Dynamical analysis of a discrete-time SIR epidemic model

In this paper, a discrete-time seasonally forced SIR epidemic model is investigated for different types of bifurcations. Although, many researchers already suggested numerically that this model can exhibit chaotic dynamics but not much focus is given to the bifurcation theory of the model. We prove analytically and numerically the existence of different types of bifurcations in the model. First, the one and two parameters bifurcations of this model are investigated by computing their critical normal form coefficients. Secondly, the flip, Neimark–Sacker, and strong resonances bifurcations are detected for this model. The critical coefficients identify the scenario associated with each bifurcation. The complete complex dynamical behavior of the model is investigated. Some graphical representations of the model are presented to verify the obtained results.     

Dynamical analysis and optimal control simulation for an age-structured cholera transmission model

Cholera is an infectious disease caused by the bacterium vibrio cholerae, which can lead to widespread epidemics in the deterioration of public health systems or the associated infrastructure. Vaccination and water sanitation are two well-known methods for the prevention and intervention of cholera epidemics. In this paper, we propose an age-structured cholera model that incorporates both the environment-to-human and human-to-human transmission pathways and that includes host vaccination and water sanitation as disease control measures. We rigorously investigate the threshold dynamics of this model using the basic reproduction number derived from our analysis. Meanwhile, we perform an optimal control study to explore cost-effective intervention strategies for cholera. Our numerical simulation results show that the outcome of the optimal control is shaped by the complex interactions among the age structure of the hosts, the costs of the control measures, the transmission modes of the disease, and the different approaches of cholera intervention.     

Electrodynamics of synchronous machines

A simple analysis of the salient-pole synchronous machine is presented from the field viewpoint. The results obtained confirm the relevance of the model.     

Electrodynamics of solid-rotor induction machines

In this paper a simplified model of the solid-rotor induction machine is discussed. Analysis is provided on the basis of Maxwell's equations yielding a dimensionless thrust-slip characteristic which permits rapid evaluation of various machine parameters in its performance. The salient feature of this kind of induction device—flat thrust-slip response—is borne out by the obtained curves.