On the validation of an epidemiological model (original) (raw)
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AIP Conference Proceedings, 2019
AIP Conference Proceedings, Volume 2075, Issue 1 https://aip.scitation.org/doi/abs/10.1063/1.5091434 The main purpose of the study above is to analyze the epidemiological model developed in the paper “A Core Group Model for disease transmission” written by K.P. Hadeler and C. Castill-Chavez [K.P. Hadeler and C. Castill-Chavez,“A Core Group Model for Disease Transmission”, Math. Biosci. 128, 41-55 (1995)]”. The paper focuses on the presentation of the model formulation process as well as the mathematical analysis process of the model. What is more the paper also covers the biological aspects emerging from the previous processes and the demographic results obtained after the application of an educational/prophylactics/vaccination program. The S.I.V. epidemiological model introduced here is expressed by a non-linear dynamic system which involves the population groups, the death and birth rate of every group, the disease transmission rate, the recovery and vaccination rate. The paper attempts to determine and explore the threshold conditions for the spread of the disease, the multiple stationary states and the parametric areas where backward bifurcation occurs. Finally, a lot of emphasis is given on the significance of the backward bifurcation phenomena concerning the prophylactics or partially effective vaccination enforced on a population.
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Pandemics have always posed a great problem in the history of the world, leading to fatal dangers, which is why mathematicians have been challenged to bring their contribution to the management of pandemics, by applying their theoretical paradigms in describing, studying and forecasting their evolution. Compartmental models, i.e. exponential systems, have been remarkable for studying the spread of epidemics. This paper has three objectives: to purpose a generalization of the SEIRV (Susceptible-Exposed-Infected-Recovered-Vaccinated) model for studying the spread of an epidemics and simulation; to present conditions of existence for a solution to the purposed generalized SEIRV model; and to calculate the reproduction number in certain state conditions of the analyzed dynamic system. The conclusions are that, generally, mathematical models with many parameters can be used to forecast epidemics with better accuracy and, also, the elements from the theory of fixed points for multivalued operators can be used for the analysis of epidemics.