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Revisiting classical sir modelling in light of the COVID-19 pandemic

Infectious Disease Modelling 2023年第1期8卷 72-83页

作者： Leonid Kalachev Erin L.Landguth Jon Graham Mathematical Sciences University of MontanaMissoulaUSA Center for Population Health Research School of Public and Community Health SciencesUniversity of MontanaMissoulaUSA

Background:Classical infectious disease models during epidemics have widespread usage,from predicting the probability of new infections to developing vaccination plans for informing policy decisions and public health ***,it is important to correctly classify reported data and understand how this impacts estimation of model *** COVID-19 pandemic has provided an abundant amount of data that allow for thorough testing of disease modelling assumptions,as well as how we think about classical infectious disease modelling ***:We aim to assess the appropriateness of model parameter estimates and preiction results in classical infectious disease compartmental modelling frameworks given available data types(infected,active,quarantined,and recovered cases)for situations where just one data type is available to fit the *** main focus is on how model prediction results are dependent on data being assigned to the right model ***:We first use simulated data to explore parameter reliability and prediction capability with three formulations of the classical Susceptible-Infected-Removed(sir)modelling *** then explore two applications with reported data to assess which data and models are sufficient for reliable model parameter estimation and prediction accuracy:a classical influenza outbreak in a boarding school in England and COVID-19 data from the fall of 2020 in Missoula County,Montana,***:We demonstrated the magnitude of parameter estimation errors and subsequent prediction errors resulting from data misclassification to model compartments with simulated *** showed that prediction accuracy in each formulation of the classical disease modelling framework was largely determined by correct data classification versus *** a classical example of influenza epidemics in an England boarding school,we argue that the Susceptible-Infected-Quarantined-Recovered(SIQR)model is more appropriat

关键词： Basic disease reproduction number Communicable disease control Coronavirus COVID-19 Disease transmission Epidemics Epidemiology Influenza data Mathematical models Montana sir models

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Law of mass action and saturation in sir model with application to Coronavirus modelling

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Infectious Disease Modelling 2021年第1期6卷 91-97页

作者： Theodore Kolokolnikov David Iron Department of Mathematics and Statistics Dalhousie UniversityHalifaxNova ScotiaCanada

When using sir and related models,it is common to assume that the infection rate is proportional to the product of susceptible and infected *** this assumption works at the onset of the outbreak,the infection force saturates as the outbreak progresses,even in the absence of any *** use a simple agentebased model to illustrate this saturation *** continuum limit leads a modified sir model with exponential *** derivation is based on first principles incorporating the spread radius and population *** use the data for coronavirus outbreak for the period from March to June,to show that using sir model with saturation is sufficient to capture the disease dynamics for many jurstictions,including the overall world-wide disease curve *** model suggests the R_(0) value of above 8 at the onset of infection,but with infection quickly“flattening out”,leading to a long-term sustained sub-exponential spread.

关键词： COVID-19 sir models Saturation

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Impact of climate factors on contact rate of vector-borne diseases： Case study of malaria

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International Journal of Biomathematics 2017年第1期10卷 77-97页

作者： Ezekiel Dangbe Antoine Perasso Damakoa Irepran David Bekol1e The University Institute of Technology University of Ngaoundere UMR6249 Chrono-Environment Laboratory University of Franche-Comte The Faculty of Sciences University of Ngaoundere P. O. Boz 454 Ngaoundere Cameroon

Climate change influences more and more of our activities. These changes led to envi- ronmental changes which has in turn affected the spatial and temporal distribution of the incidence of vector-borne diseases. To establish the impact of climate on contact rate of vector-borne diseases, we examine the variation of prevalence of diseases according to season. In this paper, the goal is to establish that the basic reproductive number R0 depends on the duration of transmission period and the date of the first conta- mination case that was declared （to） in the specific ease of malaria. We described the dynamics of transmission of malaria by using non-autonomous differential equations. We analyzed the stability of endemic equilibrium （EE） and disease-free equilibrium （DFE）. We prove that the persistence of disease depends on minimum and maximum values of contact rate of vector-borne diseases.

关键词： sir models vector-borne disease impact of climate factors malaria.

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