This book consists of a series of papers focusing on the mathematical and computational modeling and analysis of some real-life phenomena in the natural and engineering sciences. The book emphasizes three main themes: (i) the design and analysis of robust and dynamically-consistent nonstandard finite-difference methods for discretizing continuous-time dynamical systems arising in the natural and engineering sciences, (ii) the mathematical study of nonlinear oscillations, and (iii) the design and analysis of models for the spread and control of emerging and re-emerging infectious diseases.
Specifically, some of the topics covered in the book include advances and challenges on the design, analysis and implementation of nonstandard finite-difference methods for approximating the solutions of continuous-time dynamical systems, the design and analysis of models for the spread and control of the COVID-19 pandemic, modeling the effect of prescribed fire and temperature on the dynamics of tick-borne disease, and the design of a novel genetic-epidemiology framework for malaria transmission dynamics and control.
The book also covers the impact of environmental factors on diseases and microbial populations, Monod kinetics in a chemostat setting, structure and evolution of poroacoustic solitary waves, mathematics of special (periodic) functions and the numerical discretization of a phase-lagging equation with heat source.
R. Anguelov and J. M.-S. Lubuma, A second-order nonstandard finite
difference scheme and application to model of biological and chemical
processes
M. T. Hoang, A generalized nonstandard finite difference method for a class
of autonomous dynamical systems and its applications
F. K. Alalhareth, M. Gupta, H. V. Kojouharov, and S. Roy, Higher-order
modified nonstandard finite difference methods for autonomous dynamical
systems
H. J. Eberl, A simple NSFD inspired method for monod kinetics with small half
saturation constants in the chemostat setting
M. Chapwanya and P. Dumani, Dynamics preserving nonstandard finite difference
scheme for a microbial population model incorporating environmental stress
T. Basu, R. Buckmire, Z. Coovadia, M. Diaz, D. A. Iniguez, and A. Scott,
Using unity approximations to construct nonstandard finite difference schemes
for Bernoulli differential equations
C. L. Shimp, J. V. Lambers, and P. M. Jordan, On the structure and evolution
of poroacoustic solitary waves: Finite-time gradient catastrophe under the
Darcy-Jordan model
C.-C. Ji and W. Dai, A fractional-order equation and its finite difference
scheme for approximating a delay equation
L. F. Strube and L. M. Childs, Multistability in a discrete-time SI epidemic
model with Ricker growth: Infection-induced changes in population dynamics
J. Mohammed-Awel and A. Gumel, A genetic-epidemiology modeling framework for
malaria mosquitoes and disease
M. A. Acuna-Zegarra, M. Santana-Cibrian, C. E. R. Hernandez-Vela, R. H. Mena,
and J. X. Velasco-Hernandez, A retrospective analysis of COVID-19 dynamics in
Mexcio and Peru: Studying hypothetical changes in the contact rate
G. M. R. Costa, M. Lobosco, M. Ehrhardt, and R. F. Reis, Mathematical
analysis and a nonstandard scheme for a model of the immune response against
COVID-19
A. Fulk and F. B. Agusto, Effects of rising temperature and prescribed fire
on $\textit{Amblyomma Americanum}$ with ehrlichiosis
E. N. Naumova, M. B. Yassai, J. Gorski, and Y. N. Naumov, Modeling T-cell
repetoire response to a viral infection with short immunity
S. A. Rucker, Geometric approach to the construction of Leah-type periodic
functions: Basic and analytic properties
I. H. Herron, Discursion on a paper of R. E. Mickens and J. E. Wilkins, Jr.
Abba Gumel, University of Maryland, College Park, MD.
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