In this paper, the Fitzhugh-Nagumo (FHN) equations and a modified FHN (MFHN) are considered. For the modified version, the recovery variable v has three different time scales. By considering different parameters in the local dynamics of the MFHN equations, it is observed that the phenomenon of reflection and annihilation at an impermeable boundary is observed just as in the Beeler-Reuter model. The interaction of spirals obtained with the FHN, MFHN, and Beeler-Reuter model, and an obstacle is also considered. The phenomenon of reflection of the spiral wave at a boundary changes when the boundary becomes an obstacle. Four properties for attachment of a spiral wave to an obstacle are presented in this work.
In this paper, we propose a SI model for the study of human and animal leptospirosis. Unlike other models for leptospirosis which consider only rodents as infection vectors, we consider that humans can be infected not only through contact with rodents, but also through any other animal that serves as a reservoir for the bacteria, and through contact with bacteria that are free in the environment. We calculate the basic reproductive number for this model, which is given in terms of the basic reproductive numbers of simpler subsystems of the original model, and propose some intervention techniques for controlling the disease based on our results.
We employ a reaction diffusion equation with local dynamics specified by the Beeler-Reuter model to study the meandering of spiral waves. With the appropriate choice for the conductances of sodium and calcium channels, the trajectory of the tip of a spiral wave lies on a straight line. The phenomenon of annihilation or reflection of a spiral at the boundaries of the domain is studied. This phenomenon is analyzed in terms of the variable j , which controls the reactivation of the sodium channel in the Beeler-Reuter model. The results presented can have potential applications in the study of cardiac arrhythmias by providing insight on the interaction between spiral waves and obstacles in the heart.
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