Additional file 1: of Effects of pathogen dependency in a multi-pathogen infectious disease system including population level heterogeneity – a simulation study

Time taken to reach the peak prevalence varies according to the household size distribution in the cohort. Populations with larger households on an average experienced the epidemics at an accelerated rate compared to populations with smaller households on an average. (PNG 24 kb

Regression models of the test substances.

<p>Regression models of the test substances in the (A) YES, (B) ERα CALUX and (C) ERβ CALUX assays. Substances not eliciting an effect are not shown.</p

E2 in the YES, ERα CALUX and ERβ CALUX assays.

<p>Regression models with the indicated EC50 concentrations and the 95% confidence bands for E2 in the (A) YES, (B) ERα CALUX and (C) ERβ CALUX assays.</p

Regression models of the test substances applied in combination with E2.

<p>Regression models of the test substances in the (A) YES (with 1 nM E2) and the (B) ERα CALUX assay (with 3 pM E2). Substances not eliciting an effect are not shown.</p

Examples of generated data of iav.

<p><b>Left</b>: A realistic data set with five replicates per time point and measures at irregular time points. <b>Right</b>: An idealistic data set with thirty replicates per time point and measures every three hours. The measurement errors are assumed following <i>N</i>(0, 0.25), <i>N</i>(0, 0.01) on log base ten scale for Case 1 and Case 2, respectively.</p

Sampling time scheme and parameter bias-variance.

<p><b>Top</b>: t3 to t24 indicate regular sampling time in every 3 to 24 hours respectively; tn1 indicates sampling time similar to that of [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0167568#pone.0167568.ref011" target="_blank">11</a>]; tn2 is t24 without measurement at the peak day (3rd) and the endpoint (8th). Ten replicates were generated per time point. Each scenario (point) is the result of 1000 simulations. <b>Bottom</b>: The every day sampling scheme (t24) is used.</p

Examples of asynchrony problem.

<p>The dotted curve is the true kinetics, dots are data points. (A) Ten subjects with measurement error and asynchrony; red points are the observed data; black points are the actual time the measurement should have represented; arrows indicate directions of time shift; (B) Generated asynchrony data in the absence of measurement error.</p

Trends of applied mathematical modelling in biological and medical research over the last decades.

<p><b>ODEs</b>: papers that used ordinary different equations. The data were queried directly from PubMed Central (PMC) database (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0167568#pone.0167568.s005" target="_blank">S5 Text</a>). The curtailment in the recent years is due to the embargo period of publishing to PMC database [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0167568#pone.0167568.ref025" target="_blank">25</a>].</p

Summary of different simulation settings.

<p>Summary of different simulation settings.</p

Parameters profiles in different initial conditions.

<p>The vertical dashed lines indicate the reference values, the triangles are the point estimated for the corresponding initial condition. The data include thirty replicates per time point with minimal measurement error, samples are collected in every three hours during 12 days of the experiment.</p