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308 results on '"Ma, Wanbiao"'

13. Rich dynamics of a hepatitis C virus infection model with logistic proliferation and time delays.

Author

Guo, Ke and Ma, Wanbiao

Subjects
*HEPATITIS C, *HEPATITIS C virus, *HOPF bifurcations, *LIVER cells, *DYNAMIC models
Abstract

In this paper, we study a dynamic model of hepatitis C virus (HCV) infection with density‐dependent proliferation of uninfected and infected hepatocytes and two time delays, which is derived from a three‐dimensional model by the quasi‐steady‐state approximation. The model can exhibit forward bifurcation or backward bifurcation, and an explicit control threshold parameter Rc$R_c$ is obtained for the case of backward bifurcation. It is shown that if the proliferation rate of infected hepatocytes is greater than the proliferation rate of uninfected hepatocytes by a certain amount, it becomes more difficult for the virus to be removed. The model has rich dynamical properties: (i) In some parameter regions, bistability can occur; (ii) both time delays τ1$\tau _{1}$ (virus‐to‐cell delay) and τ2$\tau _{2}$ (cell‐to‐cell delay) can lead to Hopf bifurcations; (iii) same length of time delays τ1$\tau _{1}$ and τ2$\tau _{2}$ can lead to at most one stability switch, but different time delays can lead to multiple stability switches. Several sufficient conditions for the global stability of the disease‐free equilibrium and the endemic equilibrium are obtained for both forward and backward bifurcation scenarios. In particular, several sharp results on global stability are obtained. Theoretical and numerical results portray the complexity of viral evolutionary dynamics in chronic HCV‐infected patients. [ABSTRACT FROM AUTHOR]

Published
2024
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23. Dynamical Models of Biology and Medicine

Author

Fan, Meng, Kuang, Yang, Ma, Wanbiao, and Liu, Shengqiang

Abstract

Mathematical and computational modeling approaches in biological and medical research are experiencing rapid growth globally. This Special Issue Book intends to scratch the surface of this exciting phenomenon. The subject areas covered involve general mathematical methods and their applications in biology and medicine, with an emphasis on work related to mathematical and computational modeling of the complex dynamics observed in biological and medical research. Fourteen rigorously reviewed papers were included in this Special Issue. These papers cover several timely topics relating to classical population biology, fundamental biology, and modern medicine. While the authors of these papers dealt with very different modeling questions, they were all motivated by specific applications in biology and medicine and employed innovative mathematical and computational methods to study the complex dynamics of their models. We hope that these papers detail case studies that will inspire many additional mathematical modeling efforts in biology and medicine

Published
2019

38. Delayed SIR Epidemic Models for Vector Diseases?

Author

Takeuchi, Yasuhiro, Ma, Wanbiao, Greenbaum, Elias, editor, Aizawa, Masuo, editor, Andersen, Olaf S., editor, Austin, Robert H., editor, Barber, James, editor, Berg, Howard C., editor, Bloomfield, Victor, editor, Callender, Robert, editor, Chance, Britton, editor, Chu, Steven, editor, DeFelice, Louis J., editor, Deisenhofer, Johann, editor, Feher, George, editor, Frauenfelder, Hans, editor, Giaever, Ivar, editor, Gruner, Sol M., editor, Herzfeld, Judith, editor, Joliot, Pierre, editor, Keszthelyi, Lajos, editor, Knox, Robert S., editor, Lewis, Aaron, editor, Lindsay, Stuart M., editor, Mauzerall, David, editor, Mielczarek, Eugenie V., editor, Niemz, Markolf, editor, Parsegian, V. Adrian, editor, Powers, Linda S., editor, Prohofsky, Earl W., editor, Rubin, Andrew, editor, Seibert, Michael, editor, Thomas, David, editor, Williamson, Samuel J., editor, Takeuchi, Yasuhiro, editor, Iwasa, Yoh, editor, and Sato, Kazunori, editor

Published
2007
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