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| William E. Schiesser | ||||
| Springer | ||||
| 2022 | ||||
| English | ||||
| 178 pages | ||||
| 8.6 MB | ||||
| DJVU | ||||
[tab] [content title="Summary"] The reproduction and dissemination of a virus during an epidemic begins when the virus attaches to a host cell, allowing its viral genetic material (VGM)—which may include proteins, DNA, or RNA—to enter the cell. Inside, the VGM replicates and may mutate, a process characterized by spatiotemporal dynamics. This book models these dynamics using a system of ordinary and partial differential equations (ODE/PDEs). The movement of viral proteins across the cell membrane is represented as a diffusion process, described by the diffusion PDE (Fick’s second law). Once inside the cell, the time evolution of the VGM is modeled using ODEs. The changes in the dependent variables are calculated through numerical integration of the ODE/PDEs, beginning from zero initial conditions (ICs). These variables deviate from zero in response to the concentration of viral proteins at the cell's outer membrane, where the virus binds. Numerical integration of the ODE/PDEs is executed using routines written in R, a high-quality, open-source scientific computing system that is easily accessible online. The book minimizes formal mathematics, opting instead for a presentation style focused on detailed examples that can be run on standard computers. The ODE/PDE dependent variables are visualized using basic R plotting utilities. Readers can download the R routines via a provided link, enabling them to run the example models without needing prior knowledge of numerical methods or coding. These routines can also be adapted for variations and extensions of the ODE/PDE model, such as altering parameters or modifying the model equations. [/content] [content title="Content"] [/content] [content title="Author(s)"] [/content] [/tab]
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