We propose a probabilistic approach to modelling the propagation of the coronavirus disease 2019 (COVID-19) in Madagascar, with all its specificities. With the strategy of the Malagasy state, which consists of isolati...We propose a probabilistic approach to modelling the propagation of the coronavirus disease 2019 (COVID-19) in Madagascar, with all its specificities. With the strategy of the Malagasy state, which consists of isolating all suspected cases and hospitalized confirmed case, we get an epidemic model with seven compartments: susceptible (S), Exposed (E), Infected (I), Asymptomatic (A), Hospitalized (H), Cured (C) and Death (D). In addition to the classical deterministic models used in epidemiology, the stochastic model offers a natural representation of the evolution of the COVID-19 epidemic. We inferred <span><span style="font-family:Verdana;">the models with the official data provided by the COVID-19 Command Center (CCO) of Madagascar, between March and August 2020. The basic reproduction number <i></i></span><i><i><span style="font-family:Verdana;">R<sub></sub></span></i></i></span><i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><i><span style="font-family:Verdana;"><sub>0</sub></span></i></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><i><span style="font-family:Verdana;"></span></i></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"></span></span></span></i> and the other parameters were estimated with a Bayesian approach. We developed an algorithm that allows having a temporal estimate of this number with confidence intervals. The estimated values are slightly lower than the international references. Generally, we were able to obtain a simple but effective model to describe the spread of the disease.展开更多
The stage of a tumor is sometimes hard to predict, especially early in its development. The size and complexity of its observations are the major problems that lead to false diagnoses. Even experienced doctors can mak...The stage of a tumor is sometimes hard to predict, especially early in its development. The size and complexity of its observations are the major problems that lead to false diagnoses. Even experienced doctors can make a mistake in causing terrible consequences for the patient. We propose a mathematical tool for the diagnosis of breast cancer. The aim is to help specialists in making a decision on the likelihood of a patient’s condition knowing the series of observations available. This may increase the patient’s chances of recovery. With a multivariate observational hidden Markov model, we describe the evolution of the disease by taking the geometric properties of the tumor as observable variables. The latent variable corresponds to the type of tumor: malignant or benign. The analysis of the covariance matrix makes it possible to delineate the zones of occurrence for each group belonging to a type of tumors. It is therefore possible to summarize the properties that characterize each of the tumor categories using the parameters of the model. These parameters highlight the differences between the types of tumors.展开更多
<span style="font-family:Verdana;">For Madagascar, with the uncertainty over vaccines against the novel coronavirus 2019 and its variants, non-pharmaceutical approach is widely used. Our objective is t...<span style="font-family:Verdana;">For Madagascar, with the uncertainty over vaccines against the novel coronavirus 2019 and its variants, non-pharmaceutical approach is widely used. Our objective is to propose a mathematical control model which will serve as a tool to help decision-makers in the strategy to be implemented to better face the pandemic</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">.</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> By separating asymptomatic cases which are often not reported and symptomatic who are hospitalized after tests;we develop a mathematical model of the propagation of covid-19 in Madagascar, by integrating control strategies. We study the stability of the model by expressing the basic reproduction number using the next-generation matrix. Simulation with different parameters shows the effects of non-pharmaceutical measures on the speed of the disease spread. By integrating a control parameter linked to compliance with barrier measures in the virus propagation equation, we were able to show the impacts of the implementation of social distancing measures on the basic reproduction number. The strict application of social distancing measures and total confinement </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">is</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> unfavorable for economic situation even if they allow the contamination to be reduced quickly. Without any restrictions, the disease spreads at high speed and the peak is reached fairly quickly. In this condition, hospitals are overwhelmed and the death rate increases rapidly. With 50% respect for non-pharmaceutical strategies such as rapid detection and isolation of positive cases and barrier gestures;the basic reproduction numbe展开更多
文摘We propose a probabilistic approach to modelling the propagation of the coronavirus disease 2019 (COVID-19) in Madagascar, with all its specificities. With the strategy of the Malagasy state, which consists of isolating all suspected cases and hospitalized confirmed case, we get an epidemic model with seven compartments: susceptible (S), Exposed (E), Infected (I), Asymptomatic (A), Hospitalized (H), Cured (C) and Death (D). In addition to the classical deterministic models used in epidemiology, the stochastic model offers a natural representation of the evolution of the COVID-19 epidemic. We inferred <span><span style="font-family:Verdana;">the models with the official data provided by the COVID-19 Command Center (CCO) of Madagascar, between March and August 2020. The basic reproduction number <i></i></span><i><i><span style="font-family:Verdana;">R<sub></sub></span></i></i></span><i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><i><span style="font-family:Verdana;"><sub>0</sub></span></i></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><i><span style="font-family:Verdana;"></span></i></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"></span></span></span></i> and the other parameters were estimated with a Bayesian approach. We developed an algorithm that allows having a temporal estimate of this number with confidence intervals. The estimated values are slightly lower than the international references. Generally, we were able to obtain a simple but effective model to describe the spread of the disease.
文摘The stage of a tumor is sometimes hard to predict, especially early in its development. The size and complexity of its observations are the major problems that lead to false diagnoses. Even experienced doctors can make a mistake in causing terrible consequences for the patient. We propose a mathematical tool for the diagnosis of breast cancer. The aim is to help specialists in making a decision on the likelihood of a patient’s condition knowing the series of observations available. This may increase the patient’s chances of recovery. With a multivariate observational hidden Markov model, we describe the evolution of the disease by taking the geometric properties of the tumor as observable variables. The latent variable corresponds to the type of tumor: malignant or benign. The analysis of the covariance matrix makes it possible to delineate the zones of occurrence for each group belonging to a type of tumors. It is therefore possible to summarize the properties that characterize each of the tumor categories using the parameters of the model. These parameters highlight the differences between the types of tumors.
文摘<span style="font-family:Verdana;">For Madagascar, with the uncertainty over vaccines against the novel coronavirus 2019 and its variants, non-pharmaceutical approach is widely used. Our objective is to propose a mathematical control model which will serve as a tool to help decision-makers in the strategy to be implemented to better face the pandemic</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">.</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> By separating asymptomatic cases which are often not reported and symptomatic who are hospitalized after tests;we develop a mathematical model of the propagation of covid-19 in Madagascar, by integrating control strategies. We study the stability of the model by expressing the basic reproduction number using the next-generation matrix. Simulation with different parameters shows the effects of non-pharmaceutical measures on the speed of the disease spread. By integrating a control parameter linked to compliance with barrier measures in the virus propagation equation, we were able to show the impacts of the implementation of social distancing measures on the basic reproduction number. The strict application of social distancing measures and total confinement </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">is</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> unfavorable for economic situation even if they allow the contamination to be reduced quickly. Without any restrictions, the disease spreads at high speed and the peak is reached fairly quickly. In this condition, hospitals are overwhelmed and the death rate increases rapidly. With 50% respect for non-pharmaceutical strategies such as rapid detection and isolation of positive cases and barrier gestures;the basic reproduction numbe
