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Estimating the basic reproductive ratio for the Ebola outbreak in Liberia and Sierra Leone

Infectious Diseases of Poverty 2015年第1期4卷 114-121页

作者： Adnan Khan Mahim Naveed Muhammad Dur-e-Ahmad Mudassar Imran Department of Mathematics Lahore University of Management SciencesLahorePakistan Department of Mathematics State University of New York at PlattsburghPlattsburghNYUSA Department of Mathematics Waterloo UniversityWaterlooONCanada Department of Mathematics and Natural Sciences GULF University for Science and TechnologyMubarak Al-AbdullahWest MishrefKuwait

Background:Ebola virus disease has reemerged as a major public health crisis in Africa,with isolated cases also observed globally,during the current ***:To estimate the basic reproductive ratio R0,which is a measure of the severity of the outbreak,we developed a SEIR(susceptible-exposed-infected-recovered)type deterministic model,and used data from the Centers for Disease Control and Prevention(CDC),for the Ebola outbreak in Liberia and Sierra *** different data sets are available:one with raw reported data and one with corrected data(as the CDC suspects under-reporting).Results:Using a deterministic ordinary differential equation transmission model for Ebola epidemic,the basic reproductive ratio R0 for Liberia resulted to be 1.757 and 1.9 for corrected and uncorrected case data,*** Sierra Leone,R0 resulted to be 1.492 and 1.362 for corrected and uncorrected case data,*** each of the two cases we considered,the estimate for the basic reproductive ratio was initially greater than unity leading to an epidemic ***:We obtained robust estimates for the value of R0 associated with the 2014 Ebola outbreak,and showed that there is close agreement between our estimates of *** of our model also showed that effective isolation is required,with the contact rate in isolation less than one quarter of that for the infected non-isolated population,and that the fraction of high-risk individuals must be brought to less than 10%of the overall susceptible population,in order to bring the value of R0 to less than 1,and hence control the outbreak.

关键词： Epidemiology Ebola virus disease Transmission model basic reproductive ratio

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Modelling the Effect of Self-Immunity and the Impacts of Asymptomatic and Symptomatic Individuals on COVID-19 Outbreak

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Computer Modeling in Engineering & Sciences 2020年第12期125卷 1033-1060页

作者： M.H.A.Biswas M.A.Islam S.Akter S.Mandal M.S.Khatun S.A.Samad A.K.Paul M.R.Khatun Mathematics Discipline Science Engineering and Technology SchoolKhulna UniversityKhulna9208Bangladesh Department of Mathematics Bangabandhu Sheikh Mujibur Rahman Science and Technology UniversityGopalganj8100Bangladesh

COVID-19 is one of themost highly infectious diseases ever emerged and caused by newly discovered severe acute respiratory syndrome coronavirus 2(SARS-CoV-2).It has already led the entire world to health and economic *** has invaded the whole universe all most every *** present study demonstrates with a nine mutually exclusive compartmental model on transmission dynamics of this pandemic disease(COVID-19),with special focus on the transmissibility of symptomatic and asymptomatic infection from susceptible ***,the compartmental model has been investigated with mathematical analysis and computer simulations in order to understand the dynamics of COVID-19 ***,mathematical analysis of the model has been carried out in broadly by illustrating some well-known methods including exactness,equilibrium and stability analysis in terms of basic reproduction *** investigate the sensitivity of the model with respect to the variation of the parameters’***,computer simulations are performed to illustrate the *** analysis reveals that the death rate from coronavirus disease increases as the infection rate increases,whereas infection rate extensively decreases with the increase of quarantined *** quarantined individuals also lead to increase the concentration of recovered ***,the infection rate of COVID-19 increases more surprisingly as the rate of asymptomatic individuals increases than that of the symptomatic ***,the infection rate decreases significantly due to increase of self-immunity rate.

关键词： COVID-19 asymptomatic and symptomatic individuals selfimmunity mathematical model basic reproductive ratio numerical simulations

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Analysis of a hepatitis B viral infection model with immune response delay

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International Journal of Biomathematics 2017年第2期10卷 93-110页

作者： Jianhua Pang Jing-An Cui School of Science Guangxi University of Science and Technology Liuzhou 545006 P. R. China School of ScienceBeijing University of Civil Engineering and Architecture Beijing 100044 P. R. China

In this paper, a hepatitis B viral infection model with a density-dependent proliferation rate of cytotoxic T lymphocyte （CTL） cells and immune response delay is investigated. By analyzing the model, we show that the virus-free equilibrium is globally asymptotically stable, if the basic reproductive ratio is less than one and an endemic equilibrium exists if the basic reproductive ratio is greater than one. By using the stability switches criterion in the delay-differential system with delay-dependent parameters, we present that the stability of endemic equilibrium changes and eventually become stable as time delay increases. This means majority of hepatitis B infection would eventually become a chronic infection due to the immune response time delay is fairly long. Numerical simulations are carried out to explain the mathematical conclusions and biological implications.

关键词： Immune response delay density-dependent rate basic reproductive ratio stability switch.

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Stochastic and spatio-temporal analysis of the Middle East Respiratory Syndrome outbreak in South Korea, 2015

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Infectious Disease Modelling 2019年第1期4卷 227-238页

作者： Hyunsun Lee Department of Mathematics Hawai'i Pacific UniversityHonoluluHI 96813USA

South Korea was free of the Middle East Respiratory Syndrome(MERS)until *** MERS outbreak in South Korea during 2015 was the largest outbreak of the Coronavirus outside the Middle *** major characteristic of this outbreak is inter-or intra-hospital *** recent MERS outbreak in South Korea is examined and assessed in this *** main objectives of the study is to characterize the pattern of the MERS outbreak in South Korea based on a basic reproductive ratio,the probability of ultimate extinction of the disease,and the spatio-temporal proximity of occurrence between *** survival function method and stochastic branching process model are adapted to calculate the basic reproductive ratio and the probability of ultimate extinction of the *** further investigate the occurrence pattern of the outbreak using a spatio-temporal autocorrelation function.

关键词： Middle East Respiratory Syndrome basic reproductive ratio Probability of ultimate extinction Autocorrelation

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