Mathematical modeling and analysis of multiple infectious diseases
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.
Share and Cite
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
Keywords
- Co-infection
- Malaria
- Ebola
- Typhoid
- stability analysis
- sensitivity analysis
- impact of diseases on each other
- numerical simulation
MSC
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