Mathematical Analysis of Malaria and Cholera Disease by Homotopy Perturbation Method

P N Vijaya Kumar; P Balaganesan; J Renuka

P N Vijaya Kumar Research Scholar,Department of Mathematics, Academy of Maritime Education and Training (AMET) Deemed to be University, Chennai, Tamil Nadu, India.
P Balaganesan Professor, Department of Mathematics, Academy of Maritime Education and Training (AMET) Deemed to be University, Chennai, Tamil Nadu, India.
J Renuka Assistant Professor, Department of Mathematics, Women’s Christian College, Chennai, Tamil Nadu, India.

Keywords: Malaria, Cholera, Co-infection, Homotopy Perturbation Method, Optimality Control of Disease

Abstract

The mathematical model for co-infection with malaria and cholera was developed in this problem, and it was researched to see if there was a synergistic link between the two diseases in the presence of medicines.
The effects of malaria and its treatment on cholera dynamics were investigated in greater depth. Malaria infection raises the chances of cholera, while cholera infection doesn’t really enhance the risk of malaria infection. The model was numerically investigated using the fourth-order Runge-Kutta method and analytically using the Homotopy Perturbation Method. The impact of each parameter on the governing equation was investigated and the effective control strategy was determined using the exact solutions (analytical).

How to cite this article:
Kumar PNV, Balaganesan P, Renuka J.
Mathematical Analysis of Malaria and Cholera
Disease by Homotopy Perturbation Method. J
Commun Dis. 2024;56(1):57-69.

DOI: https://doi.org/10.24321/0019.5138.202410

References

Okosun KO, Ouifki R, Marcus N. Optimal control analysis of a malaria disease transmission model that includes

treatment and vaccination with waning immunity. Biosystems. 2011;106(2-3):136-45. [PubMed] [Google Scholar]

Agarwal M, Verma V. Modelling and analysis of the spread of an infectious disease cholera with environmental fluctuations. Appl Appl Math. 2012;7(1):406-25. [Google Scholar]

Snow J. On the mode of communication of cholera. England: John Churchill; 1855.

Sanches RP, Ferreira CP, Kraenkel RA. The role of immunity and seasonality in cholera epidemics. Bull Math Biol. 2011;73:2916-31. [Google Scholar]

Ross R. The prevention of malaria. 2nd ed. London: Murray; 1911.

Koella JC, Anita R. Epidemiological models for the spread of anti-malarial resistance. Malar J. 2003;2:3. [PubMed] [Google Scholar]

Anderson RM, May RM. Infectious diseases of humans: dynamics and control. Oxford University Press; 1991. [Google Scholar]

Stilianakis NI, Dietz K, Schenzle D. Analysis of a model for the pathogenesis of AIDS. Math Biosci. 1997;145(1):27- 46. [PubMed] [Google Scholar]

Kribs-Zaleta CM, Vealsco-Hernandez JX. A simple vaccination model with multiple endemic states. Math Biosci. 2000;164(2):183-201. [PubMed] [Google Scholar]

Mukandavire Z, Gumel AB, Garira W, Tchuenche JM. Mathematical analysis of a model for HIV-malaria co- infection. Math Biosci Eng. 2009;6(2):333-62. [PubMed] [Google Scholar]

Mtisi E, Rwezaura H, Tchuenche JM. A mathematical analysis of malaria and tuberculosis co-dynamics.

Discret Contin Dyn Syst B. 2009;12(4):827-64. [Google Scholar]

Mushayabasa S, Bhunu CP. Is HIV infection associated with an increased risk for cholera? Insights from a mathematical model. BioSystems. 2012;109(2):203- 13. [PubMed] [Google Scholar]

Nielan RL, Schaefer E, Gaff H, Fister KR, Lenhart S. Modeling optimal intervention strategies for cholera.

Bull Math Biol. 2010;72(8):2004-18. [PubMed] [Google Scholar]

Okosun KO, Makinde OD. A co-infection model of malaria and cholera diseases with optimal control.

Math Biosci. 2014;258:19-32. [PubMed] [Google Scholar]

Osman M, Adu IK. Simple mathematical model for malaria transmission. J Adv Math Comput Sci. 2017;25(6):1-24.

Eikenberry SE, Gumel AB. Mathematical modeling of climate change and malaria transmission dynamics: a historical review. J Math Biol. 2018;77(4):857-933. [PubMed] [Google Scholar]

Bakary T, Boureima S, Sado T. A mathematical model of malaria transmission in a periodic environment. J Biol

Dyn. 2018;12(1):400-32. [PubMed] [Google Scholar]

Koutou O, Traoré B, Sangaré B. Mathematical modeling of malaria transmission global dynamics: taking into

account the immature stages of the vectors. Adv Differ Equ. 2018;2018:220. [Google Scholar]

Hntsa KH, Kahsay BN. Analysis of cholera epidemic controlling using mathematical modeling. Int J Math

Math Sci. 2020;7369204:13. [Google Scholar]

Egeonu KU, Omame A, Inyama SC. A co-infection model for two-strain malaria and cholera with optimal control. Int J Dyn Control. 2021;9:1612-32. [Google Scholar]

Ibrahim MM, Kamran MA, Mannan MM, Kim S, Jung IH. Impact of awareness to control malaria disease: a mathematical modeling approach. Hindawi Complex. 2020:8657410:13. [Google Scholar]

Baihaqi MA, Adi-Kusumo F. Modelling malaria transmission in a population with SEIRSp method. AIP Conf Proc. 2020;2264(1):020002. [Google Scholar]

Ndamuzi E, Gahungu P. Mathematical modeling of malaria transmission dynamics: case of Burundi. J Appl Math Phys. 2021;9(10):2447-60. [Google Scholar]

Adeniran GA, Olopade IA, Ajao SO, Akinrinmade VA, Aderele OR, Adewale SO. Sensitivity and mathematical analysis of malaria and cholera co-infection. Asian J Pure Appl Math. 2022;4(3):290-317. [Google Scholar]

Shah NH, Sheoran N, Jayswal E. Fractional order model for malaria-cholera co-infection. Math Eng Sci Aerosp.

;13(3):833-52. [Google Scholar]

Sinan M, Ahmad H, Ahmad Z, Baili J, Murtaza S, Aiyashi MA, Botmart T. Fractional mathematical modeling of

malaria disease with treatment & insecticides. Result Phys. 2022;34:105220. [Google Scholar]