In this paper, we studied and formulated the relapsed SIR model of a constant size population with standard incidence rate. Also, the optimal control problem with treatment and vaccination as controls, subject to the model is formulated. The analysis carried out on the model, clearly showed that the infection free steady state is globally asymptotically stable if the bas...

An adaptive model reduction method is proposed for linear timeinvariant systems based on the continuous-time rational orthogonal basis (TakenakaMalmquist basis). The method is to find an adaptive approximation in the energy sense by selecting optimal points for the rational orthogonal basis. The stability of the reduced models holds, and the steady-state values of step responses are kept to be ...

This study reviews common calculations and mathematical models used in stable isotopic studies. Some approximations are adopted to simplify the algebra for use in steady state models, with more rigorous mathematics outlined in an Appendix. Review shows that steady-state isotopic models are easy to construct, provide good approximations of system behavior, and are very helpful in evaluating isot...

Aggregation phenomena occur across the biological sciences, from cell adhesion to insect swarms, animal home ranges human cities. Understanding mechanisms by which they may spontaneously emerge has therefore generated much interest applied mathematicians. Partial differential equations (PDEs) with nonlocal advection offer a popular formalism for studying aggregations. However, inherent nonlocal...

This paper studies an overlapping generations (OLG) model with production under the assumption that capital investment is completely irreversible: installed capital cannot be transformed back into consumption good nor transferred from one firm to another. Since firms cannot be dismantled at each generational change without loosing their value, their ownership is transmitted from generations to ...