1. Study of an Epidemiological Model for Plant Virus Diseases with Periodic Coefficients.
- Author
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Coronel, Aníbal, Huancas, Fernando, and Berres, Stefan
- Subjects
VIRUS diseases of plants ,FAMILIAL Mediterranean fever ,EPIDEMIOLOGICAL models ,COINCIDENCE theory ,PLANT populations - Abstract
In the present article, we research the existence of the positive periodic solutions for a mathematical model that describes the propagation dynamics of a pathogen living within a vector population over a plant population. We propose a generalized compartment model of the susceptible–infected–susceptible (SIS) type. This model is derived primarily based on four assumptions: (i) the plant population is subdivided into healthy plants, which are susceptible to virus infection, and infected plants; (ii) the vector population is categorized into non-infectious and infectious vectors; (iii) the dynamics of pathogen propagation follow the standard susceptible–infected–susceptible pattern; and (iv) the rates of pathogen propagation are time-dependent functions. The main contribution of this paper is the introduction of a sufficient condition for the existence of positive periodic solutions in the model. The proof of our main results relies on a priori estimates of system solutions and the application of coincidence degree theory. Additionally, we present some numerical examples that demonstrate the periodic behavior of the system. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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