Statistical Inference on a Stochastic Epidemic Model

Fierro, Raúl; Leiva, Víctor

doi:10.1080/03610918.2013.835409

Cited by 14 publications

(18 citation statements)

References 21 publications

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“…Regarding the effectiveness of these measures, note that the spread has been successfully controlled in most regions, which permits us to observe at least two waves of contagion. This situation was simulated in [23] and modeled with a susceptible-exposedinfectious-recovered (SEIR) structure (see Appendix and [12] for details of the SEIR model). In that study, after adding the adaptive confinement for the transmission of the disease (in which quarantines are decreed and lifted when cases exceed or fall below a threshold of cases), successive waves of contagion were registered whose amplitudes decreased over time.…”

Section: Based On Tablementioning

confidence: 99%

“…Another fundamental concept of the epidemic models is the basic reproduction number (R 0 ), a quantity that is useful in establishing vaccination policies [12]. Note that R 0 is defined as the expected number of secondary (new) infected cases, produced by a primary infected case, during the entire period of infectiousness (epidemic), when this infected case is introduced into a large population of susceptible cases [13].…”

Section: Introductionmentioning

confidence: 99%

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A statistical analysis for the epidemiological surveillance of COVID-19 in Chile

2021

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Background: The emergence of COVID-19 so far and in the immediate future has brought significant uncertainties that negatively impact institutions and individuals in developing and planning their activities worldwide. The uncertainty of the effectiveness of vaccines has forced the authorities to adopt different protocols, the most relevant of which is the isolation of people through quarantine to avoid contagion, drastically affecting our way of life. For this reason, it is crucial to evaluate the effectiveness of quarantines. Objective: To analyze the spread of the disease in Chile according to the quarantines decreed by the sanitary authority. Methods: Inferential study to estimate the trend changes in COVID-19 cases and their basic and instantaneous reproduction numbers, which allows us to evaluate the decreed measures and establish vaccination policies. Results: According to the data obtained until 03 March 2021 of confirmed COVID-19 cases disaggregated at a regional level in Chile, we observe a heterogeneous spread in most Chilean regions. When incorporating the dynamic quarantines decreed, effectiveness is detected in most regions, except in some few of them. Conclusion: Our results indicate that we are unable to identify the measures in the step-by-step protocols partly responsible for non-compliance with quarantines. However, our specific findings that can be extrapolated to daily practice and enlighten the ways of other countries are as follows. On the one hand, a measure that has been effective in curbing the spread of the disease is the strict early quarantine as detected in some Chilean regions. Therefore, indexes are needed to measure the mobility of citizens. On the other hand, as time passes without stopping infections, quarantines lose effectiveness even if the estimated instantaneous reproduction number is small and stable. In addition, other factors can cause this number to not be within the expected ranges which must be further studied. Also, we have estimated the basic reproduction number whose value confirms the suitability of the pandemic declaration.

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Section: Based On Tablementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A statistical analysis for the epidemiological surveillance of COVID-19 in Chile

2021

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“…WHO declared the Covid-19 outbreak a Public Health Emergency of International Concern (PHEIC) on 30 January 2020, and a pandemic [05] on 11 March 2020 and countries around the world are struggling to contain the surge of confirmed cases. Meanwhile, scientists are exploring potential treatments and are undertaking clinical trials to test new vaccines and therapies for the same.…”

Section: Analysis Of 2019-ncov In Indiamentioning

confidence: 99%

Modelling and Analysis of 2019-nCov Epidemic in India : A study on Attack & Recovery Rate, Basic & Effective Reproductive Number, Herd Immunity Threshold & Case Fatality Ratio of Coronavirus Covid-19 in India.

Malik¹

2020

Preprint

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Mathematical modelling of any epidemic plays a crucial role in quantifying the impact of such pathogens. This paper focuses on building a Stochastic SIR Model with non-linear parameters (to account for the effect of lockdowns) to gain a broader cognition of the 2019 novel Coronavirus pathogen (2019-nCov), widely known as Covid-19, in India. Such models help in gauging the virulence and fecundity of pathogens. Based on early transmission dynamics the basic reproductive number (R0) is computed to be 1.605. Whereas, effective reproductive number (Rt) is computed to be 4.880 as on 19 March, 2.756 as on 19 April, and 1.995 as on 19 May. Furthermore, the proportion of population that needs to be immunized (through inoculation, recovery, or death) to halt the infection spread is estimated to be 37.69%, ergo, the Herd Immunity Threshold is estimated to be 51.36 crores recoveries, if the Rt remains below 2. Rt is expected to fall below 2, and the Case Fatality Ratio (CFR) to fall to 2.14%, circa early-September (assuming minimal or no medical breakthroughs). The formulated model also provides inferential evidence manifesting the extent to which lockdowns contained the spread of the virus.

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“…Comparatively the problem of parameter estimation concerning transmission rate involving media effect has not been fully discussed. One main challenge in these inferential tasks is attributed to the burden of computational load of minimizing/maximizing corresponding object functions, including likelihood functions or the squared differences [8][9][10][11]. In this paper, we consider a stochastic Susceptible-Infected-Removed (SIR) model [12] with media coverage.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation on a Stochastic SIR Model with Media Coverage

Pei

Zhu

et al. 2018

Discrete Dynamics in Nature and Society

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Media coverage reduces the transmission rate from infective to susceptible individuals and is reflected by suitable nonlinear functions in mathematical modeling of the disease. We here focus on estimating the parameters in the transmission rate based on a stochastic SIR epidemic model with media coverage. In order to reduce the computational load, the Newton-Raphson algorithm and Markov Chain Monte Carlo (MCMC) technique are incorporated with maximum likelihood estimation. Simulations validate our estimation results and the necessity of a model with media coverage when modeling the contagious diseases. Katriel [12] proposed a stochastic discrete time model with infection age. Suppose that the population of size is Hindawi Model Formulation

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Statistical Inference on a Stochastic Epidemic Model

Cited by 14 publications

References 21 publications

A statistical analysis for the epidemiological surveillance of COVID-19 in Chile

A statistical analysis for the epidemiological surveillance of COVID-19 in Chile

Modelling and Analysis of 2019-nCov Epidemic in India : A study on Attack & Recovery Rate, Basic & Effective Reproductive Number, Herd Immunity Threshold & Case Fatality Ratio of Coronavirus Covid-19 in India.

Parameter Estimation on a Stochastic SIR Model with Media Coverage

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Statistical Inference on a Stochastic Epidemic Model

Cited by 14 publications

References 21 publications

A statistical analysis for the epidemiological surveillance of COVID-19 in Chile

A statistical analysis for the epidemiological surveillance of COVID-19 in Chile

Modelling and Analysis of 2019-nCov Epidemic in India : A study on Attack &amp; Recovery Rate, Basic &amp; Effective Reproductive Number, Herd Immunity Threshold &amp; Case Fatality Ratio of Coronavirus Covid-19 in India.

Parameter Estimation on a Stochastic SIR Model with Media Coverage

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Modelling and Analysis of 2019-nCov Epidemic in India : A study on Attack & Recovery Rate, Basic & Effective Reproductive Number, Herd Immunity Threshold & Case Fatality Ratio of Coronavirus Covid-19 in India.