Chaotic attractors in cancer and epidemic models: insights from predator-prey interactions
- Biometrics & Biostatistics International Journal
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Moises Meza Pariona
Abstract
The current study, in conjunction with an examination of existing literature, demonstrates
that the emergence of chaotic behavior is predominantly attributed to interactions between
predators and prey, as well as competitive dynamics. Similar patterns have been observed
in the context of pandemics and cancer models, where deterministic chaos or chaotic
dynamics result in complex oscillations and nonlinear interactions among cell populations.
It is notable that the current pandemic exhibits key characteristics of a chaotic system and
is recognized as one of the deadliest pandemics in contemporary history.
This study presents an analysis of a dynamical model of an ecosystem comprising one
predator and three prey species, one of them is sick, one is healthy and one is immune. The
findings indicate that variations in the reproduction rates of healthy prey and predator-prey
interactions induce chaotic dynamic transients, which manifest as damped oscillations over
extended periods. Upon monitoring the disease infectivity parameter (R) over time, a rapid
decline in the healthy prey population is observed within days. In contrast, the infected
prey population demonstrates a damped oscillatory growth and decay pattern, indicating
that the predator consumes both healthy and infected prey. Over extended periods, all
variables exhibit a tendency towards equilibrium. Phase portrait diagrams, generated using
3-D and 2-D representations with varied reproduction rates of healthy prey (parameter a)
and disease infectivity (parameter R), reveal the existence of stable points, unstable points,
saddle points, and bifurcation diagrams. The equilibrium points demonstrate characteristics
of chaotic attractors. The chaotic propagation of a pandemic is highly sensitive to minor
variations in the initial conditions (ICs) of physical factors. Mathematical models serve
as crucial tools for devising strategic action plans to control epidemics and pandemics,
offering real-time data for effective outbreak management. This research holds significant
implications for ecological dynamics and disease modeling, with practical applications in
public health and epidemiology.
Keywords
The chaotic dynamics, prey-predator interaction, time series, phase portraits diagrams, bifurcation diagram, Lyapunov exponents.
