The Impact of Realistic Age Structure in Simple Models of Tuberculosis Transmission
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Scopus | Further Information

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  • {"files"=>["https://ndownloader.figshare.com/files/431271"], "description"=>"<div><h3>Background</h3><p>Mathematical models of tuberculosis (TB) transmission have been used to characterize disease dynamics, investigate the potential effects of public health interventions, and prioritize control measures. While previous work has addressed the mathematical description of TB natural history, the impact of demography on the behaviour of TB models has not been assessed.</p><h3>Methods</h3><p>A simple model of TB transmission, with alternative assumptions about survivorship, is used to explore the effect of age structure on the prevalence of infection, disease, basic reproductive ratio and the projected impact of control interventions. We focus our analytic arguments on the differences between constant and exponentially distributed lifespans and use an individual-based model to investigate the range of behaviour arising from realistic distributions of survivorship.</p><h3>Results</h3><p>The choice of age structure and natural (non-disease related) mortality strongly affects steady-state dynamics, parameter estimation and predictions about the effectiveness of control interventions. Since most individuals infected with TB develop an asymptomatic latent infection and never progress to active disease, we find that assuming a constant mortality rate results in a larger reproductive ratio and an overestimation of the effort required for disease control in comparison to using more realistic age-specific mortality rates.</p><h3>Conclusions</h3><p>Demographic modelling assumptions should be considered in the interpretation of models of chronic infectious diseases such as TB. For simple models, we find that assuming constant lifetimes, rather than exponential lifetimes, produces dynamics more representative of models with realistic age structure.</p></div>", "links"=>[], "tags"=>["models", "tuberculosis"], "article_id"=>145110, "categories"=>["Mathematics", "Cancer", "Biotechnology"], "users"=>["Ellen Brooks-Pollock", "Ted Cohen", "Megan Murray"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0008479"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/The_Impact_of_Realistic_Age_Structure_in_Simple_Models_of_Tuberculosis_Transmission/145110", "title"=>"The Impact of Realistic Age Structure in Simple Models of Tuberculosis Transmission", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2010-01-07 01:25:10"}
  • {"files"=>["https://ndownloader.figshare.com/files/868001"], "description"=>"<p>(A) The age-specific mortality rate in Ukraine in 1959 (green solid line) and 2006 (black solid line), arising from constant (dashed red line), exponential (solid blue line) and Gompertz-like (dot-dashed grey line) lifespans, fitted to Ukraine 2006 data. (B) The probability of surviving until a given age for the same three types of survival functions: constant, exponential and Gompertz-like lifespans. The probability of survival for Ukraine in 2006 is taken from the life tables in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0008479#pone.0008479-Human1\" target=\"_blank\">[28]</a>. The life expectancy was 69 years and the fitted Gompertz parameters were and .</p>", "links"=>[], "tags"=>["functions", "fitted", "ukraine", "1959", "2006"], "article_id"=>538455, "categories"=>["Biotechnology", "Mathematics", "Infectious Diseases"], "users"=>["Ellen Brooks-Pollock", "Ted Cohen", "Megan Murray"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0008479.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mortality_and_survival_functions_fitted_Ukraine_1959_and_2006_data_/538455", "title"=>"Mortality and survival functions fitted Ukraine 1959 and 2006 data.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-07 02:20:55"}
  • {"files"=>["https://ndownloader.figshare.com/files/868080"], "description"=>"<p>Red dashed lines: all individuals live for a constant lifetime; blue solid lines: individuals experience a constant mortality rate and have exponentially distributed lifetimes. (A) The basic reproductive ratio () for TB as a function of the progression rate from latency to disease, . As the latent period decreases, , the <i>SEIR</i> models approach an <i>SIR</i> description. Conversely, as , estimates from models with constant and exponential lifetimes diverge. (B) The percentage of that is contributed by slow progressors to TB disease as a function of progression rate, . In all scenarios, the exponential model predicts that a greater proportion of disease is due to reactivation.</p>", "links"=>[], "tags"=>["models", "assumptions"], "article_id"=>538543, "categories"=>["Biotechnology", "Mathematics", "Infectious Diseases"], "users"=>["Ellen Brooks-Pollock", "Ted Cohen", "Megan Murray"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0008479.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_comparison_of_two_models_with_alternative_assumptions_about_mortality_/538543", "title"=>"A comparison of two models with alternative assumptions about mortality.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-07 02:22:23"}
  • {"files"=>["https://ndownloader.figshare.com/files/868160"], "description"=>"<p>Red dashed lines: all individuals live for a constant lifetime; blue solid lines: individuals experience a constant mortality rate and have exponentially distributed lifespans; grey dot-dashed lines: mortality increases exponentially with age (Gompertz mortality). Each model is fitted to an equilibrium prevalence rate of 350/100,000 by allowing the transmission rate to vary. (Baseline parameters given in Table S1 of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0008479#pone.0008479.s001\" target=\"_blank\">Technical Appendix S1</a>). (A) The epidemic profile in time. (B) The epidemic growth rate as a function of prevalence. The initial period of epidemic growth is highlighted using the thick shaded lines in both figure (A) and (B).</p>", "links"=>[], "tags"=>["epidemics", "produced", "models", "assumptions"], "article_id"=>538617, "categories"=>["Biotechnology", "Mathematics", "Infectious Diseases"], "users"=>["Ellen Brooks-Pollock", "Ted Cohen", "Megan Murray"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0008479.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_TB_epidemics_produced_using_three_models_with_alternative_assumptions_about_mortality_/538617", "title"=>"TB epidemics produced using three models with alternative assumptions about mortality.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-07 02:23:37"}
  • {"files"=>["https://ndownloader.figshare.com/files/868231"], "description"=>"<p>Red dashed lines: constant lifespan; solid blue lines: exponential lifespan and black dot-dashed lines Gompertz survival. In each case, we determined the necessary decrease in parameters for the prevalence to fall to zero. (A) Reduction in transmission rate, , and (B) reduction in average infectious period, . The lines denote the average of 10 model runs.</p>", "links"=>[], "tags"=>["types"], "article_id"=>538698, "categories"=>["Biotechnology", "Mathematics", "Infectious Diseases"], "users"=>["Ellen Brooks-Pollock", "Ted Cohen", "Megan Murray"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0008479.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Investigation_into_epidemic_control_for_a_model_with_three_types_of_survival_/538698", "title"=>"Investigation into epidemic control for a model with three types of survival.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-07 02:24:58"}

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