Abstract
Infectious disease and competition play important roles in the dynamics of a population due to their capability to increase the mortality rate for each organism. In this paper, the dynamical behaviors of a single species population are studied by considering the existence of the infectious disease, intraspecific competition, and interspecific competition. The fractional-order derivative with a power-law kernel is utilized to involve the impact of the memory effect. The population is divided into two compartments namely the susceptible class and the infected class. The existence, uniqueness, non-negativity, and boundedness of the solution are investigated to confirm the biological validity. Three types of feasible equilibrium points are identified namely the origin, the disease-free, and the endemic points. All biological conditions which present the local and global stability are investigated. The global sensitivity analysis is given to investigate the most influential parameter to the basic reproduction number and the density of each class. Some numerical simulations including bifurcation diagrams and time series are also portrayed to explore more the dynamical behaviors.
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