Tempered fractional order compartment models and applications in biology

<p style='text-indent:20px;'>Compartment models with classical derivatives have diverse applications and attracted a lot of interest among scientists. To model the dynamical behavior of the particles that existed in the system for a long period of time with little chance to be removed, a power-law waiting time technique was introduced in the most recent work of Angstmann et al. [<xref ref-type="bibr" rid="b2">2</xref>]. The divergent first moment makes the power-law waiting time distribution less physical because of the finite lifespan of the particles. In this work, we take the tempered power-law function as the waiting time distribution, which has finite first moment while keeping the power-law properties. From the underlying physical stochastic process with the exponentially truncated power-law waiting time distribution, we build the tempered fractional compartment model. As an application, the tempered fractional SEIR epidemic model is proposed to simulate the real data of confirmed cases of pandemic AH1N1/09 influenza from Bogotá D.C. (Colombia). Some analysis and numerical simulations are carried out around the equilibrium behavior.</p>