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2016, 13(5): 1011-1041. doi: 10.3934/mbe.2016028

Modeling the role of healthcare access inequalities in epidemic outcomes

1. 

Harvard T.H. Chan School of Public Health, Department of Biostatistics, Boston, MA, United States

2. 

SAL MCMSC, School of Human Evolution and Social Change, Arizona State University, Tempe, AZ, United States, United States

3. 

School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, United States

Received  August 2015 Revised  April 2016 Published  July 2016

Urban areas, with large and dense populations, offer conditions that favor the emergence and spread of certain infectious diseases. One common feature of urban populations is the existence of large socioeconomic inequalities which are often mirrored by disparities in access to healthcare. Recent empirical evidence suggests that higher levels of socioeconomic inequalities are associated with worsened public health outcomes, including higher rates of sexually transmitted diseases (STD's) and lower life expectancy. However, the reasons for these associations are still speculative. Here we formulate a mathematical model to study the effect of healthcare disparities on the spread of an infectious disease that does not confer lasting immunity, such as is true of certain STD's. Using a simple epidemic model of a population divided into two groups that differ in their recovery rates due to different levels of access to healthcare, we find that both the basic reproductive number ($\mathcal{R}_{0}$) of the disease and its endemic prevalence are increasing functions of the disparity between the two groups, in agreement with empirical evidence. Unexpectedly, this can be true even when the fraction of the population with better access to healthcare is increased if this is offset by reduced access within the disadvantaged group. Extending our model to more than two groups with different levels of access to healthcare, we find that increasing the variance of recovery rates among groups, while keeping the mean recovery rate constant, also increases $\mathcal{R}_{0}$ and disease prevalence. In addition, we show that these conclusions are sensitive to how we quantify the inequalities in our model, underscoring the importance of basing analyses on appropriate measures of inequalities. These insights shed light on the possible impact that increasing levels of inequalities in healthcare access can have on epidemic outcomes, while offering plausible explanations for the observed empirical patterns.
Citation: Oscar Patterson-Lomba, Muntaser Safan, Sherry Towers, Jay Taylor. Modeling the role of healthcare access inequalities in epidemic outcomes. Mathematical Biosciences & Engineering, 2016, 13 (5) : 1011-1041. doi: 10.3934/mbe.2016028
References:
[1]

E. Alirol, L. Getaz, B. Stoll, F. Chappuis and L. Loutan, Urbanisation and infectious diseases in a globalised world,, The Lancet Infectious Diseases, 11 (2011), 131.  doi: 10.1016/S1473-3099(10)70223-1.  Google Scholar

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F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology,, Springer, (2012).  doi: 10.1007/978-1-4614-1686-9.  Google Scholar

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C. Castillo-Chavez, W. Huang and J. Li, Competitive exclusion in gonorrhea models and other sexually transmitted diseases,, SIAM Journal on Applied Mathematics, 56 (1996), 494.  doi: 10.1137/S003613999325419X.  Google Scholar

[8]

C. Castillo-Chavez, W. Huang and J. Li, The effects of females' susceptibility on the coexistence of multiple pathogen strains of sexually transmitted diseases,, Journal of Mathematical Biology, 35 (1997), 503.  doi: 10.1007/s002850050063.  Google Scholar

[9]

C. Castillo-Chavez, W. Huang and J. Li, Competitive exclusion and coexistence of multiple strains in an SIS STD model,, SIAM Journal on Applied Mathematics, 59 (1999), 1790.  doi: 10.1137/S0036139997325862.  Google Scholar

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C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications,, Math. Biosci. Eng., 1 (2004), 361.  doi: 10.3934/mbe.2004.1.361.  Google Scholar

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A. Chen, E. Oster and H. Williams, Why is Infant Mortality Higher in the US than in Europe?,, National Bureau of Economic Research, (2014).   Google Scholar

[12]

K. C. Chow, X. Wang and C. Castillo-Chavez, A mathematical model of nosocomial infection and antibiotic resistance: Evaluating the efficacy of antimicrobial cycling programs and patient isolation on dual resistance,, Mathematical and Theoretical Biology Institute archive, (2007).   Google Scholar

[13]

C. Cohen, D. Horlacher and F. L. MacKellar, Is urbanization good for a nation's health,, 2010. Available from: , ().   Google Scholar

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C. Dye, Health and urban living,, Science, 319 (2008), 766.  doi: 10.1126/science.1150198.  Google Scholar

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D. N. Fisman, G. M. Leung and M. Lipsitch, Nuanced risk assessment for emerging infectious diseases,, Lancet, 383 (2014).   Google Scholar

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K. Ford and A. Norris, Sexual networks of African-American and Hispanic youth,, Sexually Transmitted Diseases, 24 (1997), 327.  doi: 10.1097/00007435-199707000-00004.  Google Scholar

[17]

K. Ford, W. Sohn and J. Lepkowski, American adolescents: Sexual mixing patterns, bridge partners, and concurrency,, Sexually Transmitted Diseases, 29 (2002), 13.  doi: 10.1097/00007435-200201000-00003.  Google Scholar

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S. Galea, Urbanization, urbanicity, and health,, Journal of Urban Health, 79 (2002).   Google Scholar

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S. Galea, N. Freudenberg and D. Vlahov, Cities and population health,, Social Science & Medicine, 60 (2005), 1017.  doi: 10.1016/j.socscimed.2004.06.036.  Google Scholar

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M. G. M. Gomes, M. Lipsitch, A. R. Wargo, G. Kurath, C. Rebelo, G. F. Medley and A. Coutinho, A missing dimension in measures of vaccination impacts,, PLoS Pathogens, 10 (2014).   Google Scholar

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T. Harpham and C. Molyneux, Urban health in developing countries: A review,, Progress in Development Studies, 1 (2001), 113.   Google Scholar

[22]

H. W. Hethcote and J. A. Yorke, Gonorrhea Transmission Dynamics and Control, 56,, Springer, (1984).  doi: 10.1007/978-3-662-07544-9.  Google Scholar

[23]

D. R. Holtgrave and R. A. Crosby, Social capital, poverty, and income inequality as predictors of gonorrhoea, syphilis, chlamydia and AIDS case rates in the United States,, Sexually Transmitted Infections, 79 (2003), 62.  doi: 10.1136/sti.79.1.62.  Google Scholar

[24]

M. J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals,, Princeton University Press, (2008).   Google Scholar

[25]

M. J. Keeling and B. T. Grenfell, Effect of variability in infection period on the persistence and spatial spread of infectious diseases,, Mathematical Biosciences, 147 (1998), 207.  doi: 10.1016/S0025-5564(97)00101-6.  Google Scholar

[26]

D. A. Leon, Cities, urbanization and health,, International Journal of Epidemiology, 37 (2008), 4.  doi: 10.1093/ije/dym271.  Google Scholar

[27]

J. Li, Z. Ma, S. P. Blythe and C. Castillo-Chavez, Coexistence of pathogens in sexually-transmitted disease models,, Journal of Mathematical Biology, 47 (2003), 547.  doi: 10.1007/s00285-003-0235-5.  Google Scholar

[28]

M. Lipsitch, T. Cohen, B. Cooper, J. M. Robins, S. Ma, L. James, G. Gopalakrishna, S. K. Chew, C. C. Tan, M. H. Samore, et al., Transmission dynamics and control of severe acute respiratory syndrome,, Science, 300 (2003), 1966.  doi: 10.1126/science.1086616.  Google Scholar

[29]

A. L. Lloyd, Realistic distributions of infectious periods in epidemic models: Changing patterns of persistence and dynamics., Theoretical Population Biology, 60 (2001), 59.   Google Scholar

[30]

A. L. Lloyd, Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods,, Proceedings of the Royal Society of London. Series B: Biological Sciences, 268 (2011), 985.   Google Scholar

[31]

J. O. Lloyd-Smith, S. J. Schreiber, P. E. Kopp and W. M. Getz, Superspreading and the effect of individual variation on disease emergence,, Nature, 438 (2005), 355.   Google Scholar

[32]

K. Lönnroth, E. Jaramillo, B. G. Williams, C. Dye and M. Raviglione, Drivers of tuberculosis epidemics: the role of risk factors and social determinants,, Social Science & Medicine, 68 (2009), 2240.   Google Scholar

[33]

M. Marmot, Social determinants of health inequalities,, The Lancet, 365 (2005), 1099.  doi: 10.1016/S0140-6736(05)74234-3.  Google Scholar

[34]

D. M. Morens and A. S. Fauci, Emerging infectious diseases: Threats to human health and global stability,, PLoS Pathogens, 9 (2013).  doi: 10.1371/journal.ppat.1003467.  Google Scholar

[35]

B. Morin, Variable susceptibility with an open population: A transport equation approach,, preprint, ().   Google Scholar

[36]

B. R. Morin, C. Castillo-Chavez, S.-F. Hsu Schmitz, A. Mubayi and X. Wang, Notes from the heterogeneous: A few observations on the implications and necessity of affinity,, Journal of Biological Dynamics, 4 (2010), 456.  doi: 10.1080/17513758.2010.510212.  Google Scholar

[37]

O. Patterson-Lomba, E. Goldstein, A. Gómez-Liévano, C. Castillo-Chavez and S. Towers, Per capita incidence of sexually transmitted infections increases systematically with urban population size: A cross-sectional study,, Sexually Transmitted Infections, 91 (2015), 610.  doi: 10.1136/sextrans-2014-051932.  Google Scholar

[38]

K. Pickett and R. Wilkinson, The Spirit Level: Why More Equal Societies Almost Always do Better,, London: Allen Lane, (2009).   Google Scholar

[39]

E. Saez and G. Zucman, Wealth inequality in the united states since 1913: Evidence from capitalized income tax data,, The Quarterly Journal of Economics, 131 (2016), 519.  doi: 10.1093/qje/qjw004.  Google Scholar

[40]

C. Stephens, Healthy cities or unhealthy islands? The health and social implications of urban inequality,, Environment and Urbanization, 8 (1996), 9.  doi: 10.1177/095624789600800211.  Google Scholar

[41]

S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering,, Addison-Wesley Pub., (1994).   Google Scholar

[42]

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.  doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[43]

, United Nations, World Urbanization Prospects: The 2011 Revision,, 2012. Available from: , ().   Google Scholar

[44]

J. Wallinga and M. Lipsitch, How generation intervals shape the relationship between growth rates and reproductive numbers,, Proceedings of the Royal Society B: Biological Sciences, 274 (2007), 599.   Google Scholar

[45]

R. G. Wilkinson, Socioeconomic determinants of health. Health inequalities: Relative or absolute material standards?,, BMJ: British Medical Journal, 314 (1997), 591.  doi: 10.1136/bmj.314.7080.591.  Google Scholar

[46]

R. G. Wilkinson and K. E. Pickett, Income inequality and population health: A review and explanation of the evidence,, Social Science & Medicine, 62 (2006), 1768.  doi: 10.1016/j.socscimed.2005.08.036.  Google Scholar

[47]

P. Zhang and P. M. Atkinson, Modelling the effect of urbanization on the transmission of an infectious disease,, Mathematical Biosciences, 211 (2008), 166.  doi: 10.1016/j.mbs.2007.10.007.  Google Scholar

show all references

References:
[1]

E. Alirol, L. Getaz, B. Stoll, F. Chappuis and L. Loutan, Urbanisation and infectious diseases in a globalised world,, The Lancet Infectious Diseases, 11 (2011), 131.  doi: 10.1016/S1473-3099(10)70223-1.  Google Scholar

[2]

L. J. Allen, An Introduction to Stochastic Processes with Applications to Biology,, $2^{nd}$ edition, (2003).   Google Scholar

[3]

J. P. Aparicio, A. F. Capurro and C. Castillo-Chávez, Markers of disease evolution: The case of tuberculosis,, Journal of Theoretical Biology, 215 (2002), 227.  doi: 10.1006/jtbi.2001.2489.  Google Scholar

[4]

P. H. Bamaiyi, The role of demographics and human activities in the spread of diseases,, Current Trends in Technology and Sciences, 2 (2013), 253.   Google Scholar

[5]

S. P. Blythe and C. Castillo-Chavez, Like-with-like preference and sexual mixing models,, Mathematical Biosciences, 96 (1989), 221.   Google Scholar

[6]

F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology,, Springer, (2012).  doi: 10.1007/978-1-4614-1686-9.  Google Scholar

[7]

C. Castillo-Chavez, W. Huang and J. Li, Competitive exclusion in gonorrhea models and other sexually transmitted diseases,, SIAM Journal on Applied Mathematics, 56 (1996), 494.  doi: 10.1137/S003613999325419X.  Google Scholar

[8]

C. Castillo-Chavez, W. Huang and J. Li, The effects of females' susceptibility on the coexistence of multiple pathogen strains of sexually transmitted diseases,, Journal of Mathematical Biology, 35 (1997), 503.  doi: 10.1007/s002850050063.  Google Scholar

[9]

C. Castillo-Chavez, W. Huang and J. Li, Competitive exclusion and coexistence of multiple strains in an SIS STD model,, SIAM Journal on Applied Mathematics, 59 (1999), 1790.  doi: 10.1137/S0036139997325862.  Google Scholar

[10]

C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications,, Math. Biosci. Eng., 1 (2004), 361.  doi: 10.3934/mbe.2004.1.361.  Google Scholar

[11]

A. Chen, E. Oster and H. Williams, Why is Infant Mortality Higher in the US than in Europe?,, National Bureau of Economic Research, (2014).   Google Scholar

[12]

K. C. Chow, X. Wang and C. Castillo-Chavez, A mathematical model of nosocomial infection and antibiotic resistance: Evaluating the efficacy of antimicrobial cycling programs and patient isolation on dual resistance,, Mathematical and Theoretical Biology Institute archive, (2007).   Google Scholar

[13]

C. Cohen, D. Horlacher and F. L. MacKellar, Is urbanization good for a nation's health,, 2010. Available from: , ().   Google Scholar

[14]

C. Dye, Health and urban living,, Science, 319 (2008), 766.  doi: 10.1126/science.1150198.  Google Scholar

[15]

D. N. Fisman, G. M. Leung and M. Lipsitch, Nuanced risk assessment for emerging infectious diseases,, Lancet, 383 (2014).   Google Scholar

[16]

K. Ford and A. Norris, Sexual networks of African-American and Hispanic youth,, Sexually Transmitted Diseases, 24 (1997), 327.  doi: 10.1097/00007435-199707000-00004.  Google Scholar

[17]

K. Ford, W. Sohn and J. Lepkowski, American adolescents: Sexual mixing patterns, bridge partners, and concurrency,, Sexually Transmitted Diseases, 29 (2002), 13.  doi: 10.1097/00007435-200201000-00003.  Google Scholar

[18]

S. Galea, Urbanization, urbanicity, and health,, Journal of Urban Health, 79 (2002).   Google Scholar

[19]

S. Galea, N. Freudenberg and D. Vlahov, Cities and population health,, Social Science & Medicine, 60 (2005), 1017.  doi: 10.1016/j.socscimed.2004.06.036.  Google Scholar

[20]

M. G. M. Gomes, M. Lipsitch, A. R. Wargo, G. Kurath, C. Rebelo, G. F. Medley and A. Coutinho, A missing dimension in measures of vaccination impacts,, PLoS Pathogens, 10 (2014).   Google Scholar

[21]

T. Harpham and C. Molyneux, Urban health in developing countries: A review,, Progress in Development Studies, 1 (2001), 113.   Google Scholar

[22]

H. W. Hethcote and J. A. Yorke, Gonorrhea Transmission Dynamics and Control, 56,, Springer, (1984).  doi: 10.1007/978-3-662-07544-9.  Google Scholar

[23]

D. R. Holtgrave and R. A. Crosby, Social capital, poverty, and income inequality as predictors of gonorrhoea, syphilis, chlamydia and AIDS case rates in the United States,, Sexually Transmitted Infections, 79 (2003), 62.  doi: 10.1136/sti.79.1.62.  Google Scholar

[24]

M. J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals,, Princeton University Press, (2008).   Google Scholar

[25]

M. J. Keeling and B. T. Grenfell, Effect of variability in infection period on the persistence and spatial spread of infectious diseases,, Mathematical Biosciences, 147 (1998), 207.  doi: 10.1016/S0025-5564(97)00101-6.  Google Scholar

[26]

D. A. Leon, Cities, urbanization and health,, International Journal of Epidemiology, 37 (2008), 4.  doi: 10.1093/ije/dym271.  Google Scholar

[27]

J. Li, Z. Ma, S. P. Blythe and C. Castillo-Chavez, Coexistence of pathogens in sexually-transmitted disease models,, Journal of Mathematical Biology, 47 (2003), 547.  doi: 10.1007/s00285-003-0235-5.  Google Scholar

[28]

M. Lipsitch, T. Cohen, B. Cooper, J. M. Robins, S. Ma, L. James, G. Gopalakrishna, S. K. Chew, C. C. Tan, M. H. Samore, et al., Transmission dynamics and control of severe acute respiratory syndrome,, Science, 300 (2003), 1966.  doi: 10.1126/science.1086616.  Google Scholar

[29]

A. L. Lloyd, Realistic distributions of infectious periods in epidemic models: Changing patterns of persistence and dynamics., Theoretical Population Biology, 60 (2001), 59.   Google Scholar

[30]

A. L. Lloyd, Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods,, Proceedings of the Royal Society of London. Series B: Biological Sciences, 268 (2011), 985.   Google Scholar

[31]

J. O. Lloyd-Smith, S. J. Schreiber, P. E. Kopp and W. M. Getz, Superspreading and the effect of individual variation on disease emergence,, Nature, 438 (2005), 355.   Google Scholar

[32]

K. Lönnroth, E. Jaramillo, B. G. Williams, C. Dye and M. Raviglione, Drivers of tuberculosis epidemics: the role of risk factors and social determinants,, Social Science & Medicine, 68 (2009), 2240.   Google Scholar

[33]

M. Marmot, Social determinants of health inequalities,, The Lancet, 365 (2005), 1099.  doi: 10.1016/S0140-6736(05)74234-3.  Google Scholar

[34]

D. M. Morens and A. S. Fauci, Emerging infectious diseases: Threats to human health and global stability,, PLoS Pathogens, 9 (2013).  doi: 10.1371/journal.ppat.1003467.  Google Scholar

[35]

B. Morin, Variable susceptibility with an open population: A transport equation approach,, preprint, ().   Google Scholar

[36]

B. R. Morin, C. Castillo-Chavez, S.-F. Hsu Schmitz, A. Mubayi and X. Wang, Notes from the heterogeneous: A few observations on the implications and necessity of affinity,, Journal of Biological Dynamics, 4 (2010), 456.  doi: 10.1080/17513758.2010.510212.  Google Scholar

[37]

O. Patterson-Lomba, E. Goldstein, A. Gómez-Liévano, C. Castillo-Chavez and S. Towers, Per capita incidence of sexually transmitted infections increases systematically with urban population size: A cross-sectional study,, Sexually Transmitted Infections, 91 (2015), 610.  doi: 10.1136/sextrans-2014-051932.  Google Scholar

[38]

K. Pickett and R. Wilkinson, The Spirit Level: Why More Equal Societies Almost Always do Better,, London: Allen Lane, (2009).   Google Scholar

[39]

E. Saez and G. Zucman, Wealth inequality in the united states since 1913: Evidence from capitalized income tax data,, The Quarterly Journal of Economics, 131 (2016), 519.  doi: 10.1093/qje/qjw004.  Google Scholar

[40]

C. Stephens, Healthy cities or unhealthy islands? The health and social implications of urban inequality,, Environment and Urbanization, 8 (1996), 9.  doi: 10.1177/095624789600800211.  Google Scholar

[41]

S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering,, Addison-Wesley Pub., (1994).   Google Scholar

[42]

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.  doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[43]

, United Nations, World Urbanization Prospects: The 2011 Revision,, 2012. Available from: , ().   Google Scholar

[44]

J. Wallinga and M. Lipsitch, How generation intervals shape the relationship between growth rates and reproductive numbers,, Proceedings of the Royal Society B: Biological Sciences, 274 (2007), 599.   Google Scholar

[45]

R. G. Wilkinson, Socioeconomic determinants of health. Health inequalities: Relative or absolute material standards?,, BMJ: British Medical Journal, 314 (1997), 591.  doi: 10.1136/bmj.314.7080.591.  Google Scholar

[46]

R. G. Wilkinson and K. E. Pickett, Income inequality and population health: A review and explanation of the evidence,, Social Science & Medicine, 62 (2006), 1768.  doi: 10.1016/j.socscimed.2005.08.036.  Google Scholar

[47]

P. Zhang and P. M. Atkinson, Modelling the effect of urbanization on the transmission of an infectious disease,, Mathematical Biosciences, 211 (2008), 166.  doi: 10.1016/j.mbs.2007.10.007.  Google Scholar

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