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Global stability analysis and control of leptospirosis

100%
Okosun K. O., Mukamuri M., Makinde D. O.
Open Mathematics
|
2016
|
tom 14
|
nr 1
567-585
EN
The aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters’ case is analyzed, also calculate the basic reproduction number and investigate the existence and stability of equilibria. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved when the basic reproduction number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Furthermore, to assess the relative impact of each of the constant control parameters measures the sensitivity index of the basic reproductive number to the model’s parameters are calculated. In the time-dependent constant control case, Pontryagin’s Maximum Principle is used to derive necessary conditions for the optimal control of the disease. The cost-effectiveness analysis is carried out by first of all using ANOVA to check on the mean costs. Then followed by Incremental Cost-Effectiveness Ratio (ICER) for all the possible combinations of the disease control measures. Our results revealed that the most cost-effective strategy for the control of leptospirosis is the combination of the vaccination and treatment of infective livestocks. Though the combinations of all control measures is also effective, however, this strategy is not cost-effective and so too costly. Therefore, more efforts from policy makers on vaccination and treatment of infectives livestocks regime would go a long way to combat the disease epidemic.
2
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Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs

68%
Koksal M. E.
Open Mathematics
|
2016
|
tom 14
|
nr 1
693-704
EN
Necessary and sufficiently conditions are derived for the decomposition of a second order linear time- varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation of the system itself.
3
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Coulomb Interaction Effects on the Spin Polarization and Currents in Quantum Wires with Spin Orbit Interaction

68%
Heidar Thorolfsson A., Manolescu A., Marinescu D. C., Gudmundsson V.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
|
2012
|
tom 1
23-37
EN
We analyze the charge and spin distributions induced in an interacting electron system confined inside a semiconductor quantum wire with spin orbit interaction in the presence of an external magnetic field. The wire, assumed to be infinitely long, is obtained through lateral confinement in three different materials: GaAs, InAs, and InSb. The spin-orbit coupling, linear in the electron momentum is of both Rashba and Dresselhaus type. Within the Hartree-Fock approximation the many-body Hamiltonian is diagonalized directly and its eigenfunctions and single-particle spectra are obtained selfconsistently. Further, we calculate charge, and spin densities, as well as the charge and spin currents and compare them with those obtained in the absence of the interaction. Thus we observe an enhancement of the spin polarization associated with the spin-orbit intreractions, on account of the exchange Coulomb effects, in GaAs, but not in InAs and InSb. However, in the later materials the direct Coulomb interaction may amplify or modify the spin currents.
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