Over the past years, scientists from different fields, extending from medicine and biology to applied mathematics and computer science, have teamed up to assess emerging diseases. Mathematical modelling plays an important role in predicting, forecasting and controlling disease outbreaks. Despite control measures, it often happens that outbreaks remain a serious public health risk in areas where recurrent outbreaks have been observed for a long time. Therefore, it is crucial to evaluate the effectiveness of the control intervention of diseases using mathematical modelling, especially for those such as Ebola virus for which no specific treatment or vaccine exists. Researchers have studied and applied numerous models and algorithms for the different types of disease outbreaks. One of the models that is widely used in the infectious disease model is the susceptible-exposed-infectious-recovered (SEIR) model, also called the compartmental model, is often used for infectious diseases. Chowell et al.(2004) have developed a deterministic SEIR and a stochastic continuous-time Markov chain version with control intervention for the 1995 epidemic of Ebola in the Democratic Republic of Congo.
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Two years after, the Chowell et al. research publication, Lekone and Finkenstadt at the University of Warwick have modified the model of Chowell et al. for discrete-time and stochastic progression at Ebola as a case study. Lekone and Finkenstadt concluded that their model can be used by epidemiologists to study the disease and the effectiveness of control interventions. In this critical analysis paper, I will provide the summary of this research paper and identify strengths and weaknesses, and provide evaluative comments. I will summarize the literature titled “Statistical Inference in a Stochastic Epidemic SEIR Model with Control Intervention: Ebola as a Case Study” and published by Lekone and Finkenstadt on Biometrics journal in 2006. I will identify its strengths and weaknesses and provide evaluative comments. Using the discrete-time SEIR model, the paper by Lekone and Finkenstadt strives to estimate the reproduction number and transmission rates of Ebola between the health states in compartmental model for the 1995 epidemic of Ebola in Congo. After estimating transmission rates, this paper addresses how effectively control intervention was used during the outbreak. With control intervention, the outbreak lasted for approximately 200 days. It is recorded that the first case became ill on January 6th, the last case died on July 16th, with a total of 316 cases were identified resulting in a rate of an 81% fatality rate. To study transmission rates, the researchers established the parameters that are derived from the compartmental model. To explore the posterior distribution of the parameters, the authors of the paper apply the SEIR model for the Ebola epidemic and the maximum-likelihood (ML) estimator for the parameters as well as the Markov chain Monte Carlo (MCMC) method. First the researchers simulated the time of epidemic series with the ML estimated parameter values obtained from complete data, then they validated using MCMC with various distributions. Their parameter results are shown on Table 2 and are verified by the literature of Chowell et al. Notably, the researchers concluded that the epidemic could have been lasted more than five times longer and epidemic size could have covered two thirds of the whole population of Congo in absence of intervention. Lekone and Frankstadt have written an important and timely research paper on discrete-time SEIR model with control
Two years after, the Chowell et al. research publication, Lekone and Finkenstadt at the University of Warwick have modified the model of Chowell et al. for discrete-time and stochastic progression at Ebola as a case study. Lekone and Finkenstadt concluded that their model can be used by epidemiologists to study the disease and the effectiveness of control interventions. In this critical analysis paper, I will provide the summary of this research paper and identify strengths and weaknesses, and provide evaluative comments. I will summarize the literature titled “Statistical Inference in a Stochastic Epidemic SEIR Model with Control Intervention: Ebola as a Case Study” and published by Lekone and Finkenstadt on Biometrics journal in 2006. I will identify its strengths and weaknesses and provide evaluative comments. Using the discrete-time SEIR model, the paper by Lekone and Finkenstadt strives to estimate the reproduction number and transmission rates of Ebola between the health states in compartmental model for the 1995 epidemic of Ebola in Congo. After estimating transmission rates, this paper addresses how effectively control intervention was used during the outbreak. With control intervention, the outbreak lasted for approximately 200 days. It is recorded that the first case became ill on January 6th, the last case died on July 16th, with a total of 316 cases were identified resulting in a rate of an 81% fatality rate. To study transmission rates, the researchers established the parameters that are derived from the compartmental model. To explore the posterior distribution of the parameters, the authors of the paper apply the SEIR model for the Ebola epidemic and the maximum-likelihood (ML) estimator for the parameters as well as the Markov chain Monte Carlo (MCMC) method. First the researchers simulated the time of epidemic series with the ML estimated parameter values obtained from complete data, then they validated using MCMC with various distributions. Their parameter results are shown on Table 2 and are verified by the literature of Chowell et al. Notably, the researchers concluded that the epidemic could have been lasted more than five times longer and epidemic size could have covered two thirds of the whole population of Congo in absence of intervention. Lekone and Frankstadt have written an important and timely research paper on discrete-time SEIR model with control