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- W4385144592 abstract "The spread of an infectious disease which confers immunity after recovery from infection, can be described by a SIR model, i.e. a system of three differential equations for the dependent variables (S), (I), and (R), which are the numbers (densities) of susceptible, infectious and recovered (immune) individuals, respectively. The equations for (S) and (I) are typically nonlinear. In this article, we consider two spatio-temporal SIR models. The first model is similar to reaction-diffusion systems in chemistry. A simple birth-and-death process is incorporated, and it is assumed, that a fraction f of the newborns is vaccinated and is then immune for life. We show how the smallest eigenvalue of the eigenvalue problem associated with the linearized equation for I is related to the basic reproduction number (mathcal{R}_0), a key concept in the mathematical theory of infectious diseases. Here it is defined by a variational principle. We show that the disease-free equilibrium is asymptotically stable if (mathcal{R}_0<1), or if (mathcal{R}_0ge 1) and (f>1-1/{mathcal{R}_0}), and unstable if (mathcal{R}_0>1) and (f<1-1/mathcal{R}_0). In the other model we assume that the population consists of sedentary individuals who leave their home only temporarily. Both models suggest that restriction of mobility may be counterproductive for the control of an epidemic outbreak. For more information see https://ejde.math.txstate.edu/special/01/k2/abstr.html" @default.
- W4385144592 created "2023-07-23" @default.
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- W4385144592 date "2022-03-18" @default.
- W4385144592 modified "2023-09-27" @default.
- W4385144592 title "SIR epidemic models with spatial spread in bounded domains" @default.
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- W4385144592 doi "https://doi.org/10.58997/ejde.sp.01.k2" @default.
- W4385144592 hasPublicationYear "2022" @default.
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