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Optimal control and stability analysis of an epidemic model with education campaign and treatment
1. | Department of Mathematics and Computer Science, Fisk University, Nashville TN 37208, United States |
2. | Department of Ecology and Evolutionary Biology, University of Kansas, Lawrence, KS 66045 |
3. | Department of Mathematics, Xavier University, Cincinnati, OH 45207-4441, United States |
4. | Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300 |
References:
[1] |
R. M. Anderson and R. May, Infectious Diseases of Humans, Oxford University Press, (1991), New York. |
[2] |
D. N. Bhatta, U. R. Aryal and K. Khanal, Education: The Key to Curb HIV and AIDS Epidemic, Kathmandu Univ Med J, 42(2) (2013), 158-161. |
[3] |
H. Behncke, Optimal control of deterministic epidemics, Optimal Control Applications and Methods, 21 (2000), 269-285. |
[4] |
O. Diekmann, J. A. P. Heesterbeek and J. A. P. Metz, On the definition and computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol, 28 (1990) 503-522. |
[5] |
E. Fenichel, C. Castillo-Chavez and C. Villalobos, et al, Adaptive human behavior in epidemiological models, Proceedings of the National Academy of Sciences of the United States of America, 108(15) (2011), 6306-6311. |
[6] |
S. Funk, M. Salath and V. Jansen, Modelling the influence of human behaviour on the spread of infectious diseases: A review, J R Soc Interface, 7 (2010), 1247-1256. |
[7] |
E. Green, D. Halperin, V. Nantulya, and J. Hogle, Uganda's HIV Prevention Success: The Role of Sexual Behavior Change and the National Response, AIDS Behav., 10(4) (2006), 335-346. |
[8] |
Global Campaign for Education (GCE), Learning to survive: How education for all would save millions of young people from HIV/AIDS, London, GCE, 2004, http://www.campaignforeducation.org/resources. |
[9] |
H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42(4) (2000), 599-653. |
[10] |
H. R. Joshi, S. Lenhart, K. Albright and K. Gipson, Modeling the Effect of Information Campaigns On the HIV Epidemic In Uganda, Mathematical Biosciences and Engineering, 5(4) (2008), 757-770. |
[11] |
H. R. Joshi, S. Lenhart, S. Hota and F. Agusto, Optimal Control of SIR Model with Changing Behavior through an Education Campaign, Electronic Journal of Differential Equations, 50 (2015), 1-14. |
[12] |
W. O. Kermack and A. G. McKendrick, Contribution to the mathematical theory of epidemics, Proc. Roy. Soc., A 115 (1927), 700-721. |
[13] |
W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics II. The problem of endemicity, Proc. Roy. Soc., A 138 (1932), 55-83. |
[14] |
H. Laarabi, M. Rachik, O. E. Kahlaoui and E. H. Labriji, Optimal Vaccination Strategies of an SIR Epidemic Model with a Saturated Treatment, Universal Journal of Applied Mathematics, 1(3) (2013), 185-191. |
[15] |
S. Lenhart and J. T. Workman, Optimal Control Applied to Biological Models, 1st Edition, Chapman and Hall/CRC, 2007. |
[16] |
D. Low-Beer, R. Stoneburner, T. Barnett and M. Whiteside, Knowledge Diffusion and Personalizing Risk: Key Indicators of Behavior Change in Uganda Compared to South Africa,, XIII International AIDS Conference, ().
|
[17] |
S. Okware, J. Kinsman, S. Onyango, A. Opio, and P. Kaggwa, Revisiting the ABC strategy: HIV prevention in Uganda in the era of antiretroviral therapy, Postgraduate Medical Journal, 81(960) (2005), 625-628. |
[18] |
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Interscience Publishers, 1962. |
[19] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48. |
[20] |
Control of communicable diseases and prevention of epidemics, Environmental health in emergencies and disasters: a practical guide, World Health Organization 2003, http://www.who.int/water_sanitation_health/hygiene/emergencies/em2002chap11.pdf |
show all references
References:
[1] |
R. M. Anderson and R. May, Infectious Diseases of Humans, Oxford University Press, (1991), New York. |
[2] |
D. N. Bhatta, U. R. Aryal and K. Khanal, Education: The Key to Curb HIV and AIDS Epidemic, Kathmandu Univ Med J, 42(2) (2013), 158-161. |
[3] |
H. Behncke, Optimal control of deterministic epidemics, Optimal Control Applications and Methods, 21 (2000), 269-285. |
[4] |
O. Diekmann, J. A. P. Heesterbeek and J. A. P. Metz, On the definition and computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol, 28 (1990) 503-522. |
[5] |
E. Fenichel, C. Castillo-Chavez and C. Villalobos, et al, Adaptive human behavior in epidemiological models, Proceedings of the National Academy of Sciences of the United States of America, 108(15) (2011), 6306-6311. |
[6] |
S. Funk, M. Salath and V. Jansen, Modelling the influence of human behaviour on the spread of infectious diseases: A review, J R Soc Interface, 7 (2010), 1247-1256. |
[7] |
E. Green, D. Halperin, V. Nantulya, and J. Hogle, Uganda's HIV Prevention Success: The Role of Sexual Behavior Change and the National Response, AIDS Behav., 10(4) (2006), 335-346. |
[8] |
Global Campaign for Education (GCE), Learning to survive: How education for all would save millions of young people from HIV/AIDS, London, GCE, 2004, http://www.campaignforeducation.org/resources. |
[9] |
H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42(4) (2000), 599-653. |
[10] |
H. R. Joshi, S. Lenhart, K. Albright and K. Gipson, Modeling the Effect of Information Campaigns On the HIV Epidemic In Uganda, Mathematical Biosciences and Engineering, 5(4) (2008), 757-770. |
[11] |
H. R. Joshi, S. Lenhart, S. Hota and F. Agusto, Optimal Control of SIR Model with Changing Behavior through an Education Campaign, Electronic Journal of Differential Equations, 50 (2015), 1-14. |
[12] |
W. O. Kermack and A. G. McKendrick, Contribution to the mathematical theory of epidemics, Proc. Roy. Soc., A 115 (1927), 700-721. |
[13] |
W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics II. The problem of endemicity, Proc. Roy. Soc., A 138 (1932), 55-83. |
[14] |
H. Laarabi, M. Rachik, O. E. Kahlaoui and E. H. Labriji, Optimal Vaccination Strategies of an SIR Epidemic Model with a Saturated Treatment, Universal Journal of Applied Mathematics, 1(3) (2013), 185-191. |
[15] |
S. Lenhart and J. T. Workman, Optimal Control Applied to Biological Models, 1st Edition, Chapman and Hall/CRC, 2007. |
[16] |
D. Low-Beer, R. Stoneburner, T. Barnett and M. Whiteside, Knowledge Diffusion and Personalizing Risk: Key Indicators of Behavior Change in Uganda Compared to South Africa,, XIII International AIDS Conference, ().
|
[17] |
S. Okware, J. Kinsman, S. Onyango, A. Opio, and P. Kaggwa, Revisiting the ABC strategy: HIV prevention in Uganda in the era of antiretroviral therapy, Postgraduate Medical Journal, 81(960) (2005), 625-628. |
[18] |
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Interscience Publishers, 1962. |
[19] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48. |
[20] |
Control of communicable diseases and prevention of epidemics, Environmental health in emergencies and disasters: a practical guide, World Health Organization 2003, http://www.who.int/water_sanitation_health/hygiene/emergencies/em2002chap11.pdf |
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