Mathematical modeling and analysis of multiple infectious diseases

Volume 38, Issue 4, pp 446--463 https://dx.doi.org/10.22436/jmcs.038.04.03
Publication Date: January 24, 2025 Submission Date: August 22, 2024 Revision Date: October 19, 2024 Accteptance Date: January 02, 2025

Authors

S. Ullah - Department of Mathematics, University of Malakand, Chakdara, Pakistan. G. Zaman - Department of Mathematics, University of Malakand, Chakdara, Pakistan. Gh. Alobaidi - Department of Mathematics and Statistics, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates. G. Rahman - Department of Mathematics and Statistics, Hazara University, Mansehra 21300, Pakistan.


Abstract

This paper investigates and develops a deterministic mathematical model for three infectious diseases, i.e., Malaria, Ebola and Typhoid multi-infections. First the three sub-models of the Malaria, Ebola, and Typhoid multi-infection are presented. Each sub-model, and the multi-infection model, are analyzed to rigorous mathematical analysis. The positivity of the model solution, invariant region, stability of disease-free, and endemic equilibrium points are discussed in detail. The next generation matrix is used to obtain a reproduction number for the study of the elements of the stability of the equilibria, global disease-free equilibrium's asymptotic stability and endemic equilibrium. Then sensitivity analysis is performed to detect the influence of every parameter on the spread or control of the diseases. Further, investigation is made about the influence of Malaria on the dynamics of Typhoid, impact of Ebola on the dynamics of Malaria, and impact of Ebola on the dynamics of Typhoid. Finally the effects of treating Ebola, Malaria, Typhoid, and multi-infected are identified and shown numerically.


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ISRP Style

S. Ullah, G. Zaman, Gh. Alobaidi, G. Rahman, Mathematical modeling and analysis of multiple infectious diseases, Journal of Mathematics and Computer Science, 38 (2025), no. 4, 446--463

AMA Style

Ullah S., Zaman G., Alobaidi Gh., Rahman G., Mathematical modeling and analysis of multiple infectious diseases. J Math Comput SCI-JM. (2025); 38(4):446--463

Chicago/Turabian Style

Ullah, S., Zaman, G., Alobaidi, Gh., Rahman, G.. "Mathematical modeling and analysis of multiple infectious diseases." Journal of Mathematics and Computer Science, 38, no. 4 (2025): 446--463


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