Research Artcle Journal of Communicable Diseases (P-ISSN: 0019-5138 & E-ISSN: 2581-351X) Copyright (c) 2024: Author(s). Published by Indian Society for Malaria and Other Communicable Diseases Journal of Communicable Diseases Volume 56, Issue 1 - 2024, Pg. No. 57-69 Peer Reviewed & Open Access Journal Corresponding Author: P Balaganesan, Department of Mathematcs, AMET Deemed to be University, Chennai, Tamil Nadu, India. E-mail Id: balaganesanpp@gmail.com Orcid Id: htps://orcid.org/0000-0003-4581-0608 How to cite this artcle: Kumar PNV, Balaganesan P, Renuka J. Mathematcal Analysis of Malaria and Cholera Disease by Homotopy Perturbaton Method. J Commun Dis. 2024;56(1):57-69. Date of Submission: 2024-01-11 Date of Acceptance: 2024-02-22 I N F O A B S T R A C T Mathematical Analysis of Malaria and Cholera Disease by Homotopy Perturbation Method PN Vijaya Kumar 1 , P Balaganesan 2 , J Renuka 3 1 Research Scholar, 2 Professor, Department of Mathematcs, Academy of Maritme Educaton and Training (AMET) Deemed to be University, Chennai, Tamil Nadu, India. 3 Assistant Professor, Department of Mathematcs, Women’s Christan College, Chennai, Tamil Nadu, India. DOI: htps://doi.org/10.24321/0019.5138.202410 Introduction Malaria is a disease transmited by mosquitoes that may be prevented and treated. Mosquito bitng is stopped by the distributon of low-cost bed nets and sprays, as well as by mosquito abatement tactcs such as sprinkling insectcide indoors and draining flthy water where vectors thrive. 1 “Recent fooding in Africa and Asia has created a signifcant danger to environmental sanitaton and clean water supply, allowing malaria and cholera to spread”. 2 John Snow was the frst to examine cholera epidemiology, which paved the way for modern epidemiology study. 3 The relatonshi p between cholera and contaminated water has long been known. Cholera is a life-threatening bacterium infecton that can cause vomitng and diarrhoea. It is spread by drinking water infected with the bacteria Vibrio cholerae (typically via faeces or wastewater) and can lead to “severe thirst, electrolyte imbalance, and death”, if not treated. Cholera colonisaton by humans results in a super infectous conditon that persists afer transmission, contributng to epidemic illness. Good sanitaton and water treatment can help prevent cholera. 4 Mathematcal modelling has been useful in gaining a beter understanding of disease transmission dynamics as well as in making decisions about disease control interventon techniques. Ross, for example, was the frst to establish “Mathematcal models of malaria transmission”. 5 His major objectve was vector management, and he established that the mosquito populaton must be decreased to a The mathematcal model for co-infecton with malaria and cholera was developed in this problem, and it was researched to see if there was a synergistc link between the two diseases in the presence of medicines. The efects of malaria and its treatment on cholera dynamics were investgated in greater depth. Malaria infecton raises the chances of cholera, while cholera infecton doesn’t really enhance the risk of malaria infecton. The model was numerically investgated using the fourth-order Runge-Kuta method and analytcally using the Homotopy Perturbaton Method. The impact of each parameter on the governing equaton was investgated and the efectve control strategy was determined using the exact solutons (analytcal). Keywords: Malaria, Cholera, Co-infecton, Homotopy Perturbaton Method, Optmality Control of Disease