{"title":"Modeling of human breath: conceptual and mathematical statements","authors":"P.V. Trusov, N.V. Zaitseva, M.Yu. Tsinker","doi":"10.17537/2023.18.t38","DOIUrl":"https://doi.org/10.17537/2023.18.t38","url":null,"abstract":"","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135353944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper proposes and studies a two-component discrete-time model of the prey-predator community considering zooplankton and fish interactions and their development features. Discrete-time systems of equations allow us to take into account naturally the rhythm of many processes occurring in marine and freshwater communities, which are subject to cyclical fluctuations due to the daily and seasonal cycle. We describe the dynamics of fish and zooplankton populations constituting the community by Ricker’s model, which is well-studied and widely used in population modeling. To consider the species interaction, we use the Holling-II type response function taking into account predator saturation. We carried out the study of the proposed model. The system is shown to have from one to three non-trivial equilibria, which gives the existence of the complete community. In addition to the saddle-node bifurcation, which generates bistability of stationary dynamics, a nontrivial equilibrium loses its stability according to the Neimark-Sacker scenario with an increase in the reproductive potential of both predator and prey species, as a result of which the community exhibits long-period oscillations similar to those observed in experiments. With the higher bifurcation parameter, the reverse Neimark-Sacker bifurcation is shown to occur followed by the closed invariant curve collapses, and dynamics of the population stabilizes, later losing stability through a cascade of period-doubling bifurcations. Multistability complicates the birth and disappearance of the invariant curve in the phase space scenario by the emergence of another irregular dynamics in the system with the single unstable nontrivial fixed point. At fixed values of the model parameters and different initial conditions, the system considered is shown to demonstrate various quasi-periodic oscillations. Despite extreme simplicity, the proposed discrete-time model of community dynamics demonstrates a wide variety and variability of dynamic modes. It shows that the influence of environmental conditions can change the type and nature of the observed dynamics.
{"title":"Complex Dynamics Modes in a Simple Model of Prey-Predator Community: Bistability and Multistability","authors":"G. P. Neverova, O. Zhdanova","doi":"10.17537/2023.18.308","DOIUrl":"https://doi.org/10.17537/2023.18.308","url":null,"abstract":"\u0000 The paper proposes and studies a two-component discrete-time model of the prey-predator community considering zooplankton and fish interactions and their development features. Discrete-time systems of equations allow us to take into account naturally the rhythm of many processes occurring in marine and freshwater communities, which are subject to cyclical fluctuations due to the daily and seasonal cycle. We describe the dynamics of fish and zooplankton populations constituting the community by Ricker’s model, which is well-studied and widely used in population modeling. To consider the species interaction, we use the Holling-II type response function taking into account predator saturation. We carried out the study of the proposed model. The system is shown to have from one to three non-trivial equilibria, which gives the existence of the complete community. In addition to the saddle-node bifurcation, which generates bistability of stationary dynamics, a nontrivial equilibrium loses its stability according to the Neimark-Sacker scenario with an increase in the reproductive potential of both predator and prey species, as a result of which the community exhibits long-period oscillations similar to those observed in experiments. With the higher bifurcation parameter, the reverse Neimark-Sacker bifurcation is shown to occur followed by the closed invariant curve collapses, and dynamics of the population stabilizes, later losing stability through a cascade of period-doubling bifurcations. Multistability complicates the birth and disappearance of the invariant curve in the phase space scenario by the emergence of another irregular dynamics in the system with the single unstable nontrivial fixed point. At fixed values of the model parameters and different initial conditions, the system considered is shown to demonstrate various quasi-periodic oscillations. Despite extreme simplicity, the proposed discrete-time model of community dynamics demonstrates a wide variety and variability of dynamic modes. It shows that the influence of environmental conditions can change the type and nature of the observed dynamics.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87362504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E.M. Pozdnyakov, A. Korneichuk, A. V. Rogacheva, G. Vasilev
Breaks that appear in DNA and violate its integrity are a serious threat to the life of the cell. There is a special repair system for their recovery, which includes many different enzymes. However, the exact mechanisms of this process are currently still unclear. In this article, we considered single-strand discontinuities based on the Michaelis–Menten equation and using the quasi-equilibrium approximation. A scheme of interaction between the mechanisms of the reparation system was developed and a computational model was built in the COPASI software to verify it. As a result of the work, the dependences of the concentrations of the participants in the repair system were obtained, and the known experimental data were also approximated. We observed that the plot with a logarithmic scale of fully corrected DNA concentration versus time is close to a sigmoid. We obtained that, the polymerase enzymatic reaction is the limiting factor for the rate of DNA repair and the rate of ligase operation is limited by the rate of DNA appearance. Being a regulatory link in the DNA repair system, polymerase and its parameters exert a control influence on the rest of the model parameters. In turn, the parameters for PARP1, PNKP, and LIG3α should provide rates of enzymatic reactions higher than the rate of polymerase operation.
{"title":"Polymerase β Limits the Rate of DNA Single-Strand Break Repair","authors":"E.M. Pozdnyakov, A. Korneichuk, A. V. Rogacheva, G. Vasilev","doi":"10.17537/2023.18.294","DOIUrl":"https://doi.org/10.17537/2023.18.294","url":null,"abstract":"\u0000 Breaks that appear in DNA and violate its integrity are a serious threat to the life of the cell. There is a special repair system for their recovery, which includes many different enzymes. However, the exact mechanisms of this process are currently still unclear. In this article, we considered single-strand discontinuities based on the Michaelis–Menten equation and using the quasi-equilibrium approximation. A scheme of interaction between the mechanisms of the reparation system was developed and a computational model was built in the COPASI software to verify it. As a result of the work, the dependences of the concentrations of the participants in the repair system were obtained, and the known experimental data were also approximated. We observed that the plot with a logarithmic scale of fully corrected DNA concentration versus time is close to a sigmoid. We obtained that, the polymerase enzymatic reaction is the limiting factor for the rate of DNA repair and the rate of ligase operation is limited by the rate of DNA appearance. Being a regulatory link in the DNA repair system, polymerase and its parameters exert a control influence on the rest of the model parameters. In turn, the parameters for PARP1, PNKP, and LIG3α should provide rates of enzymatic reactions higher than the rate of polymerase operation.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83354344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
By producing the required proteins, the process of gene expression establishes the physical properties of living things. Gene expression from DNA or RNA may be recorded using a variety of approaches. Regression analysis has evolved in prominence in the area of genetic research recently. Several of the genes in high dimensional gene expression information for statistical inference may not be related to their illnesses, which is one of the major problems. The ability of gene selection to enhance the outcomes of several techniques has been demonstrated. For censored survival data, the Cox proportional hazards regression model is the most widely used model. In order to identify important genes and achieve high classification accuracy, a new technique for selecting the tuning parameter is suggested in this study using an optimization algorithm. According to experimental findings, the suggested strategy performs much better than the two rival methods in terms of the area under the curve and the number of chosen genes. This study provides a comprehensive assessment of the latest work on performance evaluation of regression analysis in gene selection. In addition to its performance analysis, this research conducts a thorough assessment of the numerous efforts done on various extended models based on gene selection in recent years.
{"title":"An Investigational Modeling Approach for Improving Gene Selection using Regularized Cox Regression Model","authors":"G. Abdallh, Z. Algamal","doi":"10.17537/2023.18.282","DOIUrl":"https://doi.org/10.17537/2023.18.282","url":null,"abstract":"\u0000 By producing the required proteins, the process of gene expression establishes the physical properties of living things. Gene expression from DNA or RNA may be recorded using a variety of approaches. Regression analysis has evolved in prominence in the area of genetic research recently. Several of the genes in high dimensional gene expression information for statistical inference may not be related to their illnesses, which is one of the major problems. The ability of gene selection to enhance the outcomes of several techniques has been demonstrated. For censored survival data, the Cox proportional hazards regression model is the most widely used model. In order to identify important genes and achieve high classification accuracy, a new technique for selecting the tuning parameter is suggested in this study using an optimization algorithm. According to experimental findings, the suggested strategy performs much better than the two rival methods in terms of the area under the curve and the number of chosen genes. This study provides a comprehensive assessment of the latest work on performance evaluation of regression analysis in gene selection. In addition to its performance analysis, this research conducts a thorough assessment of the numerous efforts done on various extended models based on gene selection in recent years.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81343232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Targeted approach to recognition of coronavirus subgenus on the base of codon frequency distribution in the N-gene of nucleocapsid protein was proposed in the work. Deviation of codon frequency distribution in the N-gene of coronavirus genome analyzed from the same distributions for the 67 prototypic strains, which characterize the 23 subgenera in the four coronavirus genera, is calculated on the base of statistics in the approach proposed. The smallest value of such a deviation from certain prototypic strain points at subgenus to which this strain belongs. The approach proposed appeared to be effective and supports significance for recognizing coronavirus subgenus at least 99 %. Populations of the 38 and 7 codons providing for needed efficiency level were selected out of all codons of the genetic code in accordance with their frequency distribution. The codons from the populations outlined fix taxonomic structure of coronavirus subgenus.
{"title":"Choice of Target in the Genomes of Prototypic Strains to Recognize Subgenus of Coronaviruses","authors":"M. Chaley, V. Kutyrkin","doi":"10.17537/2023.18.267","DOIUrl":"https://doi.org/10.17537/2023.18.267","url":null,"abstract":"\u0000 Targeted approach to recognition of coronavirus subgenus on the base of codon frequency distribution in the N-gene of nucleocapsid protein was proposed in the work. Deviation of codon frequency distribution in the N-gene of coronavirus genome analyzed from the same distributions for the 67 prototypic strains, which characterize the 23 subgenera in the four coronavirus genera, is calculated on the base of statistics in the approach proposed. The smallest value of such a deviation from certain prototypic strain points at subgenus to which this strain belongs. The approach proposed appeared to be effective and supports significance for recognizing coronavirus subgenus at least 99 %. Populations of the 38 and 7 codons providing for needed efficiency level were selected out of all codons of the genetic code in accordance with their frequency distribution. The codons from the populations outlined fix taxonomic structure of coronavirus subgenus.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81765169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A.D. Borodulina, E. Kutumova, G. Lifshits, F. Kolpakov
Hypertension is a pathology caused by increased systolic and/or diastolic blood pressure. The disease can be controlled by various antihypertensive drugs. This study simulates the response of the human cardiovascular and renal systems to the action of the angiotensin II receptor blocker azilsartan medoxomil, taking into account dual combinations of this drug with the thiazide diuretic hydrochlorothiazide, the $upbeta$-blocker bisoprolol and the calcium channel blocker amlodipine. For this purpose, we consider an agent-based mathematical model of blood pressure regulation, previously developed in the BioUML software and including pharmacodynamic functions for hydrochlorothiazide, bisoprolol, and amlodipine. To simulate the effect of azilsartan, we extended the model with a dose-dependent constant that reduces the rate of binding of angiotensin II to AT1 receptors in accordance with the pharmacological action of the drug. The identification of this constant was carried out on the basis of known clinical trials of azilsartan. The model was tested on a population of virtual patients (equilibrium parametrizations of the model within the specified physiological constraints) with uncomplicated hypertension and uniformly distributed values of systolic/diastolic blood pressure and heart rate. Then, a methodological issue of adapting the model to the clinical parameters of a real patient was considered.
{"title":"Mathematical Modeling of Antihypertensive Therapy with Azilsartan Medoxomil on the Example of Clinical Data of a Real Patient","authors":"A.D. Borodulina, E. Kutumova, G. Lifshits, F. Kolpakov","doi":"10.17537/2023.18.228","DOIUrl":"https://doi.org/10.17537/2023.18.228","url":null,"abstract":"\u0000Hypertension is a pathology caused by increased systolic and/or diastolic blood pressure. The disease can be controlled by various antihypertensive drugs. This study simulates the response of the human cardiovascular and renal systems to the action of the angiotensin II receptor blocker azilsartan medoxomil, taking into account dual combinations of this drug with the thiazide diuretic hydrochlorothiazide, the $upbeta$-blocker bisoprolol and the calcium channel blocker amlodipine. For this purpose, we consider an agent-based mathematical model of blood pressure regulation, previously developed in the BioUML software and including pharmacodynamic functions for hydrochlorothiazide, bisoprolol, and amlodipine. To simulate the effect of azilsartan, we extended the model with a dose-dependent constant that reduces the rate of binding of angiotensin II to AT1 receptors in accordance with the pharmacological action of the drug. The identification of this constant was carried out on the basis of known clinical trials of azilsartan. The model was tested on a population of virtual patients (equilibrium parametrizations of the model within the specified physiological constraints) with uncomplicated hypertension and uniformly distributed values of systolic/diastolic blood pressure and heart rate. Then, a methodological issue of adapting the model to the clinical parameters of a real patient was considered.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83997359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper develops an approach to modeling the processes of self-assembly of complex molecular nanostructures by molecular dynamics methods using a molecular dynamics manipulator. Previously, this approach was considered using the example of assembling a phenylalanine helical nanotube from a linear set of chains of phenylalanine (F) molecules of different chirality: left-handed L-F and right-handed D-F chirality L-FF and D-FF. The process of self-assembly of dipeptide chains into helical structures of nanotubes is an imitation of applying certain forces to the existing initial linear structure in order to obtain the final structure of the same chemical composition, but with a different helical geometry. The PUMA-CUDA molecular dynamics simulation software package was used as the main software. Using this tool, one can investigate the formation of helical structures from a linear sequence of any amino acids. A comparative analysis of the structures of nanotubes obtained by assembling by molecular dynamics methods and by their experimental self-assembly was performed using the method of visual differential analysis. It has been established that the obtained data correspond to the law of the sign change of chirality of molecular helical structures with the complication of their hierarchical level of organization.
{"title":"Assembly of a Diphenylalanine Peptide Nanotube by Molecular Dynamics Methods","authors":"I. Likhachev, V. Bystrov, S. Filippov","doi":"10.17537/2023.18.251","DOIUrl":"https://doi.org/10.17537/2023.18.251","url":null,"abstract":"\u0000 The paper develops an approach to modeling the processes of self-assembly of complex molecular nanostructures by molecular dynamics methods using a molecular dynamics manipulator. Previously, this approach was considered using the example of assembling a phenylalanine helical nanotube from a linear set of chains of phenylalanine (F) molecules of different chirality: left-handed L-F and right-handed D-F chirality L-FF and D-FF. The process of self-assembly of dipeptide chains into helical structures of nanotubes is an imitation of applying certain forces to the existing initial linear structure in order to obtain the final structure of the same chemical composition, but with a different helical geometry. The PUMA-CUDA molecular dynamics simulation software package was used as the main software. Using this tool, one can investigate the formation of helical structures from a linear sequence of any amino acids. A comparative analysis of the structures of nanotubes obtained by assembling by molecular dynamics methods and by their experimental self-assembly was performed using the method of visual differential analysis. It has been established that the obtained data correspond to the law of the sign change of chirality of molecular helical structures with the complication of their hierarchical level of organization.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73271200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bioinformatics technologies play a significant and growing role in life science research, and as these technologies develop, so does the complexity of data. The challenge of biological data growth has given rise to a number of bioinformatics data centers that offer services and solutions ranging from large-scale biosystems analyze that accounts for entire OMICs to nanoscale experiments where molecular modeling can provide insight o structure and dynamics of molecular complexes of biological components. Obviously, this kind of research requires a highly specialized level of computational and statistical expertise, as well as high-performance resources. The importance of information technology is growing, as is the use of computer information systems throughout the world. There are more and more specialized data centers and they consume more energy. The development of new strategies for energy efficiency of data centers is becoming relevant. These strategies aim to reduce the amount of energy consumed by data centers and their environmental impact without sacrificing performance. The article examines performance metrics, proposes a new method for data center energy efficiency, and discusses the role of artificial intelligence techniques in achieving these goals.
{"title":"Data Center Efficiency Model: A New Approach and the Role of Artificial Intelligence","authors":"E. Isaev, V. Kornilov, A. A. Grigoriev","doi":"10.17537/2023.18.215","DOIUrl":"https://doi.org/10.17537/2023.18.215","url":null,"abstract":"\u0000Bioinformatics technologies play a significant and growing role in life science research, and as these technologies develop, so does the complexity of data. The challenge of biological data growth has given rise to a number of bioinformatics data centers that offer services and solutions ranging from large-scale biosystems analyze that accounts for entire OMICs to nanoscale experiments where molecular modeling can provide insight o structure and dynamics of molecular complexes of biological components. Obviously, this kind of research requires a highly specialized level of computational and statistical expertise, as well as high-performance resources. The importance of information technology is growing, as is the use of computer information systems throughout the world. There are more and more specialized data centers and they consume more energy. The development of new strategies for energy efficiency of data centers is becoming relevant. These strategies aim to reduce the amount of energy consumed by data centers and their environmental impact without sacrificing performance. The article examines performance metrics, proposes a new method for data center energy efficiency, and discusses the role of artificial intelligence techniques in achieving these goals.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"114 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80247226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper is devoted to the short review and application of sensitivity-based identifiability approaches for analyzing mathematical models of epidemiology and related processes described by systems of differential equations and agent-based models. It is shown that for structural identifiability of basic SIR models (describe the dynamic of Susceptible, Infected and Removed groups based on nonlinear ordinary differential equations) of epidemic spread and linear compartmental models it is possible to use a priori information about the process. It is demonstrated that a model can be structurally identifiable but be practically non-identifiable due to incomplete data. The paper uses methods for analyzing the sensitivity of parameters to data variation, as well as analyzing the sensitivity of model states to parameter variation, based on linear and differential algebra, Bayesian, and Monte Carlo approaches. It was shown that in the SEIR-HCD model of COVID-19 propagation, described by a system of seven ordinary differential equations and based on the mass balance law, the parameter of humoral immunity acquisition is the least sensitive to changes in the number of diagnosed, critical and mortality cases of COVID-19. The spatial SEIR-HCD model of COVID-19 propagation demonstrated an increase the sensitivity of the partial immunity duration parameter over time, as well as a decrease in the limits of change in the infectivity and infection parameters. In the case of the SEIR-HCD mean-field model of COVID-19 propagation, the sensitivity of the system to the self-isolation index and the lack of sensitivity of the stochastic parameters of the system are shown. In the case of the agent-based COVID-19 propagation model, the change in the infectivity parameter was reduced by more than a factor of 2 compared to the statistics. A differential model of co-infection HIV and tuberculosis spread with multiple drug resistance was developed and its local identifiability was shown.
{"title":"The Identifiability of Mathematical Models in Epidemiology: Tuberculosis, HIV, COVID-19","authors":"O. Krivorotko, S. Kabanikhin, V. Petrakova","doi":"10.17537/2023.18.177","DOIUrl":"https://doi.org/10.17537/2023.18.177","url":null,"abstract":"\u0000The paper is devoted to the short review and application of sensitivity-based identifiability approaches for analyzing mathematical models of epidemiology and related processes described by systems of differential equations and agent-based models. It is shown that for structural identifiability of basic SIR models (describe the dynamic of Susceptible, Infected and Removed groups based on nonlinear ordinary differential equations) of epidemic spread and linear compartmental models it is possible to use a priori information about the process. It is demonstrated that a model can be structurally identifiable but be practically non-identifiable due to incomplete data. The paper uses methods for analyzing the sensitivity of parameters to data variation, as well as analyzing the sensitivity of model states to parameter variation, based on linear and differential algebra, Bayesian, and Monte Carlo approaches. It was shown that in the SEIR-HCD model of COVID-19 propagation, described by a system of seven ordinary differential equations and based on the mass balance law, the parameter of humoral immunity acquisition is the least sensitive to changes in the number of diagnosed, critical and mortality cases of COVID-19. The spatial SEIR-HCD model of COVID-19 propagation demonstrated an increase the sensitivity of the partial immunity duration parameter over time, as well as a decrease in the limits of change in the infectivity and infection parameters. In the case of the SEIR-HCD mean-field model of COVID-19 propagation, the sensitivity of the system to the self-isolation index and the lack of sensitivity of the stochastic parameters of the system are shown. In the case of the agent-based COVID-19 propagation model, the change in the infectivity parameter was reduced by more than a factor of 2 compared to the statistics. A differential model of co-infection HIV and tuberculosis spread with multiple drug resistance was developed and its local identifiability was shown.\u0000\u0000\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83334037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A continuous-discrete stochastic model of the epidemic process is presented. The model takes into account several stages of the development of an infectious disease, as well as the distributions of the durations of stay of individuals in these stages. The variables of the model are integer random variables that denote the quantity of individuals in cohorts, and sets of unique types of individuals that take into account the current state and history of stay of individuals in the stages of development of an infectious disease, distributions of durations of these stages are different from exponential or geometric. The results of an analytical and numerical research of the dynamics of the epidemic process are presented. The probabilities of infection eradication during a finite period of time are examined, depending on the numerical values of the infection spread coefficient and the distributions of the durations of the latent stage of the disease and the stage of preservation of immunity to infection.
{"title":"Stochastic Modeling of the Epidemic Process Based On a Stage-Dependent Model with Non-Markov Constraints for Individuals","authors":"N. Pertsev, V. Topchii, K. Loginov","doi":"10.17537/2023.18.145","DOIUrl":"https://doi.org/10.17537/2023.18.145","url":null,"abstract":"\u0000A continuous-discrete stochastic model of the epidemic process is presented. The model takes into account several stages of the development of an infectious disease, as well as the distributions of the durations of stay of individuals in these stages. The variables of the model are integer random variables that denote the quantity of individuals in cohorts, and sets of unique types of individuals that take into account the current state and history of stay of individuals in the stages of development of an infectious disease, distributions of durations of these stages are different from exponential or geometric. The results of an analytical and numerical research of the dynamics of the epidemic process are presented. The probabilities of infection eradication during a finite period of time are examined, depending on the numerical values of the infection spread coefficient and the distributions of the durations of the latent stage of the disease and the stage of preservation of immunity to infection.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82551938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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