On the stability analysis of solutions of an integral equation with an application in epidemiology
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Authors
Ümit Çakan
- Department of Mathematics, İnönü University, Malatya, Turkey.
Abstract
This paper concerns a nonlinear integral equation modeling the spread of
epidemics in which immunity does not occur after recovery. The model is
mainly based on the return of some of the individuals who have been exposed
to the pathogen and who have completed the incubation period, into the
susceptible class. We first prove the uniqueness of the global solution of
the model with the given initial conditions. After determining the
positively invariant region for the model, using LaSalle invariance
principle [J. P. LaSalle, IRE Trans. CT, \({\bf 7} (1960)\), 520--527] and the concept of persistence we present some
results about the stability analysis of the solutions according to the case
of the reproduction number \(\mathcal{R}_{0}\) which is a vital threshold in the spread of diseases.
Share and Cite
ISRP Style
Ümit Çakan, On the stability analysis of solutions of an integral equation with an application in epidemiology, Mathematics in Natural Science, 7 (2021), no. 1, 16--25
AMA Style
Çakan Ümit, On the stability analysis of solutions of an integral equation with an application in epidemiology. Math. Nat. Sci. (2021); 7(1):16--25
Chicago/Turabian Style
Çakan, Ümit. "On the stability analysis of solutions of an integral equation with an application in epidemiology." Mathematics in Natural Science, 7, no. 1 (2021): 16--25
Keywords
- Global stability analysis
- Lyapunov function
- LaSalle invariance principle
- mathematical epidemiology
- persistence
MSC
- 34D05
- 34D08
- 34D20
- 92B05
- 92D25
- 92D30
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