PMC:7102659 / 5532-10182
Annnotations
{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/7102659","sourcedb":"PMC","sourceid":"7102659","source_url":"https://www.ncbi.nlm.nih.gov/pmc/7102659","text":"A conceptual model\nWe adopt the ‘Susceptible-Exposed-Infectious-Removed’ (SEIR) framework with the total population size N with two extra classes (1) “D” mimicking the public perception of risk regarding the number of severe and critical cases and deaths; and (2) “C” representing the number of cumulative cases (both reported and not reported). Let S, E, and I represent the susceptible, exposed and infectious populations and R represent the removed population (i.e., recovered or dead). In a recent study (Wu and McGoogan, 2020), Wu and McGoogan found that 81% of cases were of mild symptom (without pneumonia or only mild pneumonia), 14% were severe case with difficulty breathing, and 5% were critical with respiratory failure, septic shock, and/or multiple organ dysfunction or failure.\nWe adopt the transmission rate function formulated in He et al. (2013). We rename the school term effect as the governmental action effect, since the former belongs to the latter. We also assume a period of zoonotic transmission during December 2019. We model the zoonotic transmission (denoted as F) as a stepwise function, which takes zero after the shutdown of Huanan seafood market (presumably). We then only model the sustained human-to-human transmission of COVID-19 after this date, along with the emigration of 5 million population before Wuhan was officially locked down (South China Morning Post, 2020). Thus, a compartmental model is formulated as follows:(1) S'=-β0SFN-β(t)SIN-μS,E'=β0SFN+β(t)SIN-(σ+μ)E,I'=σE-(γ+μ)I,R'=γI-μR,N'=-μN,D'=d γI-λD,andC'=σE,where(2) β(t)=β0(1−α)1−DNκ.\nThe transmission rate, β(t) in Eq. (2), incorporates the impact of governmental action (all actions which can be modelled as a step function), and the decreasing contacts among individuals responding to the proportion of deaths (i.e., the severity of the epidemic). We also incorporate the individuals leaving Wuhan before the lock-down in the model. We assume (i) the zoonotic cases only make impacts during December 2019 (Huang et al., 2020); (ii) the effect of governmental action starts on 23 January 2020 (in particular, α = 0.4249 during 23–29 January 2020 and α = 0.8478 after that); (iii) the emigration from Wuhan starts on 31 December 2019 and ends on 22 January 2020.\nIn this outbreak it seems children are spared. Only 0.9% cases are from age 15 or less (Guan et al., 2020), while in China, 0–14 years are 17.2%. To take this effect into account, we assume 10% of the population are ‘protected’. Recent studies showed the serial interval of COVID-19 could be as short as 5 days (Nishiura et al., 2020a), and the median incubation period could be as short as 4 days (Guan et al., 2020). These characteristics imply short latent period and infectious period. Thus, we adopt a relatively shorter mean latent period (3 days) and mean infectious period (4 days). Different from (He et al., 2013), we use the severe cases and deaths in the individual reaction function, instead of deaths only. We also increase the intensity of the governmental action such that the model outcomes (increments in cases) largely match the observed, with a reporting ratio. Namely only a proportion of the model generated cases will be reported in reality. Many evidences and studies, e.g., (Tuite and Fisman, 2020, Zhao et al., 2020a, Zhao et al., 2020b), suggest the reporting ratio is time-varying. We summarise our parameters in Table 1 .\nTable 1 Summary table of the parameters in model (1).\nParameter Notation Value or range Remark Reference\nNumber of zoonotic cases F {0, 10} A stepwise function J.T. Wu et al. (2020)\nInitial population size N0 14 million Constant South China Morning Post (2020)\nInitial susceptible population S0 0.9N0 Constant Assumed\nTransmission rate β0 {0.5944, 1.68}a (day−1) A stepwise function Assumed\nGovernmental action strength α {0,0.4239,0.8478} A stepwise function He et al. (2013)\nIntensity of responds κ 1117.3 Constant He et al. (2013)\nEmigration rate μ {0, 0.0205} (day−1) A stepwise function South China Morning Post (2020)\nMean latent period σ−1 3 (days) Constant J.T. Wu et al. (2020)\nMean infectious period γ−1 5 (days) Constant J.T. Wu et al. (2020)\nProportion of severe cases d 0.2 Constant Worldometers. (2020)\nMean duration of public reaction λ−1 11.2 (days) Constant He et al. (2013)\na It is derived by assuming that the basic reproduction number, R0=β0γ·σσ+μ=2.8 (referring to Imai et al., 2020, Riou and Althaus, 2020, J.T. Wu et al., 2020, Zhao et al., 2020a, Zhao et al., 2020b) when α = 0, by using the next generation matrix approach (van den Driessche and Watmough, 2002). The time unit is in year if not 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