HIV–TB co-infection treatment: Modeling and optimal control theory perspectives

Journal of Computational and Applied Mathematics - Tập 307 - Trang 143-161 - 2016
Abhishek Mallela1, Suzanne Lenhart2, Naveen K. Vaidya1
1Department of Mathematics and Statistics, University of Missouri-Kansas City, MO, USA
2Department of Mathematics, University of Tennessee, Knoxville, TN, USA

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Diedrich, 2011, HIV-1/Mycobacterium tuberculosis coinfection immunology: How does HIV-1 exacerbate tuberculosis?, Infect. Immun., 79, 1407, 10.1128/IAI.01126-10

Karim, 2010, Timing of initiation of antiretroviral drugs during tuberculosis therapy, N. Engl. J. Med., 362, 697, 10.1056/NEJMoa0905848

Kwan, 2011, HIV and tuberculosis: a deadly human syndemic, Clin. Microbiol. Rev., 24, 351, 10.1128/CMR.00042-10

Long, 2008, Controlling co-epidemics: Analysis of HIV and tuberculosis infection dynamics, Oper. Res., 56, 1366, 10.1287/opre.1080.0571

AVERT.ORG. 2013. Tuberculosis & HIV. Horsham, UK. Retrieved November 24, 2013. http://www.avert.org/tuberculosis-and-hiv.htm.

World Health Organization (WHO). 2014. Tuberculosis (TB): TB/HIV. Geneva, Switzerland. Retrieved August 3, 2014. http://www.who.int/tb/challenges/hiv/en/.

S. Swati, HIV and TB co-infection. San Francisco, CA, 2008. Retrieved August 3, 2014. http://www.slideshare.net/swati2084/hiv-and-tb-coinfection.

Shastri, 2013, TB treatment outcomes among TB-HIV co-infections in Karnataka, India: how do these compare with non-HIV tuberculosis outcomes in the province?, BMC Publ. Health, 13, 1

Blanc, 2011, Earlier versus later start of antiretroviral therapy in HIV-infected adults with tuberculosis, N. Engl. J. Med., 365, 1471, 10.1056/NEJMoa1013911

Havlir, 2011, Timing of antiretroviral therapy for HIV-1 infection and tuberculosis, N. Engl. J. Med., 365, 1482, 10.1056/NEJMoa1013607

Karim, 2011, Integration of antiretroviral therapy with tuberculosis treatment, N. Engl. J. Med., 365, 1492, 10.1056/NEJMoa1014181

Lönnroth, 2010, Tuberculosis control and elimination 2010-50: cure, care, and social development, Lancet, 375, 1814, 10.1016/S0140-6736(10)60483-7

Manissero, 2010, Analysis of tuberculosis treatment outcomes in the European Union and European Economic Area: efforts needed towards optimal case management and control, Euro Surveill., 15, 10.2807/ese.15.11.19514-en

Anandaiah, 2011, Novel developments in the epidemic of human immunodeficiency virus and tuberculosis coinfection, Am. J. Respir. Crit. Care Med., 183, 987, 10.1164/rccm.201008-1246CI

Guo, 2014, Animal models to study Mycobacterium tuberculosis and HIV co-infection, Zool. Res., 35, 163

Török, 2011, Timing of initiation of antiretroviral therapy in human immunodeficiency virus (HIV)-associated tuberculous meningitis, Clin. Infect. Dis., 52, 1374, 10.1093/cid/cir230

Bonnet, 2013, Incidence of paradoxical tuberculosis-associated immune reconstitution inflammatory syndrome and impact on patient outcome, PLoS One, 8, 1, 10.1371/journal.pone.0084585

Lai, 2013, The immunopathogenesis of the HIV tuberculosis immune reconstitution inflammatory syndrome, Eur. J. Immunol., 43, 1995, 10.1002/eji.201343632

Laureillard, 2013, Paradoxical tuberculosis-associated immune reconstitution inflammatory syndrome after early initiation of antiretroviral therapy in a randomized clinical trial, AIDS, 27, 2577, 10.1097/01.aids.0000432456.14099.c7

Luetkemeyer, 2014, Tuberculosis immune reconstitution inflammatory syndrome in A5221 STRIDE: Timing, severity, and implications for HIV-TB programs, J. Acquir. Immune Defic. Syndr., 65, 423, 10.1097/QAI.0000000000000030

Müller, 2010, Immune reconsitution inflammatory syndrome for patients starting antiretroviral therapy for HIV infection: A systematic review and meta-analysis, Lancet Infect. Dis., 10, 251, 10.1016/S1473-3099(10)70026-8

Agusto, 2014, Optimal control of a two-strain tuberculosis-HIV/AIDS co-infection model, Biosystems, 119, 20, 10.1016/j.biosystems.2014.03.006

Roeger, 2011, Modeling TB and HIV co-infections, Math. Biosci. Eng., 6, 815

Sharomi, 2008, Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment, Math. Biosci. Eng., 5, 145, 10.3934/mbe.2008.5.145

Alere, 2012. TB & HIV. Waltham. Retrieved November 21, 2013. http://alerehiv.com/hiv-comorbidities/tb-hiv/.

NAM Publications. 2015. When to Start Treatment. London, England. Retrieved December 11, 2015. http://www.aidsmap.com/When-to-start-treatment/page/1254940/.

Padmapriyadarsini, 2011, Diagnosis & treatment of tuberculosis in HIV co-infected patients, Indian J. Med. Res., 134, 850, 10.4103/0971-5916.92630

Lakshmikantham, 1989

Driessche, 2008, Further notes on the basic reproduction number, 159

J.H. Jones, Notes on R0. Department of Anthropological Sciences. Stanford University, California, 2007.

Diekmann, 1990, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28, 365, 10.1007/BF00178324

Driessche, 2002, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180, 29, 10.1016/S0025-5564(02)00108-6

Census Population. 2011. Population Census 2011. Retrieved December 10, 2015. http://www.census2011.co.in/.

The World Factbook 2013-14. Washington, DC: Central Intelligence Agency. 2013. https://www.cia.gov/library/publications/the-world-factbook/index.html.

India Guide: Population of India. 2011. Retrieved December 10, 2015. http://www.indiaonlinepages.com/population/.

Planning Commission Government of India. 2014. Projected Levels of Expectation of Life at Birth in India & Major States (2001-05 to 2021-25). New Delhi, India. Retrieved January 3, 2014. http://planningcommission.nic.in/data/datatable/0306/table%20226.pdf.

Blayneh, 2010, Backward bifurcation and optimal control in transmission dynamics of west nile virus, Bull. Math. Biol., 72, 1006, 10.1007/s11538-009-9480-0

Fleming, 1975

Pontryagin, 1962

Lenhart, 2007

Gulbudak, 2013, Forward hysteresis and backward bifurcation caused by culling in an avian influenza model, N. Engl. J. Med. Math. Biosci., 68, 202, 10.1016/j.mbs.2013.09.001

Waltman, 1984, Persistence in models of three interacting predator–prey populations, Math. Biosci., 68, 213, 10.1016/0025-5564(84)90032-4

Perko, 1991

Waltman, 2004, Limit cycles and the Poincare–Bendixson theorem, 141