On a Discrete SEIR Epidemic Model with Two-Doses Delayed Feedback Vaccination Control on the Susceptible
TL;DR: In this article, a new discrete susceptible-exposed-infectious-recovered (SEIR) epidemic model is presented subject to a feedback vaccination effort involving two doses, which are administered by respecting a certain mutual delay interval.
About: This article is published in Vaccine.The article was published on 2021-04-18 and is currently open access. It has received 10 citations till now. The article focuses on the topics: Epidemic model.
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TL;DR: In this article , the authors considered a COVID-19 model with a double-dose vaccination strategy to control the current outbreak situation in Bangladesh, and the fundamental qualitative analysis of this mathematical model has been performed.
Abstract: COVID-19 is an infectious disease that kills millions of people each year and it is a major public health problem around the globe. The current COVID-19 situation is still now concerning, though the vaccination program is running. In this study, we considered a COVID-19 model with a double-dose vaccination strategy to control the current outbreak situation in Bangladesh. The fundamental qualitative analysis of this mathematical model has been performed. The conditions of positive invariance, boundedness with suitable initial conditions were analyzed. We have estimated the basic reproduction number ( R0 ) for disease transmission and determined that our model contains two equilibrium points: the disease-free equilibrium and a disease-endemic equilibrium. We used the Routh-Hurwitz criteria to determine the stability of the equilibria. The disease will be eradicated from the community if R0 < 1, otherwise the disease persists in the population. To support the qualitative analysis of our model, we performed numerical simulations using MATLAB routine and estimated model parameters. Sensitivity analysis is used to explore the association for Mild and Critical cases concerning the corresponding model parameters. We observed that the most significant parameter to spread the virus is the transmission rate. The numerical simulations showed that a full dose vaccination program significantly reduces the mild and critical cases and has potential impact to eradicate the virus from the community. The information that we generated from our analysis may help the public health professionals to impose the best strategy effectively to control the outbreak situation of the virus in Bangladesh.
18 citations
TL;DR: In this paper , an adaptive susceptible-infected-Removed-Vaccinated (A-SIRV) epidemic model with time-dependent transmission and removal rates is constructed for investigating the dynamics of an epidemic disease such as the COVID-19 pandemic.
Abstract: Abstract An Adaptive Susceptible-Infected-Removed-Vaccinated (A-SIRV) epidemic model with time-dependent transmission and removal rates is constructed for investigating the dynamics of an epidemic disease such as the COVID-19 pandemic. Real data of COVID-19 spread is used for the simultaneous identification of the unknown time-dependent rates and functions participating in the A-SIRV system. The inverse problem is formulated and solved numerically using the Method of Variational Imbedding, which reduces the inverse problem to a problem for minimizing a properly constructed functional for obtaining the sought values. To illustrate and validate the proposed solution approach, the present study used available public data for several countries with diverse population and vaccination dynamics—the World, Israel, The United States of America, and Japan.
7 citations
TL;DR: In this paper, an agent-based model is proposed to simulate the double causality that exists between individual behaviors, influenced by the cultural orientation of a population, and the evolution of an epidemic, focusing on recent studies on the COVID-19 pandemic.
7 citations
TL;DR: In this article , an agent-based model is proposed to simulate the double causality that exists between individual behaviors, influenced by the cultural orientation of a population, and the evolution of an epidemic, focusing on recent studies on the COVID-19 pandemic.
7 citations
01 Mar 2022
TL;DR: In this paper , the authors proposed the inclusion of two vaccination doses in the SEIR model considering a stochastic cellular automaton and showed that the solution can converge early to a disease-free equilibrium for a fraction of individuals vaccinated with the first dose.
Abstract: In this work, to support decision making of immunisation strategies, we propose the inclusion of two vaccination doses in the SEIR model considering a stochastic cellular automaton. We analyse three different scenarios of vaccination: $i) unlimited doses, (ii) limited doses into susceptible individuals, and (iii) limited doses randomly distributed overall individuals. Our results suggest that the number of vaccinations and time to start the vaccination is more relevant than the vaccine efficacy, delay between the first and second doses, and delay between vaccinated groups. The scenario (i) shows that the solution can converge early to a disease-free equilibrium for a fraction of individuals vaccinated with the first dose. In the scenario (ii), few two vaccination doses divided into a small number of applications reduce the number of infected people more than into many applications. In addition, there is a low waste of doses for the first application and an increase of the waste in the second dose. The scenario (iii) presents an increase in the waste of doses from the first to second applications more than the scenario $(ii)$. In the scenario (iii), the total of wasted doses increases linearly with the number of applications. Furthermore, the number of effective doses in the application of consecutive groups decays exponentially overtime.
7 citations
References
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TL;DR: Threshold theorems involving the basic reproduction number, the contact number, and the replacement number $R$ are reviewed for classic SIR epidemic and endemic models and results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups.
Abstract: Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement number $R$ are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of $R_{0}$ and $\sigma$ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.
5,915 citations
TL;DR: It is deduced that the spread of COVID-19 can be under control in all communities considered, if proper restrictions and strong policies are implemented to control the infection rates early from thespread of the disease.
Abstract: In this paper, we study the effectiveness of the modelling approach on the pandemic due to the spreading of the novel COVID-19 disease and develop a susceptible-infected-removed (SIR) model that provides a theoretical framework to investigate its spread within a community Here, the model is based upon the well-known susceptible-infected-removed (SIR) model with the difference that a total population is not defined or kept constant per se and the number of susceptible individuals does not decline monotonically To the contrary, as we show herein, it can be increased in surge periods! In particular, we investigate the time evolution of different populations and monitor diverse significant parameters for the spread of the disease in various communities, represented by China, South Korea, India, Australia, USA, Italy and the state of Texas in the USA The SIR model can provide us with insights and predictions of the spread of the virus in communities that the recorded data alone cannot Our work shows the importance of modelling the spread of COVID-19 by the SIR model that we propose here, as it can help to assess the impact of the disease by offering valuable predictions Our analysis takes into account data from January to June, 2020, the period that contains the data before and during the implementation of strict and control measures We propose predictions on various parameters related to the spread of COVID-19 and on the number of susceptible, infected and removed populations until September 2020 By comparing the recorded data with the data from our modelling approaches, we deduce that the spread of COVID-19 can be under control in all communities considered, if proper restrictions and strong policies are implemented to control the infection rates early from the spread of the disease
477 citations
TL;DR: A model of contagion that unifies and generalizes existing models of the spread of social influences and microorganismal infections is presented, finding that epidemics inevitably die out but may be surprisingly persistent when individuals possess memory.
373 citations
138 citations