Stability Analysis of Endemic Equilibrium Points of Malaria and Dengue Fever Co-infection Model

T.J. Oluwafemi¹ , N.I. Akinwande² , E. Azuaba³

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.6 , pp.34-45, Dec-2020

Online published on Dec 31, 2020

Copyright © T.J. Oluwafemi, N.I. Akinwande, E. Azuaba . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

Abstract :
Malaria-dengue co-infection is becoming a public health challenge with the growing report of the co-infection. Much has been done on analyzing malaria, dengue, and other infection but much has not been done to study the co-infection of malaria and dengue fever. A mathematical model to understand the transmission of malaria and dengue infection was formulated using a system of ordinary differential equations. We computed the basic reproduction number and establish the equilibria point. The endemic equilibrium point was further investigated. The result shows that with the reproduction number greater than one, the endemic equilibrium point was found to be locally asymptotically stable and globally asymptotically stable.

Key-Words / Index Term :
Malaria, Dengue Fever, Co-infection, Endemic Equilibrium, Stability Analysis

References :
[1] G. Geleta, T. Ketema, “Severe Malaria Associated with Plasmodium falciparum and P. vivax among Children in Pawe Hospital, Northwest Ethiopia”, Malaria Research and Treatment, Hindawi Publishing Corporation, 2016.
[2] World Health Organization, World Malaria Report, Geneva, WHO Pres, 2018.
[3] J.P. Messina, et al. A global compendium of human dengue virus occurrence. Sci. Data 1, 140004 (2014).
[4] B.R. Murphy, S.S. Whitehead, “Immune response to dengue virus and prospects for a vaccine”. Annual Review of Immunology, vol. 29, pp. 587-619, 2011.
[5] S.E. Chong, Z.R.H. Mohamad, S. Suraiya, K.T. Lee, J.A. Lim, J. Malar, “The danger of accepting a single diagnosis: case report of concurrent Plasmodium Knowlesi malaria and dengue infection”, Malaria Journal, vol. 16, issue 2, 2017.
[6] M.R.K. Rao, N.P. Rabindra, K.D. Manoj, “Prevalence of dengue viral and malaria parasitic co-infections in an epidemic district, Angul of Odisha, India: Aneco-epidemiological and cross-sectional study for the prospective aspects of public health”, Journal of Infection and Public Health, Vol. 9, pp 421—428, 2016.
[7] E.A. Bakare, C.R. Nwozo, “Mathematical Analysis of Malaria-Schistosomiasis Co-infection model”, Epidemiology Research International.. Article ID 3854902, 19 pages. Hindawi Publishing Corporation. http://dx.doi.org/10.1155/2016/3854902 , 2016.
[8] J. Amoah-Mensah, I.K. Dontwi, E. Bonyah, ”Stability Analysis of Zika-Malaria Co-infection Model for Model Endemic Region”, Journal of Advances in Mathematics and Computer Science, Vol. 26, Issue 1, 1-22, 2018.
[9] D. Aldila, M.R. Agustin, “A Mathematical Model of Dengue-Chikungunya Co-Infection in a Closed Population”, Journal of Physics: Conf. Series DOI: 10.1088/1742-6596/974/1/012001, 2018.
[10] E. Bonyah, M.A. Khan, K.O. Okosun, J.F. Gomez-Aguilar,“On the co-infection of dengue fever and Zika Virus”, Optim Control Appl Meth, Vol. 40, pp 394-421, 2019.
[11] M.O. Ogunmiloro, “Mathematical Modeling of the Co-infection Dynamics of Malaria-Toxoplasmosis in the Tropics”, Biometrical Letters, Vol. 56, issue 2, pp 139 – 163, 2019.
[12] O. Duncan, G. L. Owuor, C. O. Okaka,“Stability analysis of the endemic equillibrium of an Ebola disease model”, Applied Mathematical Sciences, Vol. 13 issue 21, pp 1001 – 1012, 2019.
[13] X. Ma, Y. Zhou, H. Cao, “Global stability of the endemic equilibrium of a discrete SIR epidemic model”, Adv Differ Equ, 42 (2013), 2013
[14] T.T. Ashezua, I.J.M. Udoo, L.N. Ikpakyegh, “Stability Analysis of the Endemic Equilibrium State of an Infection Age-Structured HIV/AIDS Disease Pandemic”, J. Appl. Sci. Environ. Manage., Vol. 20, issue 2, pp350-354, 2016.
[15] Y. Deepthi, A. Radhika, Ch. Praneeth, “Analysis of Epidemic Diseases Using Big Data Analytics”, International Journal of Computer Sciences and Engineering, Vol. 6, Issue 7, pp756-761, 2018.
[16] A. Gumel, C. Castillo-Chavez, R.E. Mickens, D.P. Clemence, “Simulation of the pertussis epidemiology in the united states. Effects of Adults booster doses, mathematical equations, and application of Biology and industry”, 2009.
[17] C. Castillo-Chavez, B. Song, “Dynamical Models of Tuberculosis and their Applications”, Mathematical Biosciences and Engineering, Vol. 1, issue 2, pp 361-404, 2009.
[18] C.V. De-Leon, “Constructions of Lyapunov functions for classics SIS, SIR and SIRS epidemic model with variable population size. Unite Academica de Mathematicas, Universidadn Autonoma de Guerrere, Mexico Facultad de Estudios Superiores Zarogoza, UNAM, Mexico,” Pp 1-12, 2009.