ABSTRACT
The aim is to study the dynamics of Coronavirus model using stochastic methods. Threshold parameter R0 is obtained for the model. Afterwards, both the disease-free equilibrium (DFE) and endemic equilibrium (EE) points are acquired and the stability of the model is discussed. Both the equilibrium points are locally asymptotically stable. Euler–Maruyama, stochastic Euler scheme (SES), stochastic fourth-order Runge–Kutta scheme (SRKS) and stochastic non-standard finite difference technique (SNFDT) are applied to solve the model equations. Euler–Maruyama, SES, SRKS fail for large time step size, while, SNFDT preserves the dynamics of the proposed model for any step size. Numerical comparison of applied methods is provided using different step sizes. [ FROM AUTHOR] Copyright of Fractals is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)
ABSTRACT
In this paper, the mathematical modeling of the novel corona virus (COVID-19) is considered. A brief relationship between the unknown hosts and bats is described. Then the interaction among the seafood market and peoples is studied. After that, the proposed model is reduced by assuming that the seafood market has an adequate source of infection that is capable of spreading infection among the people. The reproductive number is calculated and it is proved that the proposed model is locally asymptotically stable when the reproductive number is less than unity. Then, the stability results of the endemic equilibria are also discussed. To understand the complex dynamical behavior, fractal-fractional derivative is used. Therefore, the proposed model is then converted to fractal-fractional order model in Atangana-Baleanu (AB) derivative and solved numerically by using two different techniques. For numerical simulation Adam-Bash Forth method based on piece-wise Lagrangian interpolation is used. The infection cases for Jan-21, 2020, till Jan-28, 2020 are considered. Then graphical consequences are compared with real reported data of Wuhan city to demonstrate the efficiency of the method proposed by us.