Abstract
Abstract In this work, we will introduce two novel positivity preserving operator splitting nonstandard finite difference (NSFD) schemes for the numerical solution of SEIR reaction diffusion epidemic model. In epidemic model of infection diseases, positivity is an important property of the continuous system because negative value of a subpopulation is meaningless. The proposed operator splitting NSFD schemes are dynamically consistent with the solution of the continuous model. First scheme is conditionally stable while second operator splitting scheme is unconditionally stable. The stability of the diffusive SEIR model is also verified numerically with the help of Routh-Hurwitz stability condition. Bifurcation value of transmission coefficient is also carried out with and without diffusion. The proposed operator splitting NSFD schemes are compared with the well-known operator splitting finite difference (FD) schemes.
Highlights
IntroductionMeasles is considered as highly infectious disease, spread due to respiratory infection by a traveling virus
In childhood epidemic diseases, Measles is considered as highly infectious disease, spread due to respiratory infection by a traveling virus
We developed two positivity preserving nonstandard nite di erence schemes which did not bring contrived chaos
Summary
Measles is considered as highly infectious disease, spread due to respiratory infection by a traveling virus. Hamer [1] in 1906 presented a model for transmission dynamics of Measles. The principle of “mass action” was introduced which became a fundamental statute in present theory of infectious disease modeling [2,3,4,5]. Infectious disease dynamics is an important application of dynamical systems. Steady states or the equilibrium points of a continuous dynamical systems are the values of variables that do not change over time. If a system starts at a nearby state and converges to the equilibrium point, this equilibrium point is attractive. Many dynamical systems in di erent elds of science and engineering show the chaotic behavior
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