Created with https://github.com/matthiaskoenig/sbmlutils.
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+ SBML format.
++ version: 1
+Changelog
++ version 1 +
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- initial model +
PEtab implementation of the model from Alkan et al. (2018), Science Signaling 24 Jul 2018: Vol. 11, Issue 540, eaat0229+ +
Created with https://github.com/matthiaskoenig/sbmlutils.
+
+
+ SBML format.
++ version: 1
++ version 1 +
+PEtab implementation of the model from Bachmann et al. (2011), Mol Syst Biol. ; 7: 516.+ +
PEtab implementation of the model from Beer et al. (2014), Mol Biosyst.;10(7):1709-18+ +
PEtab implementation of the model from Blasi et al. (2016), Cell Systems;Volume 2, ISSUE 1, P49-58+ +
PEtab implementation of the model from Borghans et al. (1997), Biophysical Chemistry 66(1) 25-41+ +
PEtab implementation of the model from Brannmark et al. (2010), THE JOURNAL OF BIOLOGICAL CHEMISTRY VOL. 285, NO. 26, pp. 20171–20179,+ +
PEtab implementation of the model from Bruno et al. (2016), J Exp Bot.; 67(21): 5993–6005+ +
PEtab implementation of the model from Chen et al. (2009), Mol Syst Biol. ;5:239+ +
PEtab implementation of the model from Crauste et al. (2017), Cell Syst. 2017 Mar 22;4(3):306-317.e4+ +
PEtab implementation of the model from Elowitz et al. (2000), Nature. 2000 Jan 20;403(6767):335-8+ +
PEtab implementation of the model from Fiedler et al. (2016), BMC Systems Biology volume 10, Article number: 80+ +
This is a model created on COPASI 4.27 (Build 217) which reproduces the Figures 2b, 2d, 3b, 3d, 4b, 4d in the article - https://www.nature.com/articles/s41591-020-0883-7 + +To reproduce Fig 2b and 2d, set Event_trigger_Fig3b = 0, Event_trigger_Fig3d = 0, Event_trigger_Fig4b = 0, Event_trigger_Fig4d = 0, epsilon_modifer = 1, alpha_modifer = 1 and run for t = 45 d (for Fig 2b) and t = 350 days (for Fig 2d). +Set alpha_modifier = 0 for the remaining 4 cases +To reproduce Fig 3b, set Event_trigger_Fig3b = 1, Event_trigger_Fig3d = 0, Event_trigger_Fig4b = 0, Event_trigger_Fig4d = 0, epsilon_modifer = 1 and run for t = 350 days. +To reproduce Fig 3d, set Event_trigger_Fig3b = 0, Event_trigger_Fig3d = 1, Event_trigger_Fig4b = 0, Event_trigger_Fig4d = 0, epsilon_modifer = 1 and run for t = 350 days. +To reproduce Fig 4b, set Event_trigger_Fig3b = 0, Event_trigger_Fig3d = 0, Event_trigger_Fig4b = 1, Event_trigger_Fig4d = 0, epsilon_modifer = 0 and run for t = 350 days. +To reproduce Fig 4d, set Event_trigger_Fig3b = 0, Event_trigger_Fig3d = 0, Event_trigger_Fig4b = 0, Event_trigger_Fig4d = 1, epsilon_modifer = 0 and run for t = 350 days. + + + +Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy +Giulia Giordano, Franco Blanchini, Raffaele Bruno, Patrizio Colaneri, Alessandro Di Filippo, Angela Di Matteo and Marta Colaneri +Journal - Nature Medicine +DOI - 10.1038/s41591-020-0883-7 + +In Italy, 128,948 confirmed cases and 15,887 deaths of people who tested positive for SARS-CoV-2 were registered as of 5 April 2020. Ending the global SARS-CoV-2 pandemic requires implementation of multiple population-wide strategies, including social distancing, testing and contact tracing. We propose a new model that predicts the course of the epidemic to help plan an effective control strategy. The model considers eight stages of infection: susceptible (S), infected (I), diagnosed (D), ailing (A), recognized (R), threatened (T), healed (H) and extinct (E), collectively termed SIDARTHE. Our SIDARTHE model discriminates between infected individuals depending on whether they have been diagnosed and on the severity of their symptoms. The distinction between diagnosed and non-diagnosed individuals is important because the former are typically isolated and hence less likely to spread the infection. This delineation also helps to explain misperceptions of the case fatality rate and of the epidemic spread. We compare simulation results with real data on the COVID-19 epidemic in Italy, and we model possible scenarios of implementation of countermeasures. Our results demonstrate that restrictive social-distancing measures will need to be combined with widespread testing and contact tracing to end the ongoing COVID-19 pandemic.+ +
Infected ND AS - non-diagnosed, asymptomatic (I)+ +
Infected D AS - diagnosed, asymptomatic (D)+ +
Infected ND S - non-diagnosed, symptomatic (A)+ +
Infected D S - diagnosed, symptomatic (R)+ +
Infected D IC - diagnosed, life-threatening symptoms (T)+ +
PEtab implementation of the model from Isensee et al. (2018), The Journal of Cell Biology Jun 2018, 217 (6) 2167-2184+ +
Heldt2012 - Influenza Virus Replication +The model describes the life cycle of influenza A virus in a mammalian cell including the following steps: attachment of parental virions to the cell membrane, receptor-mediated endocytosis, fusion of the virus envelope with the endosomal membrane, nuclear import of vRNPs, viral transcription and replication, translation of the structural viral proteins, nuclear export of progeny vRNPs and budding of new virions. It also explicitly accounts for the stabilization of cRNA by viral polymerases and NP and the inhibition of vRNP activity by M1 protein binding. In short, the model focuses on the molecular mechanism that controls viral transcription and replication. + +This model is described in the article: +Modeling the intracellular dynamics of influenza virus replication to understand the control of viral RNA synthesis. +Heldt FS, Frensing T, Reichl U. +J Virol. + +This model has been adapted to fit the needs for parameter optimisation using pyPESTO by Clemens Peiter. In comparison to the original model, the chemical species names are also the IDs of the species in the SBML file, which simplifies things in the PEtab files. Some species have also been added to simplify PEtab problem specification (e.g., F_rnp_nuc). + +The values of certain kinetic parameters have been adjusted to Laske et al. re-estimation of the parameters for human A549 cells. + +The original model is hosted on BioModels Database and identified by: MODEL1307270000 .+ +
virions in the extracellular medium (virions)+ +
virions in endosomes (virions)+ +
parental vRNPs in the cytoplasm (virions)+ +
vRNPs in the nucleus (virions)+ +
nascent cRNA (molecules)+ +
complex of viral polymerase and cRNA (molecules)+ +
nascent vRNA (molecules)+ +
complex of viral polymerase and vRNA (molecules)+ +
mRNA of segment 1 (molecules)+ +
mRNA of segment 2 (molecules)+ +
mRNA of segment 3 (molecules)+ +
mRNA of segment 4 (molecules)+ +
mRNA of segment 5 (molecules)+ +
mRNA of segment 6 (molecules)+ +
unspliced mRNA of segment 7 (molecules)+ +
unspliced mRNA of segment 8 (molecules)+ +
PB1 proteins (molecules)+ +
PB2 proteins (molecules)+ +
PA proteins (molecules)+ +
HA proteins (molecules)+ +
NP proteins (molecules)+ +
NA proteins (molecules)+ +
M1 proteins (molecules)+ +
NEP proteins (molecules)+ +
M1-vRNP complexes in the nucleus (virions)+ +
M1-vRNP complexes in the cytoplasm (virions)+ +
total amount of released virions (virions)+ +
viral polymerase complex (molecules)+ +
cRNPs (molecules)+ +
virions attached to high-affinity binding sites (virions)+ +
virions attached to low-affinity binding sites (virions)+ +
M2 proteins (molecules)+ +
free low-affinity binding sites (sites)+ +
free high-affinity binding sites (sites)+ +
total amount of cRNA in the cell considering an arbitrary segment (molecules)+ +
total amount of vRNA in the cell considering an arbitrary segments (molecules)+ +
The fraction of RNPs that is nuclear+ +
total amount of cRNA in the cell considering all segments (molecules)+ +
total amount of vRNA in the cell considering all segments (molecules)+ +
nuclear RNPs+ +
cytoplasmic RNPs+ +
attachment rate of virus particles to high-affinity binding sites (1/(site*h))+ +
attachment rate of virus particles to low-affinity binding sites (1/(site*h))+ +
dissociation rate of virions from high-affinity binding sites (1/h)+ +
dissociation rate of virions from low-affinity binding sites (1/h)+ +
endocytosis rate of virions bound to high-affinity or low-affinity binding sites (1/h)+ +
degradation rate of virions which do not fuse with the endosomal membrane (1/h)+ +
fusion rate of virions in late endosomes (1/h)+ +
nuclear import rate of cytoplasmic vRNPs which are not bound to M1 (1/h)+ +
Degradation of viral ribonucleoproteins.+ +
synthesis rate of cRNAs (1/h)+ +
binding rate of polymerase complexes to cRNA and vRNA (1/(h*molecule))+ +
binding rate of NP to RdRp-cRNA and RdRp-vRNA complexes (1/(h*molecule))+ +
binding rate of M1 to nuclear vRNPs (1/(h*molecule))+ +
combined rate of NEP binding to M1-vRNP complexes and subsequent transport out of the nucleus (1/(molecule*h))+ +
Degradation of viral RNA in the nucleus.+ +
degradation rate of RdRp-cRNA and RdRp-vRNA complexes (1/h)+ +
synthesis rate of mRNAs (nucleotides/h)+ +
synthesis rate of proteins (nucleotides/h)+ +
release rate of progeny virions from the cell (virions/(molecule*h))+ +
distance between two adjacent ribosomes on an mRNA (nucleotides)+ +
fraction of protein synthesis rate and distance between two adjacent ribosomes (1/h)+ +
length of segment 1's mRNA encoding PB2 (nucleotides)+ +
length of segment 2's mRNA encoding PB1 (nucleotides)+ +
length of segment 3's mRNA encoding PA (nucleotides)+ +
length of segment 4's mRNA encoding HA (nucleotides)+ +
length of segment 5's mRNA encoding HA (nucleotides)+ +
length of segment 6's mRNA encoding HA (nucleotides)+ +
length of segment 7's mRNA encoding HA (nucleotides)+ +
length of segment 8's mRNA encoding HA (nucleotides)+ +
synthesis rate of segment 1's mRNA (1/h)+ +
synthesis rate of segment 2's mRNA (1/h)+ +
synthesis rate of segment 3's mRNA (1/h)+ +
synthesis rate of segment 4's mRNA (1/h)+ +
synthesis rate of segment 5's mRNA (1/h)+ +
synthesis rate of segment 6's mRNA (1/h)+ +
synthesis rate of segment 7's mRNA (1/h)+ +
synthesis rate of segment 8's mRNA (1/h)+ +
degradation rate of mRNA (1/h)+ +
number of P_RdRp in a virion+ +
number of P_HA in a virion+ +
number of P_M1 in a virion+ +
number of P_NA in a virion+ +
number of P_NEP in a virion+ +
number of P_NP in a virion+ +
Michaelis-Menten-like constant vor virus release kinetics+ +
fraction of spliced M2 mRNAs compared to total mRNAs of segment 7 (-)+ +
synthesis rate of M1 proteins (1/h)+ +
synthesis rate of M2 proteins (1/h)+ +
fraction of spliced NEP mRNAs compared to total mRNAs of segment 8 (-)+ +
synthesis rate of NEP proteins (1/h)+ +
number of P_M2 in a virion+ +
equilibrium constant for the attachment of virions to the high-affinity binding sites (1/site)+ +
equilibrium constant for the attachment of virions to the low-affinity binding sites (1/site)+ +
fraction of fusion-competent virions (-)+ +
synthesis rate of vRNAs (1/h)+ +
Michaelis-Menten-like constant for half-maximal virus release; necessary for virus release kinetics+ +
Michaelis-Menten-like constant for half-maximal virus release; necessary for virus release kinetics+ +
Michaelis-Menten-like constant for half-maximal virus release; necessary for virus release kinetics+ +
Michaelis-Menten-like constant for half-maximal virus release; necessary for virus release kinetics+ +
Michaelis-Menten-like constant for half-maximal virus release; necessary for virus release kinetics+ +
Michaelis-Menten-like constant for half-maximal virus release; necessary for virus release kinetics+ +
Michaelis-Menten-like constant for half-maximal virus release; necessary for virus release kinetics+ +
formation rate of functional polymerase complexes from the three subunits (1/(h*molecule^2))+ +
Actual reaction: +R_V_RdRp + 71 * P_NP -> Vp_nuc+ +
Actual reaction: +Vp_nuc + 8 * P_M1 -> Vp_nuc_M1+ +
Actual reaction: +8 * Vp_cyt_M1 + 37 * P_RdRp + 433 * P_NP + 2932 * P_M1 + 157 * P_NEP + 500 * P_HA + 100 * P_NA + 40 * P_M2 -> V_rel+ +
PEtab implementation of the model from Lucarelli et al. (2018), Cell Syst. 2018 Jan 24;6(1):75-89.e11+ +
Oliveira, Nature 2021. + +https://www.nature.com/articles/s41467-020-19798-3. + +COVID-19 is affecting healthcare resources worldwide, with lower and middle-income countries being particularly disadvantaged to mitigate the challenges imposed by the disease, including the availability of a sufficient number of infirmary/ICU hospital beds, ventilators, and medical supplies. Here, we use mathematical modelling to study the dynamics of COVID-19 in Bahia, a state in northeastern Brazil, considering the influences of asymptomatic/non-detected cases, hospitalizations, and mortality. The impacts of policies on the transmission rate were also examined. Our results underscore the difficulties in maintaining a fully operational health infrastructure amidst the pandemic. Lowering the transmission rate is paramount to this objective, but current local efforts, leading to a 36% decrease, remain insufficient to prevent systemic collapse at peak demand, which could be accomplished using periodic interventions. Non-detected cases contribute to a ∽55% increase inR0. Finally, we discuss our results in light of epidemiological data that became available after the initial analyses. + +To model with a two-step transmission rate, set 'beta_2_multiplier' = 0. To model with a three-step transmission rate, set 'beta_2_multiplier' = 1. ++ +
PEtab implementation of the model from Perelson et al. (1996), Science 15 Mar 1996: Vol. 271, Issue 5255, pp. 1582-1586+ +
PEtab implementation of the model from Raia et al. (2011), Cancer Res February 1 2011 (71) (3) 693-704+ +
PEtab implementation of the model from Sneyd et al. (2002), PNAS February 19, 2002 99 (4) 2398-2403+ +
PEtab implementation of the model from Weber et al. (2015), BMC Syst. Biol., 9, 9+ +
Background - The coronavirus disease 2019 (COVID-19) is rapidly spreading in China and more than 30 countries over last two months. COVID-19 has multiple characteristics distinct from other infectious diseases, including high infectivity during incubation, time delay between real dynamics and daily observed number of confirmed cases, and the intervention effects of implemented quarantine and control measures. Methods - We develop a Susceptible, Un-quanrantined infected, Quarantined infected, Confirmed infected (SUQC) model to characterize the dynamics of COVID-19 and explicitly parameterize the intervention effects of control measures, which is more suitable for analysis than other existing epidemic models. Results - The SUQC model is applied to the daily released data of the confirmed infections to analyze the outbreak of COVID-19 in Wuhan, Hubei (excluding Wuhan), China (excluding Hubei) and four first-tier cities of China. We found that, before January 30, 2020, all these regions except Beijing had a reproductive number R > 1, and after January 30, all regions had a reproductive number R lesser than 1, indicating that the quarantine and control measures are effective in preventing the spread of COVID-19. The confirmation rate of Wuhan estimated by our model is 0.0643, substantially lower than that of Hubei excluding Wuhan (0.1914), and that of China excluding Hubei (0.2189), but it jumps to 0.3229 after February 12 when clinical evidence was adopted in new diagnosis guidelines. The number of unquarantined infected cases in Wuhan on February 12, 2020 is estimated to be 3,509 and declines to 334 on February 21, 2020. After fitting the model with data as of February 21, 2020, we predict that the end time of COVID-19 in Wuhan and Hubei is around late March, around mid March for China excluding Hubei, and before early March 2020 for the four tier-one cities. A total of 80,511 individuals are estimated to be infected in China, among which 49,510 are from Wuhan, 17,679 from Hubei (excluding Wuhan), and the rest 13,322 from other regions of China (excluding Hubei). Note that the estimates are from a deterministic ODE model and should be interpreted with some uncertainty. Conclusions - We suggest that rigorous quarantine and control measures should be kept before early March in Beijing, Shanghai, Guangzhou and Shenzhen, and before late March in Hubei. The model can also be useful to predict the trend of epidemic and provide quantitative guide for other countries at high risk of outbreak, such as South Korea, Japan, Italy and Iran.+ +
Wuhan - initial values +Stage I - 258 +Stage II - 15270 +Stage III - 4000 + +Hubei - initial values +Stage I - 270 +Stage II - 5700 + +China - initial values +Stage I - 291 (Set model initial time to -30. Keep it at 0 for everything else) +Stage II - 2800+ +
Wuhan - initial values +Stage I - 0 +Stage II - 0 +Stage III - 5000 + +Hubei - initial values +Stage I - 0 +Stage II - 1500 + +China - initial values +Stage I - 0 (Set model initial time to -30 for Stage I alone. Keep it at 0 for everything else) +Stage II - 2000+ +
Wuhan - initial values +Stage I - 258 +Stage II - 2000 +Stage III - 36000 + +Hubei - initial values +Stage I - 0 +Stage II - 1600 + +China - initial values +Stage I - 0 (Set model initial time to -30. Keep it at 0 for everything else) +Stage II - 4000+ +
PEtab implementation of the model from Zheng et al. (2012), Proc. Natl. Acad. Sci. USA, 109, 13549–13554+ +