Based on literature [J. Q. Li, Z. E. Ma and F. Q. Zhang, Stability analysis for an epidemic model with stage structure, J. Appl. Math. Comput. 9 （2008） 1672-1679], incorporating the recovery of the infected populati...Based on literature [J. Q. Li, Z. E. Ma and F. Q. Zhang, Stability analysis for an epidemic model with stage structure, J. Appl. Math. Comput. 9 （2008） 1672-1679], incorporating the recovery of the infected population with the length of the infectious periods, a modified epidemic disease SIS model with delay and stage was investigated. First, the criteria keeping stability with delay were given. Next, in order to lower the level of the infected individuals and minimize the cost of treatment, mixed, early and late therapeutic strategies were introduced into our model, respectively. Then we investigated the existence and uniqueness of optimal controls. And then, we expressed the unique optimal control in terms of the solution of the optimality systems. Finally, by numerical simulations, several important results were acquired： （1） The terminal time influenced the early optimal control largely. In detail, for a shorter terminal time it was optimal to initiate treatment with maximal effort at the start of the epidemic and continue treatment with maximal effort until the switch time was arrived. But for a longer terminal time, the maximal treatment effort need not be a prerequisite at the start or end of the epidemic but it was obligatory at the metaphase of the epidemic. （2） For our SIS model, minimizing the total infectious burden of the disease can be achieved by only early optimal treatment tactics. （3） For a disease with a shorter infectious period time,more cost would be spent to control the disease in order to achieve the optimal control objective. Otherwise, a relative lower cost would be to control the disease with a longer infectious period.展开更多
Fe-doped amorphous FexCl~ granular films were prepared on n-Si （100） substrates by d.c. magnetron sputtering. The structur- al properties of FexC1-x films were investigated by X-ray diffraction （XRD）, atomic force...Fe-doped amorphous FexCl~ granular films were prepared on n-Si （100） substrates by d.c. magnetron sputtering. The structur- al properties of FexC1-x films were investigated by X-ray diffraction （XRD）, atomic force microscope （AFM） and Raman spec- troscopy. The results show that the iron and carbon of as-deposited films are in amorphous state, and the FexC1-x films are di- amond-like carbon （DLC） films. After doping iron into the DLC films, a smooth surface morphology of the FexC1-x films has been obtained with the surface roughness Ra of about 0.231 nm for x=18at%. The FexC1-x films have good soft magnetic prop- erties with the coercivity of approximately 20 Oe. A high positive magnetoresistance （MR） up to 93% with x=lat% was ob- served in a FexCl-x granular film at 300 K. The resistance characteristic of Fe-C films is changed at about 230 K and the positive MR effect can be understood by the p-n heterojunction theory.展开更多
基金Acknowledgments The authors would like to thank the editor and the referee for constructive comments which significantly improves this paper. In addition, this work was supported by the National Natural Science Foundation of China （No. 11471243）.
文摘Based on literature [J. Q. Li, Z. E. Ma and F. Q. Zhang, Stability analysis for an epidemic model with stage structure, J. Appl. Math. Comput. 9 （2008） 1672-1679], incorporating the recovery of the infected population with the length of the infectious periods, a modified epidemic disease SIS model with delay and stage was investigated. First, the criteria keeping stability with delay were given. Next, in order to lower the level of the infected individuals and minimize the cost of treatment, mixed, early and late therapeutic strategies were introduced into our model, respectively. Then we investigated the existence and uniqueness of optimal controls. And then, we expressed the unique optimal control in terms of the solution of the optimality systems. Finally, by numerical simulations, several important results were acquired： （1） The terminal time influenced the early optimal control largely. In detail, for a shorter terminal time it was optimal to initiate treatment with maximal effort at the start of the epidemic and continue treatment with maximal effort until the switch time was arrived. But for a longer terminal time, the maximal treatment effort need not be a prerequisite at the start or end of the epidemic but it was obligatory at the metaphase of the epidemic. （2） For our SIS model, minimizing the total infectious burden of the disease can be achieved by only early optimal treatment tactics. （3） For a disease with a shorter infectious period time,more cost would be spent to control the disease in order to achieve the optimal control objective. Otherwise, a relative lower cost would be to control the disease with a longer infectious period.
基金supported by the National Natural Science Foundation of China (Grant No. U0734001)the Fundamental Research Funds for the Central Universities,SCUT (Grant Nos. 2009ZM0247 and 2012ZZ0015)
文摘Fe-doped amorphous FexCl~ granular films were prepared on n-Si （100） substrates by d.c. magnetron sputtering. The structur- al properties of FexC1-x films were investigated by X-ray diffraction （XRD）, atomic force microscope （AFM） and Raman spec- troscopy. The results show that the iron and carbon of as-deposited films are in amorphous state, and the FexC1-x films are di- amond-like carbon （DLC） films. After doping iron into the DLC films, a smooth surface morphology of the FexC1-x films has been obtained with the surface roughness Ra of about 0.231 nm for x=18at%. The FexC1-x films have good soft magnetic prop- erties with the coercivity of approximately 20 Oe. A high positive magnetoresistance （MR） up to 93% with x=lat% was ob- served in a FexCl-x granular film at 300 K. The resistance characteristic of Fe-C films is changed at about 230 K and the positive MR effect can be understood by the p-n heterojunction theory.
