Dynamics of Drug Resistance: Optimal Control of an Infectious Disease

Published Online:https://doi.org/10.1287/opre.2018.1817

References

  • Aleman DM, Wibisono TG, Schwartz B (2009) Accounting for individual behaviors in a pandemic disease spread model. Rossettti M, Hill RR, Johansson B, eds. Proc. 2009 Winter Simulation Conf., Austin, TX, 1977–1985.CrossrefGoogle Scholar
  • Alexander ME, Bowman CS, Feng Z, Gardam M, Moghadas SM, Röst G, Wu J, Yan P (2007) Emergence of drug resistance: Implications for antiviral control of pandemic influenza. Proc. Roy. Soc. London B Biol. Sci. 274(1619):1675–1684.CrossrefGoogle Scholar
  • Alirol E, Wi TE, Bala M, Bazzo ML, Chen XS, Deal C, Dillon JAR, et al.. (2017) Multidrug-resistant gonorrhea: A research and development roadmap to discover new medicines. PLoS Medicine 14(7):e1002366.CrossrefGoogle Scholar
  • Allen VG, Seah C, Martin I, Melano RG (2014) Azithromycin resistance is coevolving with reduced susceptibility to cephalosporins in Neisseria gonorrhoeae in Ontario, Canada. Antimicrobial Agents Chemotherapy 58(5):2528–2534.CrossrefGoogle Scholar
  • Ambrosch A, Rockmann F (2016) Effect of two-step hygiene management on the prevention of nosocomial influenza in a season with high influenza activity. J. Hospital Infection 94(2):143–149.CrossrefGoogle Scholar
  • Anderson RM, May RM, Anderson B (1992) Infectious Diseases of Humans: Dynamics and Control, vol. 28 (Oxford University Press, New York).Google Scholar
  • Andersson DI, Levin BR (1999) The biological cost of antibiotic resistance. Current Opinion Microbiol. 2(5):489–493.CrossrefGoogle Scholar
  • Arias CA, Murray BE (2009) Antibiotic-resistant bugs in the 21st century—A clinical super-challenge. New England J. Medicine 360(5):439–443.CrossrefGoogle Scholar
  • Barbee LA (2014) Preparing for an era of untreatable gonorrhea. Current Opinion Infectious Diseases 27(3):282–287.CrossrefGoogle Scholar
  • Barrett S (2004) Eradication versus control: The economics of global infectious disease policies. Bull. World Health Organ. 82(9):683–688.Google Scholar
  • Beceiro A, Tomás M, Bou G (2013) Antimicrobial resistance and virulence: A successful or deleterious association in the bacterial world? Clinical Microbiol. Rev. 26(2):185–230.CrossrefGoogle Scholar
  • Behncke H (2000) Optimal control of deterministic epidemics. Optim. Control Appl. Methods 21(6):269–285.CrossrefGoogle Scholar
  • Björkman J, Hughes D, Andersson DI (1998) Virulence of antibiotic-resistant Salmonella typhimurium. Proc. Natl. Acad. Sci. USA 95(7):3949–3953.CrossrefGoogle Scholar
  • Bolan GA, Sparling PF, Wasserheit JN (2012) The emerging threat of untreatable gonococcal infection. New England J. Medicine 366(6):485–487.CrossrefGoogle Scholar
  • Bonhoeffer S, Lipsitch M, Levin BR (1997) Evaluating treatment protocols to prevent antibiotic resistance. Proc. Natl. Acad. Sci. USA 94(22):12106–12111.CrossrefGoogle Scholar
  • Briggs AH, Weinstein MC, Fenwick EA, Karnon J, Sculpher MJ, Paltiel AD (2012) Model parameter estimation and uncertainty analysis: A report of the ISPOR-SMDM modeling good research practices task force working group–6. Medical Decision Making 32(5):722–732.CrossrefGoogle Scholar
  • Brockmann SO, Schwehm M, Duerr HP, Witschi M, Koch D, Vidondo B, Eichner M (2008) Modeling the effects of drug resistant influenza virus in a pandemic. Virology J. 5:133. CrossrefGoogle Scholar
  • Cane P, Chrystie I, Dunn D, Evans B, Geretti A, Green H, Phillips A, Pillay D, Porter K, Pozniak A (2005) Time trends in primary resistance to HIV drugs in the United Kingdom: Multicentre observational study. BMJ 331:1368.CrossrefGoogle Scholar
  • Centers for Disease Control and Prevention (2012) Update to CDC’s sexually transmitted diseases treatment guidelines, 2010: Oral cephalosporins no longer a recommended treatment for gonococcal infections. Morbidity Mortality Weekly Rep. 61(31):590–594.Google Scholar
  • Centers for Disease Control and Prevention (2013) Antibiotic resistance threats in the United States, 2013. Technical report, U.S. Department of Health and Human Services, Atlanta. Available at http://www.cdc.gov/drugresistance/threat-report-2013/index.html.Google Scholar
  • Centers for Disease Control and Prevention (2017a) Gonorrhea - CDC fact sheet (detailed version). Accessed February 4, 2019, https://www.cdc.gov/std/gonorrhea/stdfact-gonorrhea-detailed.htm.Google Scholar
  • Centers for Disease Control and Prevention (2017b) Sexually transmitted disease surveillance 2016. Technical report, U.S. Department of Health and Human Services, Atlanta. Accessed February 4, 2019, https://www.cdc.gov/std/stats16/default.htm.Google Scholar
  • Cosgrove SE (2006) The relationship between antimicrobial resistance and patient outcomes: Mortality, length of hospital stay, and health care costs. Clinical Infectious Diseases 42(Suppl. 2):S82–S89.CrossrefGoogle Scholar
  • Davis MH (1984) Piecewise-deterministic Markov processes: A general class of non-diffusion stochastic models. J. Roy. Statist. Soc. Ser. B (Methodological) 46(3):353–388.CrossrefGoogle Scholar
  • Deeks SG (2003) Treatment of antiretroviral-drug-resistant HIV-1 infection. Lancet 362(9400):2002–2011.CrossrefGoogle Scholar
  • Dharan NJ, Gubareva LV, Meyer JJ, Okomo-Adhiambo M, McClinton RC, Marshall SA, George KS, et al.. (2009) Infections with oseltamivir-resistant influenza A (H1N1) virus in the United States. JAMA 301(10):1034–1041.CrossrefGoogle Scholar
  • Eichner M, Schwehm M, Duerr HP, Witschi M, Koch D, Brockmann SO, Vidondo B (2009) Antiviral prophylaxis during pandemic influenza may increase drug resistance. BMC Infectious Diseases 9:4.CrossrefGoogle Scholar
  • Farley TA, Cohen DA, Elkins W (2003) Asymptomatic sexually transmitted diseases: The case for screening. Preventive Medicine 36(4):502–509.CrossrefGoogle Scholar
  • Fleming-Dutra KE, Hersh AL, Shapiro DJ, Bartoces M, Enns EA, File TM, Finkelstein JA, et al.. (2016) Prevalence of inappropriate antibiotic prescriptions among US ambulatory care visits, 2010-2011. JAMA 315(17):1864–1873.CrossrefGoogle Scholar
  • Furtado LFV, de Paiva Bello ACP, Rabelo ÉML (2016) Benzimidazole resistance in helminths: From problem to diagnosis. Acta Tropica 162:95–102.CrossrefGoogle Scholar
  • Garnett GP, Anderson RM (1996) Sexually transmitted diseases and sexual behavior: Insights from mathematical models. J. Infectious Diseases 174(Suppl. 2):S150–S161.CrossrefGoogle Scholar
  • Garnett GP, Bowden FJ (2000) Epidemiology and control and curable sexually transmitted diseases: Opportunities and problems. Sexually Transmitted Diseases 27(10):588–599.CrossrefGoogle Scholar
  • Geisler WM (2010) Duration of untreated, uncomplicated chlamydia trachomatis genital infection and factors associated with chlamydia resolution: A review of human studies. J. Infectious Diseases 201(Suppl. 2):S104–S113.CrossrefGoogle Scholar
  • Geisler WM, Lensing SY, Press CG, Hook EW III (2013) Spontaneous resolution of genital chlamydia trachomatis infection in women and protection from reinfection. J. Infectious Diseases 207(12):1850–1856.CrossrefGoogle Scholar
  • Gilchrist M, Wade P, Ashiru-Oredope D, Howard P, Sneddon J, Whitney L, Wickens H (2015) Antimicrobial stewardship from policy to practice: Experiences from UK antimicrobial pharmacists. Infectious Diseases Therapy 4(1):51–64.CrossrefGoogle Scholar
  • González-Parra PA, Lee S, Velazquez L, Castillo-Chavez C (2011) A note on the use of optimal control on a discrete time model of influenza dynamics. Math. Biosciences Engrg. 8(1):183–97.CrossrefGoogle Scholar
  • Greenfield R (2011) Study: Superbug gonorrhea strain has no known cure. The Atlantic (July 11), https://www.theatlantic.com/technology/archive/2011/07/study-superbug-gonorrhea-strain-has-no-known-cure/352693/.Google Scholar
  • Hayden FG (2006) Antiviral resistance in influenza viruses—Implications for management and pandemic response. New England J. Medicine 354(8):785–788.CrossrefGoogle Scholar
  • Hayden FG, Pavia AT (2006) Antiviral management of seasonal and pandemic influenza. J. Infectious Diseases 194(Suppl. 2):S119–S126.CrossrefGoogle Scholar
  • Hughes D, Andersson DI (2015) Evolutionary consequences of drug resistance: Shared principles across diverse targets and organisms. Nature Rev. Genetics 16(8):459–471.CrossrefGoogle Scholar
  • Jefferis J, Perera R, Everitt H, van Weert H, Rietveld R, Glasziou P, Rose P (2011) Acute infective conjunctivitis in primary care: Who needs antibiotics? An individual patient data meta-analysis. British J. General Practice 61(590):e542–e548.CrossrefGoogle Scholar
  • Kalichman SC, Price D, Eaton LA, Burnham K, Sullivan M, Finneran S, Cornelius T, Allen A (2017) Diminishing perceived threat of AIDS and increasing sexual risks of HIV among men who have sex with men, 1997–2015. Arch. Sexual Behav. 46(4): 895–902.CrossrefGoogle Scholar
  • Keeling MJ, Rohani P (2008) Modeling Infectious Diseases in Humans and Animals (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. Proc. Roy. Soc. London Ser. A Containing Papers Math. Physical Engrg. Sci. 115(772):700–721.CrossrefGoogle Scholar
  • Kidd S, Kirkcaldy R, Weinstock H, Bolan G (2012) Tackling multidrug-resistant gonorrhea: How should we prepare for the untreatable? Expert Rev. Anti-infective Therapy 10(8):831–833.CrossrefGoogle Scholar
  • Kim Y, Schneider K (2013) Evolution of drug resistance in malaria parasite populations. Nature Ed. Knowledge 4(8):6.Google Scholar
  • Larson RC (2007) Simple models of influenza progression within a heterogeneous population. Oper. Res. 55(3):399–412.LinkGoogle Scholar
  • Laxminarayan R (2001) Bacterial resistance and the optimal use of antibiotics. Technical report, Resources for the Future, Washington, DC.Google Scholar
  • Laxminarayan R (2014) Antibiotic effectiveness: Balancing conservation against innovation. Science 345(6202):1299–1301.CrossrefGoogle Scholar
  • Laxminarayan R, Bhutta ZA (2016) Antimicrobial resistance—A threat to neonate survival. Lancet Global Health 4(10):e676–e677.CrossrefGoogle Scholar
  • Laxminarayan R, Brown GM (2001) Economics of antibiotic resistance: A theory of optimal use. J. Environ. Econom. Management 42(2):183–206.CrossrefGoogle Scholar
  • Laxminarayan R, Duse A, Wattal C, Zaidi AK, Wertheim HF, Sumpradit N, Vlieghe E, et al.. (2013) Antibiotic resistance—The need for global solutions. Lancet Infectious Diseases 13(12):1057–1098.CrossrefGoogle Scholar
  • Lefavre B, Martin I, Demczuk W, Deshaies L, Michaud S, Labbe A, Beaudoin M, Longtin J (2018) Ceftriaxone-resistant Neisseria gonorrhoeae, Canada, 2017. Emerging Infectious Diseases 24(2):381–383.CrossrefGoogle Scholar
  • Lipsitch M, Cohen T, Murray M, Levin BR (2007) Antiviral resistance and the control of pandemic influenza. PLoS Med 4(1):e15.CrossrefGoogle Scholar
  • Lipsitch M, Cohen T, Cooper B, Robins JM, Ma S, James L, Gopalakrishna G, et al.. (2003) Transmission dynamics and control of severe acute respiratory syndrome. Science 300(5627):1966–1970.CrossrefGoogle Scholar
  • Lizon NE, Aleman DM, Schwartz B (2010) Incorporating healthcare systems in pandemic models. Rossettti M, Hill RR, Johansson B, eds. Proc. 2009 Winter Simulation Conf., Austin, TX, 2230–2236.CrossrefGoogle Scholar
  • Long EF, Vaidya NK, Brandeau ML (2008) Controlling co-epidemics: Analysis of HIV and tuberculosis infection dynamics. Oper. Res. 56(6):1366–1381.LinkGoogle Scholar
  • Magiorakos AP, Srinivasan A, Carey R, Carmeli Y, Falagas M, Giske C, Harbarth S, et al.. (2012) Multidrug-resistant, extensively drug-resistant and pandrug-resistant bacteria: An international expert proposal for interim standard definitions for acquired resistance. Clinical Microbiol. Infection 18(3):268–281.CrossrefGoogle Scholar
  • Manfredi P, D’Onofrio A (2013) Modeling the Interplay Between Human Behavior and the Spread of Infectious Diseases (Springer, New York).CrossrefGoogle Scholar
  • McCaw JM, Wood JG, McCaw CT, McVernon J (2008) Impact of emerging antiviral drug resistance on influenza containment and spread: Influence of subclinical infection and strategic use of a stockpile containing one or two drugs. PLoS ONE 3(6):e2362.CrossrefGoogle Scholar
  • Moghadas SM, Bowman CS, Röst G, Wu J (2008) Population-wide emergence of antiviral resistance during pandemic influenza. PLoS ONE 3(3):e1839.CrossrefGoogle Scholar
  • Moran-Gilad J, Kaliner E, Gdalevich M, Grotto I (2016) Public health response to the silent reintroduction of wild poliovirus to Israel, 2013–2014. Clinical Microbiol. Infection 22(Suppl. 5):S140–S145.CrossrefGoogle Scholar
  • Morton R, Wickwire KH (1974) On the optimal control of a deterministic epidemic. Adv. Appl. Probab. 6(4):622–635.CrossrefGoogle Scholar
  • Moscona A (2009) Global transmission of oseltamivir-resistant influenza. New England J. Medicine 360(10):953–956.CrossrefGoogle Scholar
  • Neidell MJ, Cohen B, Furuya Y, Hill J, Jeon CY, Glied S, Larson EL (2012) Costs of healthcare-and community-associated infections with antimicrobial-resistant versus susceptible organisms. Clinical Infectious Diseases 55(6):807–815.CrossrefGoogle Scholar
  • Newman L, Rowley J, Vander Hoorn S, Wijesooriya NS, Unemo M, Low N, Stevens G, Gottlieb S, Kiarie J, Temmerman M (2015) Global estimates of the prevalence and incidence of four curable sexually transmitted infections in 2012 based on systematic review and global reporting. PLoS ONE 10(12):e0143304.CrossrefGoogle Scholar
  • Nigmatulina KR, Larson RC (2009) Living with influenza: Impacts of government imposed and voluntarily selected interventions. Eur. J. Oper. Res. 195(2):613–627.CrossrefGoogle Scholar
  • Ohnishi M, Golparian D, Shimuta K, Saika T, Hoshina S, Iwasaku K, Nakayama Si, Kitawaki J, Unemo M (2011) Is Neisseria gonorrhoeae initiating a future era of untreatable gonorrhea? Detailed characterization of the first strain with high-level resistance to ceftriaxone. Antimicrobial Agents Chemotherapy 55(7):3538–3545.CrossrefGoogle Scholar
  • Owusu-Edusei K, Gift TL, Chesson HW (2010) Treatment cost of acute gonococcal infections: Estimates from employer-sponsored private insurance claims data in the United States, 2003-2007. Sexually Transmitted Diseases 37(5):316–318.Google Scholar
  • Owusu-Edusei K, Chesson HW, Gift TL, Tao G, Mahajan R, Ocfemia MCB, Kent CK (2013) The estimated direct medical cost of selected sexually transmitted infections in the United States, 2008. Sexually Transmitted Diseases 40(3):197–201.CrossrefGoogle Scholar
  • Papp JR, Abrams AJ, Nash E, Katz AR, Kirkcaldy RD, O’Connor NP, O’Brien PS, et al.. (2017) Azithromycin resistance and decreased ceftriaxone susceptibility in Neisseria gonorrhoeae, Hawaii, USA. Emerging Infectious Diseases 23(5):830–832.CrossrefGoogle Scholar
  • Rockafellar RT (1970) Convex Analysis, vol. 28 (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • Roux D, Danilchanka O, Guillard T, Cattoir V, Aschard H, Fu Y, Angoulvant F, et al.. (2015) Fitness cost of antibiotic susceptibility during bacterial infection. Sci. Translational Medicine 7(297):297ra114.CrossrefGoogle Scholar
  • Rudd J (2017) Untreatable gonorrhoea ‘superbug’ spreading around world, WHO warns. The Guardian (July 7), https://www.theguardian.com/society/2017/jul/07/untreatable-gonorrhoea-superbug-spreading-around-world-who-warns.Google Scholar
  • Sanders GD, Neumann PJ, Basu A, Brock DW, Feeny D, Krahn M, Kuntz KM, et al.. (2016) Recommendations for conduct, methodological practices, and reporting of cost-effectiveness analyses. JAMA 316(10):1093–1103.CrossrefGoogle Scholar
  • Satterwhite CL, Torrone E, Meites E, Dunne EF, Mahajan R, Ocfemia MCB, Su J, Xu F, Weinstock H (2013) Sexually transmitted infections among US women and men: Prevalence and incidence estimates, 2008. Sexually Transmitted Diseases 40(3):187–193.CrossrefGoogle Scholar
  • Schilling RL, Song R, Vondracek Z (2012) Bernstein Functions: Theory and Applications, 2nd. ed, Studies in Mathematics, vol. 37 (Walter de Gruyter, Berlin).CrossrefGoogle Scholar
  • Sethi SP (1974) Quantitative guidelines for communicable disease control program: A complete synthesis. Biometrics 30(4):681–691.CrossrefGoogle Scholar
  • Sethi SP, Staats PW (1978) Optimal control of some simple deterministic epidemic models. J. Oper. Res. Soc. 29(2):129–136.CrossrefGoogle Scholar
  • Sheikh A, Hurwitz B, Cave J (2006) Antibiotics versus placebo for acute bacterial conjunctivitis. Cochrane Database System Rev. 9:CD001211.Google Scholar
  • Silverman M, Povitz M, Sontrop JM, Li L, Richard L, Cejic S, Shariff SZ (2017) Antibiotic prescribing for nonbacterial acute upper respiratory infections in elderly personsantibiotic prescribing for nonbacterial auris in elderly persons. Ann. Internal Medicine 166(11):765–774.CrossrefGoogle Scholar
  • Singh AE, Sutherland K, Lee B, Robinson JL, Wong T (2007) Resurgence of early congenital syphilis in Alberta. Canadian Medical Assoc. J. 177(1):33–36.CrossrefGoogle Scholar
  • Spellberg B, Bartlett JG, Gilbert DN (2013) The future of antibiotics and resistance. New England J. Medicine 368(4):299–302.CrossrefGoogle Scholar
  • Spellberg B, Guidos R, Gilbert D, Bradley J, Boucher HW, Scheld WM, Bartlett JG, Edwards J, et al.. (2008) The epidemic of antibiotic-resistant infections: A call to action for the medical community from the infectious diseases society of America. Clinical Infectious Diseases 46(2):155–164.CrossrefGoogle Scholar
  • Spicknall IH, Foxman B, Marrs CF, Eisenberg JN (2013) A modeling framework for the evolution and spread of antibiotic resistance: Literature review and model categorization. Amer. J. Epidemiology 178(4):508–520.CrossrefGoogle Scholar
  • Spinks AB, Glasziou PP, Del Mar C (2013) Antibiotics for sore throat. Cochrane Database System Rev. 11:CD000023.Google Scholar
  • Stein R (2007) Drugs losing efficacy against gonorrhea. Washington Post (November 18), http://www.washingtonpost.com/wp-dyn/content/article/2007/04/12/AR2007041201497.html. http://www.washingtonpost.com/wp-_dyn/content/article/2007/04/12/AR2007041201497.html.Google Scholar
  • Stilianakis NI, Perelson AS, Hayden FG (1998) Emergence of drug resistance during an influenza epidemic: Insights from a mathematical model. J. Infectious Diseases 177(4):863–873.CrossrefGoogle Scholar
  • Tadesse DA, Singh A, Zhao S, Bartholomew M, Womack N, Ayers S, Fields PI, McDermott PF (2016) Antimicrobial resistance in salmonella in the United States from 1948 to 1995. Antimicrobial Agents Chemotherapy 60(4):2567–2571.CrossrefGoogle Scholar
  • Tapsall J (2001) Antimicrobial resistance in Neisseria gonorrhoeae. Technical report, World Health Organization, Geneva. Available at http://apps.who.int/iris/handle/10665/66963.Google Scholar
  • Terkelsen D, Tolstrup J, Johnsen CH, Lund O, Larsen HK, Worning P, Unemo M, Westh H (2017) Multidrug-resistant Neisseria gonorrhoeae infection with ceftriaxone resistance and intermediate resistance to azithromycin, Denmark, 2017. Euro Surveillance 22(42):17-00659.Google Scholar
  • Teytelman A, Larson RC (2012) Modeling influenza progression within a continuous-attribute heterogeneous population. Eur. J. Oper. Res. 220(1):238–250.CrossrefGoogle Scholar
  • Tuddenham S, Ghanem KG (2015) Delaying the widespread emergence of cephalosporin-resistant gonorrhoea: What is the best target? Sexually Transmitted Infections 91(4):232–233.CrossrefGoogle Scholar
  • Unemo M, Nicholas RA (2012) Emergence of multidrug-resistant, extensively drug-resistant and untreatable gonorrhea. Future Microbiol. 7(12):1401–1422.CrossrefGoogle Scholar
  • Unemo M, Shafer WM (2014) Antimicrobial resistance in Neisseria gonorrhoeae in the 21st century: Past, evolution, and future. Clinical Microbiol. Rev. 27(3):587–613.CrossrefGoogle Scholar
  • Vasoo S, Barreto JN, Tosh PK (2015) Emerging issues in gram-negative bacterial resistance: An update for the practicing clinician. Mayo Clinic Proc. 90(3):395–403.CrossrefGoogle Scholar
  • Weber TA (2011) Optimal Control Theory with Applications in Economics (MIT Press, Cambridge, MA).CrossrefGoogle Scholar
  • Wickwire K (1975) A note on the optimal control of Carrier-borne epidemics. J. Appl. Probab. 12(3):565–568.CrossrefGoogle Scholar
  • Wiesner PJ, Thompson SE (1980) Gonococcal diseases. Disease-a-Month 26(5):1–44.CrossrefGoogle Scholar
  • Williams RJ, Heymann DL (1998) Containment of antibiotic resistance. Science 279(5354):1153–1154.CrossrefGoogle Scholar
  • World Health Organization (2014) Antimicrobial resistance: Global report on surveillance 2014. Technical report, World Health Organization, Geneva, Switzerland. Available at https://www.who.int/drugresistance/documents/surveillancereport/en/.Google Scholar
  • World Health Organization (2017a) Global priority list of antibiotic-resistant bacteria to guide research, discovery, and development of new antibiotics. Technical report, World Health Organization, Geneva, Switzerland. Available at https://www.who.int/medicines/publications/global-priority-list-antibiotic-resistant-bacteria/en/.Google Scholar
  • World Health Organization (2017b) The selection and use of essential medicines. WHO Technical report series 1006, World Health Organization, Geneva, Switzerland. Available at https://www.who.int/medicines/publications/essentialmedicines/trs-1006-2017/en/.Google Scholar
  • Xiao Y, Brauer F, Moghadas SM (2016) Can treatment increase the epidemic size? J. Math. Biol. 72(1–2):343–361.CrossrefGoogle Scholar
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