Community behavior for mathematical model of coronavirus disease 2019 (COVID-19)

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Coronavirus disease 2019 (COVID-19) is an infectious disease caused by a coronavirus originating from the city of Wuhan in 2019. This disease affects the respiratory system. The city of Pontianak has the highest population density in West Kalimantan. This density results in a higher spread of Covid-19. In this article, the spread of COVID-19 is formulated into a mathematical model, equilibrium points are sought, stability is analyzed, and a delay time is introduced to reduce the spread of COVID-19. The magnitude of the delay time given during quarantine complies with health protocols, which is between 2 – 14 days. This article aims to analyze the influence of the delay time in modeling the spread of Covid-19. The problem of COVID-19 spread is constructed into an SIQR model, with a sub-population of recovered individuals returning to the susceptible sub-population. The population is divided into four sub-populations: susceptible (S), Infected (I), Quarantined (Q), and Recovered (R). The parameters used include the natural birth rate ( ), the rate of susceptibility to infection ( ), the rate of infection under quarantine ( ), the recovery rate from infection ( ), the recovery rate from infection under quarantine ( ), the death rate from infection ( ), the death rate under quarantine ( ), the delay time from infection to quarantine process ( ), the natural death rate ( ), and the rate of recovered immunity returning to susceptibility ( ). The simulation results show that when the basic reproduction number is less than , the disease-free equilibrium is stable, and when the basic reproduction number is greater than , the endemic equilibrium point is stable. The addition of a time delay ( ) in the SIQR model affects the stability of the endemic equilibrium point but does not affect the stability of the disease-free equilibrium point.

Guidance and Best Practices for Nuclear Cardiology Laboratories During the COVID-19 Pandemic: An Information Statement From ASNC and SNMMI.

Coronavirus Disease 2019 (COVID-19) is an infectious disease that has been declared a global pandemic by the World Health Organization (WHO). Indonesia is one of the countries affected by this disease and has spread to all provinces including West Papua Province. The purpose of writing this article is to determine a model for the spread of COVID-19 in West Papua, to analyze the point of equilibrium and stability and to determine the basic reproduction number R_0 model. The model used is the SIR epidemiological model and to analyze the equilibrium point and data collection, the author used the Mapple 13 application. The result of this study are a mathematical model based on the assumptions of the spread of COVID-19 in West Papua namely:dS/dt=-βSI/N.dI/dt=βSI/N-αI.dR/dt=αI.The equilibrium obtained based on the equilibrium analysis is the non-endemic equilibrium point, namely E=(S_0,I_0,R_0 )=(N,0,0)which is categorized as stabil neutral. The basic reproduction number (R_0 ) obtained based on the SIR COVID-19 model in West Papua isR_0=β/αwith R_0=1,2. Because the value of R_0>1 means that the spread of COVID-19 in West Papua will increase to become an epidemic.
 Keywords: SIR, COVID-19, Equilibrium Point, Basic Reproduction Number.

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<p indent="0mm">As the novel coronavirus disease 2019 (COVID-19) has become a Public Health Emergency of International Concern, it is greatly significant to accurately predict the disease's incoming trend. Herein, we performed a stage-rolling Susceptible-Exposed-Infectious-Recovered (SEIR) model to measure the evolution of the basic reproduction number of COVID-19, based on the number of confirmed infections announced by the National Health Commission of the People's Republic of China. We assumed that the infected number under the spreading of infectious diseases will generally experience two different stages. In the first stage, due to the public's ignorance of the severity and harmfulness of the disease, the infected population grows exponentially and the process of disease transmission can be considered as the classic SEIR model with a constant basic reproduction number. Consequently, with limited awareness of the epidemic situation, there is a lack of effective preventive measures to control disease transmission. In the second stage, various control measures and medical resources are introduced in succession by the government, as well as the public gradually takes effective preventions (e.g. keep social distance and wear masks) based on the knowledge of the disease transmission. Collectively, the infected population grows much slower than the first stage. We performed a stage-rolling SEIR model, in which the basic reproduction number changes every day. Based on this model, the number of daily basic reproduction is estimated from the daily new infection number. We found that the daily basic reproduction number is expected to decline continually until it is less than 1, which means the eradication of the disease. Leveraging the evolution of the basic reproduction number, we extrapolate the incoming daily basic reproduction number, based on which we further predict the incoming trend of COVID-19 spreading in terms of the daily infection number. Our predictive model estimates that at the end of the epidemic, the total number of infections in China is nearly 14000 except for Hubei Province, and 32000 except for Wuhan city. We also found that in most parts of China, the number of newly confirmed infections increases linearly rather than exponentially before the day of "Wuhan travel restrictions", implying that the prevention and containing the infected people from Wuhan at the eve of the Spring Festival has been effective from the beginning.

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