A theoretical study on mathematical modelling of an infectious disease with application of optimal control

[1]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[2]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[3]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[4]  Robert H. Martin.  Logarithmic norms and projections applied to linear differential systems , 1974 .

[5]  N. Ling.  The Mathematical Theory of Infectious Diseases and its applications , 1978 .

[6]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[7]  James S. Muldowney,et al.  A Geometric Approach to Global-Stability Problems , 1996 .

[8]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[9]  Hem Raj Joshi,et al.  Optimal control of an HIV immunology model , 2002 .

[10]  Suzanne Lenhart,et al.  Optimal control of treatments in a two-strain tuberculosis model , 2002 .

[11]  Guy Barker,et al.  Mathematical modelling and the control of lymphatic filariasis. , 2004, The Lancet. Infectious diseases.

[12]  Julien Arino,et al.  An epidemiology model that includes a leaky vaccine with a general waning function , 2004 .

[13]  Wendi Wang.  Backward bifurcation of an epidemic model with treatment. , 2006, Mathematical biosciences.

[14]  John T. Workman,et al.  Optimal Control Applied to Biological Models , 2007 .

[15]  M. Keeling,et al.  Modeling Infectious Diseases in Humans and Animals , 2007 .

[16]  Deborah Lacitignola,et al.  Global stability of an SIR epidemic model with information dependent vaccination. , 2008, Mathematical biosciences.

[17]  Yong Han Kang,et al.  Stability analysis and optimal vaccination of an SIR epidemic model , 2008, Biosyst..

[18]  Sally Blower,et al.  Modelling infectious diseases in humans and animals , 2008 .

[19]  Maia Martcheva,et al.  SEROTYPE REPLACEMENT OF VERTICALLY TRANSMITTED DISEASES THROUGH PERFECT VACCINATION , 2008 .

[20]  Zhen Jin,et al.  Analysis of a Delayed SIR Model with Nonlinear Incidence Rate , 2008 .

[21]  Mini Ghosh,et al.  Global dynamics of a dengue epidemic mathematical model , 2009 .

[22]  Mini Ghosh,et al.  Stability analysis of an HIV/AIDS epidemic model with treatment , 2009 .

[23]  Zhen Jin,et al.  Bifurcation analysis of a delayed epidemic model , 2010, Appl. Math. Comput..

[24]  Stefan Schuster,et al.  Modelling the optimal timing in metabolic pathway activation - Use of Pontryagin's Maximum Principle and role of the Golden section , 2010, Biosyst..

[25]  T. K. Kar,et al.  Global dynamics and bifurcation in delayed SIR epidemic model , 2011 .

[26]  W. Eckalbar,et al.  Dynamics of an epidemic model with quadratic treatment , 2011 .

[27]  Kazeem O. Okosun,et al.  Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity , 2011, Biosyst..

[28]  Eduardo Massad,et al.  Why dengue and yellow fever coexist in some areas of the world and not in others? , 2011, Biosyst..

[29]  Deborah Lacitignola,et al.  On the backward bifurcation of a vaccination model with nonlinear incidence , 2011 .

[30]  T. K. Kar,et al.  Stability analysis and optimal control of an SIR epidemic model with vaccination , 2011, Biosyst..

[31]  T. K. Kar,et al.  Sustainability and optimal control of an exploited prey predator system through provision of alternative food to predator , 2012, Biosyst..

[32]  Soovoojeet Jana,et al.  Dynamics of pest and its predator model with disease in the pest and optimal use of pesticide. , 2012, Journal of theoretical biology.

[33]  Dahlard L. Lukes,et al.  Differential Equations: Classical to Controlled , 2012 .