STABILITY ANALYSIS AND TURING INSTABILITY OF AN EPIDEMIC REACTION-DIFFUSION MODEL WITH VACCINATION, TWO AWARE CLASSES AND SATURATED TREATMENT
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2025
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Abstract
Abstract. In this paper, we developed a reaction-diffusion epidemic model
with two aware classes and saturated treatment considering the impact of vaccination.
We divided the total population into six classes, namely susceptible,
vaccinated, completely aware, partially aware, infected, and recovered class.
We discussed the basic properties of our system. With the help of Dirichlet
boundary conditions and positive initial data, we studied the local and
global existence in time of solutions. We performed a stability analysis of the
equilibrium points, their existence, and found the basic reproduction number
R
of the system. Then, we established the occurrence conditions of Turing
instability for our diffusive model. Finally, we have provided a thorough numerical
exploration of our model to illustrate our analytical results by choosing
a suitable set of parameters.
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