Advanced Nonlinear Dynamics of Population Biology and Epidemiology

• Published in: Abstract and Applied Analysis Vol. 2014; pp. 122 - 124-210
• Main Authors: Wang, Weiming, Kang, Yun, Banerjee, Malay, Wang, Kaifa
• Format: Journal Article
• Language: English
• Published: New York Hindawi Limiteds 2014; Hindawi Publishing Corporation; Hindawi Limited; Wiley
• Subjects: Acquired immune deficiency syndrome; AIDS; Complex systems; Disease; Endangered & extinct species; Epidemiology; Equilibrium; Extinction; Gene expression; HIV; Human immunodeficiency virus; Infections; Infertility; Mathematical models; Mathematical research; Mathematics; Neural networks; Ordinary differential equations; Partial differential equations; Physical fitness; Population biology; Studies; Tropical diseases; Viral infections
• ISSN: 1085-3375; 1687-0409
• DOI: 10.1155/2014/214514

Ordinary differential equation models, partial differential equation models, delay differential equation models, stochastic differential equation models, difference equation models, and nonautonomous models are examples of modeling approaches that are useful and capable of providing applicable strategies for the coexistence and conservation of endangered species, to prevent the overexploitation of natural resources, to control disease's outbreak, and to make optimal dosing polices for the drug administration, and so forth. C. Chen and Y. Xiao propose a mathematical model to consider the effects of saturated diagnosis and vaccination on HIV/AIDS infection and find that there exists a backward bifurcation which suggests that the disease cannot be eradicated even if the basic reproduction number is less than unity.\n Y. Wang et al. investigate a nonlinear reaction-advection-diffusion model of the interaction between nutrients and plankton and find that if the sinking velocity exceeds a certain critical value, the stable state becomes unstable and the wavelength of phytoplankton increases with the increase of sinking velocity.