Modeling Highly Random Dynamical Infectious Systems

Random dynamical processes are ubiquitous in all areas of life:- in the arts, in the sciences, in the social sciences and engineering systems etc. The rates of various types of processes in life are subject to random fluctuations leading to variability in the systems. The variabilities give rise to white noise which lead to unpredictability about the processes in the systems. This chapter exhibits compartmental random dynamical models involving stochastic systems of differential equations, Markov processes, and random walk processes etc. to investigate random dynamical processes of infectious systems such as infectious diseases of humans or animals, the spread of rumours in social networks, and the spread of malicious signals on wireless sensory networks etc. A step-to-step approach to identify, and represent the various constituents of random dynamic processes in infectious systems is presented. In particular, a method to derive two independent environmental white noise processes, general nonlinear incidence rates, and multiple random delays in infectious systems is presented. A unique aspect of this chapter is that the ideas, mathematical modeling techniques and analysis, and the examples are delivered through original research on the modeling of vector-borne diseases of human beings or other species. A unique method to investigate the impacts of the strengths of the noises on the overall outcome of the infectious system is presented. Numerical simulation results are presented to validate the results of the chapter.