# L. A. Rvachev's research while affiliated with Gamaleya Institute of Epidemiology and Microbiology and other places

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## Publications (12)

In modern medicine it becomes more and more urgent every year to solve new epidemiological problems. One of these is the evolution of resistance to antibiotics of a large spectrum of microorganisms; this resistance is a consequence of the mass administration of antibiotics. In this problem it becomes necessary to apply the mathematical methods of e...

X- susceptible; Y - ill, with a natural strain such as is cured by means of the given antibiotic; Y ill, with a new variation of the strain, resistant to the given antibiotic; Z - immune. Let the quantities x(t), y(t), y(t), z(t) denote the corresponding counts of people. We emphasize that states Y and Y are to be taken as identical in all other as...

Influenza epidemics at a city or country level can be observed only through a daily officially registered morbidity, or briefly DORM. The influenza model for any country is defined as some set of equations containing the DORM for cities in that country as unknown functions of time, these being designed to approximate the cities' real DORM.

In modern medicine it becomes more and more urgent every year to solve new epidemiological problems. One of these is the evolution of resistance to antibiotics of a large spectrum of microorganisms; this resistance is a consequence of the mass administration of antibiotics. In this problem it becomes necessary to apply the mathematical methods of e...

Influenza epidemics at a city or country level can be observed only through a daily officially registered morbidity, or briefly DORM. The influenza model for any country is defined as some set of equations containing the DORM for cities in that country as unknown functions of time, these being designed to approximate the cities' real DORM.

## Citations

... Models generate predictions that can be compared with data and extrapolated to predict, for example, the future evolution of resistance or the impact of public health interventions. Early models of antibiotic resistance evolution have been designed from the 1970s (Krus & Rvachev, 1971;Massad, Lundberg, & Yang, 1993), but more influential models were formulated from the late 1990s (Bonhoeffer, Lipsitch, & Levin, 1997;Levin et al., 1997;. ...

... Mobility restriction strategies like cordon sanitaire were implemented for controlling various epidemics such as bubonic plague (1666) [47], yellow fever (1793, 1821, 1882 [33], and cholera (1830, 1884) [9]. Some of the early efforts that estimated the impact of mobility through mathematical analysis on disease outbreak include [4,49], which are followed by few other studies. The relationship between mobility and disease spread are reported in [2,8,24,32]. ...

... Classic metapopulation dynamics focuses on the processes of local extinction, recolonization and regional persistence [21,22] as the outcome of the interplay between migration processes and population dynamics, and has been successfully applied to understand the epidemic dynamics of spatially-structured populations with well-defined social units (e.g., families, villages, towns, cities, regions) connected through individuals' mobility [3][4][5][6][7][8][9][23][24][25][26][27][28]. The metapopulation dynamics of infectious diseases has generated a wealth of models and results that consider both mechanistic approaches that take the movement of individuals explicitly into account [9,[29][30][31][32][33][34] and effective coupling approaches wherein the diffusion process is expressed as a force of infection coupling different subpopulations [6,8,[35][36][37][38][39]. Recently, the metapopulation approach has been implemented in data-driven computational models for the large-scale analysis of the geographical spreading of infectious diseases [28,[40][41][42][43][44][45]. ...

... At the forefront of global concern are diseases that can be spread through various forms of mobility including travel and trade [3,6]. Consequently, it has increasingly attracted the interest of theoreticians and epidemiologists to quantify the impact of mobility on infectious disease dynamics [7]. Indeed, epidemiologists are tasked to understand the cause of a disease, to predict its course, and to develop approaches capable of preventing and controlling outbreaks/infections. ...

... An attempt to link the ordinary differential equations for antigens j :1 · 1 " :l .j 'J (viruses) and antibodies for the individuals with the transmission dynamics in the whole population was made by Rvachev (1967), but this has not been followed up. Most infectious disease models neglect the number of parasites per host and reduce the whole process to a succession of two discrete states: latent and infectious. ...

... The first such type of models was applied by W. Kermack and A. Mc-Kendrick [4][5][6], who expanded the model of R. Ross and H. Hudson [7], and built a model based on the types S (susceptible), I (infected) and R (recovered) to study the epidemic nature of infectious diseases. The first to study the models of epidemic actions on the terrain of Ukraine and the USSR were L.A. Rvachev and O.V. Baroyan, who used this approach to model the incidence of influenza [8][9]. ...