SIR+A mathematical model for evaluating and predicting 2016–2017 ARVI-influenza incidence by using on the Moscow territory

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Influenza is a major challenge to global healthcare due to its high transmissivity and ability to cause major epidemics. Influenza epidemics and pandemics are associated with changes in the society structure that contribute to the spread of new viral strains in certain environmental and social settings. Currently, influenza is one of the most common global diseases that results in annual epidemics or even pandemics, often leading to lethal outcome. Influenza viruses are uniquely prone to variability via point mutations, recombination and gene reassortment accompanied with changes in their biological properties considered as the main cause of uncontrolled infection spread. Hence, examining cohorts of predisposed individuals by using probability models provides not only additional information about viral outbreaks, but also allows monitoring dynamics of viral epidemics in controlled areas. Understanding influenza epidemiology is crucial for restructuring healthcare resources. Public healthcare service mainly relies on influenza vaccination. However, there are vulnerable cohorts such as elderly and immunocompromised individuals, which usually contain no protective antiinfluenza virus antibody level. Despite advances in the developing vaccines and chemotherapy, large-scale influenza epidemics still continue to emerge. Upon that, no reliable methods for disease prognosis based on rate of ongoing epidemic situation are currently available. Monitoring and predicting emerging epidemics is complicated due to discrepancy between dynamics of influenza epidemics that might be evaluated by using surveillance data as well as platform for tracking influenza incidence rate. However, it may be profoundly exacerbated by mutations found in the influenza virus genome by altering genuine morbidity dynamics. Use of probabilistic models for assessing parameters of stochastic epidemics would contribute to more accurately predicted changes in morbidity rate. Here, an SIR+A probabilistic model considering a relationship between infected, susceptible and protected individuals as well as the aggressiveness of external risks for predicting changes in influenza morbidity rate that allowed to evaluate and predict the 2016 ARVI influenza incidence rate in Moscow area. Moreover, introducing an intensity of infection parameter allows to conduct a reliable analysis of incidence rate and predict its changes.

About the authors

N. A. Kontarov

I.M. Sechenov First Moscow State Medical University;
I.I. Mechnikov Research Institute of Vaccines and Sera

Author for correspondence.

PhD (Biology), Аssociate Professor, Department of Medical and Biological Physics;

Senior Researcher, Laboratory of Childhood Viral Infections, 

105064, Moscow, Small Kazenny Lane, 5a

Russian Federation

G. V. Arkharova

I.M. Sechenov First Moscow State Medical University


PhD (Biology), Аssociate Professor, Department of Medical and Biological Physics,


Russian Federation

Yu. B. Grishunina

A.N. Tikhonov Moscow Institute of Electronics and Mathematics, National Research University “Higher School of Economics”


Senior Lecturer, Department of Applied Mathematics,


Russian Federation

S. A. Grishunina

A.N. Tikhonov Moscow Institute of Electronics and Mathematics, National Research University “Higher School of Economics”;
Lomonosov Moscow State University


Assistant Professor, Department of Applied Mathematics;

PhD Student, Department of Probability Theory, Faculty of Mechanics and Mathematics,


Russian Federation

N. V. Yuminova

I.I. Mechnikov Research Institute of Vaccines and Sera


PhD, MD (Biology), Professor, Deputy Director for Science, Head of the Laboratory of Childhood Viral Infections,


Russian Federation


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Copyright (c) 2019 Kontarov N.A., Arkharova G.V., Grishunina Y.B., Grishunina S.A., Yuminova N.V.

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