good medical services for malaria patients. Here in this article, we formulate a mathematical model based on a host-vector interaction. Our model considering two types of plasmodium in the infection process and the use of medical treatment and fumigation for the eradication program. Our analytical result succeeds in proving the existence of all equilibrium points and how their existence and local stability criteria depend not only on the control reproduction number but also in the invasive reproduction number. This invasive reproduction number represent how one plasmodium can dominate other plasmodium. Our sensitivity analysis shows that fumigation is the most influential parameter in determining all control reproduction numbers. Furthermore, we find that the order in which numerous intervention measures are taken will be very crucial to determine the level of success of our malaria eradication program.
References
World Health Organization (WHO), Malaria, 2019, https://www.who.int/news-room/fact-sheets/detail/malaria, (Januari 11, 2020).
Robert, V., Macintyre, K., Keating, J., Trape, J.F., Duchemin, J.B., Warren, M. and Beier, J.C., Malaria transmission in urban sub-Saharan Africa, The American Journal of Tropical Medicine and Hygiene, 68(2), pp. 169-176, 2003.
Rosenberg, R., Andre, R.G. and Ketrangsee, S., Seasonal fluctuation of Plasmodium falciparum gametocytaemia, Transactions of the Royal Society of Tropical Medicine and Hygiene, 84(1), pp. 29-33, 1990.
Portugal, S., Drakesmith, H. and Mota, M.M., Superinfection in malaria: Plasmodium shows its iron will, EMBO Reports, 12(12), pp. 1233-1242, 2011.
Beier, M.S., Schwartz, I.K., Beier, J.C., Perkins, P.V., Onyango, F., Koros, J.K., Campbell, G.H., Andrysiak, P.M. and Brandling-Bennett, A.D., Identification of malaria species by ELISA in sporozoite and oocyst infected Anopheles from western Kenya, The American Journal of Tropical Medicine and Hygiene, 39(4), pp. 323-327, 1988.
Mayor, A., Saute, F., Aponte, J.J., Almeda, J., Gomez-Olive, F.X., Dgedge, M. and Alonso, P.L., Plasmodium falciparum multiple infections in Mozambique, its relation to other malariological indices and to prospective risk of malaria morbidity, Tropical Medicine & International Health, 8(1), pp. 3-11, 2003.
Kementerian Kesehatan Republik Indonesia (Kemenkes RI),Bersama Kita Berantas Malaria, 2010, https://www.depkes.go.id/article/print/1055/bersama-kita-berantasmalaria.html, (Januari 14, 2020).
Mutabingwa, T.K., Artemisinin-based combination therapies (ACTs): best hope for malaria treatment but inaccessible to the needy!, Acta Tropica, 95(3), pp. 305-315, 2005.
Martcheva, M., An introduction to mathematical epidemiology, New York: Springer, 2015.
Koella, J.C. and Antia, R., Epidemiological models for the spread of anti-malarial resistance, Malaria Journal, 2(1), pp. 1-11, 2003.
Mohammed-Awel, J., Iboi, E.A. and Gumel, A.B., Insecticide resistance and malaria control: A genetics-epidemiology modeling approach, Mathematical Biosciences, 325, p. 108368, 2020.
Ghosh, M., Olaniyi, S. and Obabiyi, O.S., Mathematical analysis of reinfection and relapse in malaria dynamics, Applied Mathematics and Computation, 373, p. 125044, 2020.
Taylor, A.R., Watson, J.A., Chu, C.S., Puaprasert, K., Duanguppama, J. and Day, N.P.J., Resolving the cause of recurrent Plasmodium vivax malaria probabilistically, Nat. Commun., 10(1), p. 5595, 2019.
Li, J., Zhao, Y. and Li, S., Fast and slow dynamics of malaria model with relapse, Mathematical Biosciences, 246(1), pp. 94-104, 2013.
Obabiyi, O. and Olaniyi, S., Global stability analysis of malaria transmission dynamics with vigilant compartment, Electronic Journal of Differential Equations, 2019(09), pp. 1-10, 2019.
Tasman, H., Aldila, D., Dumbela, P.A., Ndii, M.Z., Fatmawati, Herdicho, F.F. and Chukwu, C.W., Assessing the impact of relapse, reinfection and recrudescence on malaria eradication policy: a bifurcation and optimal control analysis, Tropical Medicine and Infectious Disease, 7(10), p. 263, 2022.
Aldila, D. and Seno, H., A population dynamics model of mosquito-borne disease transmission, focusing on mosquitoes? biased distribution and mosquito repellent use, Bulletin of Mathematical Biology, 81(12), pp. 4977-5008, 2019.
Aldila, D. and Angelina, M., Optimal control problem and backward bifurcation on malaria transmission with vector bias, Heliyon, 7(4), p. e06824, 2021.
Mojeeb, A.L. and Li, J., Analysis of a vector-bias malaria transmission model with application to Mexico, Sudan and Democratic Republic of the Congo, Journal of Theoretical Biology, 464, pp. 72-84, 2019.
Buonomo, B. and Vargas-De-Leon, C., Stability and bifurcation analysis of a vector-bias model of malaria transmission, Mathematical Biosciences, 242(1), pp. 59-67, 2013.
Cai, L., Li, X., Tuncer, N., Martcheva, M. and Lashari, A.A., Optimal control of a malaria model with asymptomatic class and superinfection, Mathematical Biosciences, 288, pp. 94-108, 2017.
Aldila, D., A superinfection model on malaria transmission: analysis on the invasion basic reproduction number, Commun. Math. Biol. Neurosci., 30(1), 2021. doi: 10.28919/cmbn/5612.
Okosun, K.O. and Makinde, O.D., A co-infection model of malaria and cholera diseases with optimal control, Mathematical Biosciences, 258, pp. 19-32, 2014.
Mohammed-Awel, J. and Numfor, E., Optimal insecticide-treated bed-net coverage and malaria treatment in a malaria-HIV co-infection model, Journal of Biological Dynamics, 11(sup1), pp. 160-191, 2017.
Handari, B.D., Ramadhani, R.A., Chukwu, C.W., Khoshnaw, S.H. and Aldila, D., An optimal control model to understand the potential impact of the new vaccine and transmission-blocking drugs for malaria: A case study in papua and west papua, indonesia, Vaccines, 10(8), p. 1174, 2022.
Tumwiine, J., Hove-Musekwa, S.D. and Nyabadza, F., A mathematical model for the transmission and spread of drug sensitive and resistant malaria strains within a human population, International Scholarly Research Notices, 2014.
Handari, B.D., Vitra, F., Ahya, R., Nadya S, T. and Aldila, D., Optimal control in a malaria model: intervention of fumigation and bed nets, Advances in Difference Equations, 2019(1), pp. 1-25, 2019.
Guo, Z.K., Huo, H.F. and Xiang, H., Global dynamics of an age-structured malaria model with prevention. Math. Biosci. Eng., 16(3), pp. 1625-1653, 2019.
Dudley, H.J., Goenka, A., Orellana, C.J. and Martonosi, S.E., Multi-year optimization of malaria intervention: a mathematical model, Malaria Journal, 15(1), pp. 1-23, 2016.
Borghans, J.A., De Boer, R.J. and Segel, L.A., Extending the quasi-steady state approximation by changing variables, Bulletin of Mathematical Biology, 58, pp. 43-63, 1996.
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, 7(47), pp. 873-885, 2010.
Aldila, D., Latifah, S.L. and Dumbela, P.A., Dynamical analysis of mathematical model for Bovine Tuberculosis among human and cattle population, Commun. Biomath. Sci, 2(1), pp. 55-64, 2019.
Maimunah and Aldila, D., Mathematical model for HIV spreads control program with ART treatment, In Journal of physics: Conference Series, 974, p. 012035, 2018.
Aldila, D., Rarasati, N., Nuraini, N. and Soewono, E., Optimal control problem of treatment for obesity in a closed population, International Journal of Mathematics and Mathematical Sciences, 2014.
Aldila, D., Chavez, J.P., Wijaya, K.P., Ganegoda, N.C., Simorangkir, G.M., Tasman, H. and Soewono, E., A tuberculosis epidemic model as a proxy for the assessment of the novel M72/AS01E vaccine, Communications in Nonlinear Science and Numerical Simulation, 120, p. 107162, 2023.
Aldila, D., Ndii, M.Z., Anggriani, N., Tasman, H. and Handari, B.D., Impact of social awareness, case detection, and hospital capacity on dengue eradication in Jakarta: A mathematical model approach, Alexandria Engineering Journal, 64, pp. 691-707, 2023.
Aldila, D., Optimal control for dengue eradication program under the media awareness effect, International Journal of Nonlinear Sciences and Numerical Simulation, 24(1), pp. 95-122, 2023.
Badan Pusat Statisika (BPS),Indeks Pembangunan Manusia (IPM) Indonesia pada tahun 2019, 2020, https://www.bps.go.id/pressrelease/2020/02/17/1670/indeks-pembangunan-manusia--ipm--indonesia-pada-tahun-2019-mencapai-71-92.html, (Mei 3, 2020).
Centers for Disease Control and Prevention, Pesticide Exposures, 2019, https://ephtracking.cdc.gov/showpesticideFumigants, (Februari 26, 2020).
Chinebu,T.I., Ezennorom, E.O. and Okwor, J.U., Simulation of a Mathematical Model of Malaria Transmission Dynamics in the Presence of Mosquito Net,Fumigation And Treatment, International Journal of Trend in Scientific Research and Development, 2(6), ISSN:2456-6470, 2018.
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, pp. 1272-1296, 2008.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Communication in Biomathematical Sciences

This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.