Studies of the processes of self-organization and self-assembly of various complexly organized (including spiral) structures based on amino acids intensively carried out in recent years. Various methods of molecular modeling, including molecular dynamics (MD) methods, are developed. In this paper, we propose a new approach for a relatively simple technique for conducting MD simulation (MDS) of various molecular nanostructures, determining the trajectory of the MD run and forming the final structure: a molecular dynamic manipulator (MD manipulator). It is an imitation of the operation of an existing or imaginary device or structure by applying force to the existing initial structure in order to obtain a new final structure, having the same chemical composition, but with a different geometry (topology). The PUMA-CUDA software package was applied as the main MD modeling program, which uses the physics of the PUMA software package, developed by the laboratory headed by N.K. Balabaev. Using this MDS tool, you can investigate the formation of helical structures from a linear sequence of any amino acids variation. As an example, the applicability of the developed algorithm for assembling nanotubes from linear phenylalanine (Phe) chains of different chirality (left L-Phe and right D-Phe) is considered by including additional force effects in the molecular dynamics simulation program for these structures. During the MD run, the applied actions, which are the same for the left and right helices of the formed nanotubes, lead the system to an α-helix structure. The work was carried out in an interactive mode using a number of additional programs, incl. trajectory analyzer program MD (TAMD). As a result, the modes that are most adequate for the formation of nanotubes of the right chirality D from the initial L-Phe monomer and nanotubes of the left chirality L from the D-Phe amino acid monomer were determined. The results obtained were compared with data from other works on modeling similar nanotubes of different chirality and experimental data. These are fully in line with the law of change in sign of chirality of molecular structures with complication of their hierarchical level of organization. The molecular animation of the assembly of a left-chiral nanotube from D-monomers is freely available at: http://lmd.impb.ru/Supplementary/PHE.avi.
{"title":"Assembly of a Phenylalanine Nanotube by the use of Molecular Dynamics Manipulator","authors":"I. Likhachev, V. Bystrov","doi":"10.17537/2021.16.244","DOIUrl":"https://doi.org/10.17537/2021.16.244","url":null,"abstract":"\u0000Studies of the processes of self-organization and self-assembly of various complexly organized (including spiral) structures based on amino acids intensively carried out in recent years. Various methods of molecular modeling, including molecular dynamics (MD) methods, are developed. In this paper, we propose a new approach for a relatively simple technique for conducting MD simulation (MDS) of various molecular nanostructures, determining the trajectory of the MD run and forming the final structure: a molecular dynamic manipulator (MD manipulator). It is an imitation of the operation of an existing or imaginary device or structure by applying force to the existing initial structure in order to obtain a new final structure, having the same chemical composition, but with a different geometry (topology). The PUMA-CUDA software package was applied as the main MD modeling program, which uses the physics of the PUMA software package, developed by the laboratory headed by N.K. Balabaev. Using this MDS tool, you can investigate the formation of helical structures from a linear sequence of any amino acids variation. As an example, the applicability of the developed algorithm for assembling nanotubes from linear phenylalanine (Phe) chains of different chirality (left L-Phe and right D-Phe) is considered by including additional force effects in the molecular dynamics simulation program for these structures. During the MD run, the applied actions, which are the same for the left and right helices of the formed nanotubes, lead the system to an α-helix structure. The work was carried out in an interactive mode using a number of additional programs, incl. trajectory analyzer program MD (TAMD). As a result, the modes that are most adequate for the formation of nanotubes of the right chirality D from the initial L-Phe monomer and nanotubes of the left chirality L from the D-Phe amino acid monomer were determined. The results obtained were compared with data from other works on modeling similar nanotubes of different chirality and experimental data. These are fully in line with the law of change in sign of chirality of molecular structures with complication of their hierarchical level of organization. The molecular animation of the assembly of a left-chiral nanotube from D-monomers is freely available at: http://lmd.impb.ru/Supplementary/PHE.avi.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90268464","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}
We have considered a compartmental epidemiological model with infectious disease to observe the influence of environmental stress on disease transmission. The proposed model is well-defined as the population at each compartment remains positive and bounded with time. Dynamical behaviour of the model is observed by the stability and bifurcation analysis at the equilibrium points. Also, numerical simulation supports the theoretical proofs and the result shows that the system undergoes a forward bifurcation around the disease-free equilibrium. Our results indicate that with the increase of environmental pollution, the overall infected population increases. Also, the disease transmission rate among the susceptible and stressed population from asymptomatically infected individuals plays a crucial role to make a system endemic. A corresponding optimal control problem has also been proposed to control the disease prevalence as well as to minimize the cost by choosing the vaccination policy before being infected and treatment policy to the infected as control variables. Numerical figures indicate that the vaccination provided to susceptible needs some time to reduce the disease transmission but the vaccination provided to stressed individuals works immediately after implementation. The treatment policy for symptomatically infected individuals works with a higher rate at an earlier stage but the intensity decreases with time. Simultaneous implementation of all control interventions is more useful to reduce the size of overall infective individuals and also to minimize the economic burden. Hence, this research clearly expresses the impact of environmental pollution (specifically the influence of environmental stress) on the disease transmission in the population.
{"title":"Dynamics of an Epidemic Model under the Influence of Environmental Stress","authors":"Sangeeta Saha, G. Samanta","doi":"10.17537/2021.16.201","DOIUrl":"https://doi.org/10.17537/2021.16.201","url":null,"abstract":"\u0000We have considered a compartmental epidemiological model with infectious disease to observe the influence of environmental stress on disease transmission. The proposed model is well-defined as the population at each compartment remains positive and bounded with time. Dynamical behaviour of the model is observed by the stability and bifurcation analysis at the equilibrium points. Also, numerical simulation supports the theoretical proofs and the result shows that the system undergoes a forward bifurcation around the disease-free equilibrium. Our results indicate that with the increase of environmental pollution, the overall infected population increases. Also, the disease transmission rate among the susceptible and stressed population from asymptomatically infected individuals plays a crucial role to make a system endemic. A corresponding optimal control problem has also been proposed to control the disease prevalence as well as to minimize the cost by choosing the vaccination policy before being infected and treatment policy to the infected as control variables. Numerical figures indicate that the vaccination provided to susceptible needs some time to reduce the disease transmission but the vaccination provided to stressed individuals works immediately after implementation. The treatment policy for symptomatically infected individuals works with a higher rate at an earlier stage but the intensity decreases with time. Simultaneous implementation of all control interventions is more useful to reduce the size of overall infective individuals and also to minimize the economic burden. Hence, this research clearly expresses the impact of environmental pollution (specifically the influence of environmental stress) on the disease transmission in the population.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82282617","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 stochastic stage-dependent model of spread of an epidemic in a certain region is presented. The model is written in the form of a continuous-discrete random process that takes into account the passage of individuals through various stages of an infectious disease. Within the framework of the model, the population of the region is represented in the form of cohorts of individuals, structured according to immunological, clinical, epidemiological and demographic criteria. All cohorts make up two blocks. Individuals belonging to the cohorts of the first block are considered indistinguishable within a fixed cohort and have the same type of parametric description. Individuals belonging to the cohorts of the second block differ from each other by the time of admission to a particular cohort and by the time of stay in this cohort. An algorithm for statistical modeling of the dynamics of cohorts of individuals based on the Monte Carlo method is developed. A numerical study of the dynamics of cohorts of individuals was conducted for sets of parameters reflecting different variants of transmission of infection between individuals.
{"title":"Direct Statistical Modeling of Spread of Epidemic Based On a Stage-Dependent Stochastic Model","authors":"K. Loginov, N. Pertsev","doi":"10.17537/2021.16.169","DOIUrl":"https://doi.org/10.17537/2021.16.169","url":null,"abstract":"\u0000A stochastic stage-dependent model of spread of an epidemic in a certain region is presented. The model is written in the form of a continuous-discrete random process that takes into account the passage of individuals through various stages of an infectious disease. Within the framework of the model, the population of the region is represented in the form of cohorts of individuals, structured according to immunological, clinical, epidemiological and demographic criteria. All cohorts make up two blocks. Individuals belonging to the cohorts of the first block are considered indistinguishable within a fixed cohort and have the same type of parametric description. Individuals belonging to the cohorts of the second block differ from each other by the time of admission to a particular cohort and by the time of stay in this cohort. An algorithm for statistical modeling of the dynamics of cohorts of individuals based on the Monte Carlo method is developed. A numerical study of the dynamics of cohorts of individuals was conducted for sets of parameters reflecting different variants of transmission of infection between individuals.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73702234","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 considers the problem of the distribution of a quantum particle in a classical one-dimensional lattice with a potential well. The cases of a rigid chain, a Holstein polaron model, and a polaron in a chain with temperature are investigated by direct modeling at fixed parameters. As is known, in the one-dimensional case, a particle is captured by an arbitrarily shallow potential well with an increase of the box size. In the case of a finite chain and finite temperatures, we have quite the opposite result, when a particle, being captured in a well in a short chain, turns into delocalized state with an increase in the chain length. These results may be helpful for further understanding of charge transfer in DNA, where oxoguanine can be considered as a potential well in the case of hole transfer when for excess electron transfer it is thymine dimer.
{"title":"Equilibrium Charge Distribution in a Finite Chain with a Trapping Site","authors":"N. Fialko, M. Olshevets, V. Lakhno","doi":"10.17537/2021.16.152","DOIUrl":"https://doi.org/10.17537/2021.16.152","url":null,"abstract":"\u0000The paper considers the problem of the distribution of a quantum particle in a classical one-dimensional lattice with a potential well. The cases of a rigid chain, a Holstein polaron model, and a polaron in a chain with temperature are investigated by direct modeling at fixed parameters. As is known, in the one-dimensional case, a particle is captured by an arbitrarily shallow potential well with an increase of the box size. In the case of a finite chain and finite temperatures, we have quite the opposite result, when a particle, being captured in a well in a short chain, turns into delocalized state with an increase in the chain length. These results may be helpful for further understanding of charge transfer in DNA, where oxoguanine can be considered as a potential well in the case of hole transfer when for excess electron transfer it is thymine dimer.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"12 1","pages":"152-168"},"PeriodicalIF":0.0,"publicationDate":"2021-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86686303","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}
S. Levashkin, S. Agapov, O. Zakharova, K. N. Ivanov, E. S. Kuzmina, V. Sokolovsky, A. S. Monasova, A. V. Vorobiev, D. N. Apeshin
A systemic approach to the study of a new multi-parameter model of the COVID-19 pandemic spread is proposed, which has the ultimate goal of optimizing the manage parameters of the model. The approach consists of two main parts: 1) an adaptive-compartmental model of the epidemic spread, which is a generalization of the classical SEIR model, and 2) a module for adjusting the parameters of this model from the epidemic data using intelligent optimization methods. Data for testing the proposed approach using the pandemic spread in some regions of the Russian Federation were collected on a daily basis from open sources during the first 130 days of the epidemic, starting in March 2020. For this, a so-called data farm was developed and implemented on a local server (an automated system for collecting, storing and preprocessing data from heterogeneous sources, which, in combination with optimization methods, allows most accurately tune the parameters of the model, thus turning it into an intelligent system to support management decisions). Among all model parameters used, the most important are the rate of infection transmission, the government actions and the population reaction.
{"title":"Study of SEIRD Adaptive-Compartmental Model of COVID-19 Epidemic Spread in Russian Federation Using Optimization Methods","authors":"S. Levashkin, S. Agapov, O. Zakharova, K. N. Ivanov, E. S. Kuzmina, V. Sokolovsky, A. S. Monasova, A. V. Vorobiev, D. N. Apeshin","doi":"10.17537/2021.16.136","DOIUrl":"https://doi.org/10.17537/2021.16.136","url":null,"abstract":"\u0000A systemic approach to the study of a new multi-parameter model of the COVID-19 pandemic spread is proposed, which has the ultimate goal of optimizing the manage parameters of the model. The approach consists of two main parts: 1) an adaptive-compartmental model of the epidemic spread, which is a generalization of the classical SEIR model, and 2) a module for adjusting the parameters of this model from the epidemic data using intelligent optimization methods. Data for testing the proposed approach using the pandemic spread in some regions of the Russian Federation were collected on a daily basis from open sources during the first 130 days of the epidemic, starting in March 2020. For this, a so-called data farm was developed and implemented on a local server (an automated system for collecting, storing and preprocessing data from heterogeneous sources, which, in combination with optimization methods, allows most accurately tune the parameters of the model, thus turning it into an intelligent system to support management decisions). Among all model parameters used, the most important are the rate of infection transmission, the government actions and the population reaction.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83353717","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}
It is shown that DNA molecule can be used for construction of different electronic devices. The results of investigation of DNA conducting properties are presented. The method of DNA based nanowires is considered. It is shown that the conducting properties of DNA can be used for making electronic nanobiochips, which have advantages in comparison with optical one due to their miniaturization, execution speed, absence of marking and exactness. It is also demonstrated the possibility of memory and logic devices made from DNA.
{"title":"Molecular devices based on DNA","authors":"V. Lakhno, A. V. Vinnikov","doi":"10.17537/2021.16.115","DOIUrl":"https://doi.org/10.17537/2021.16.115","url":null,"abstract":"\u0000It is shown that DNA molecule can be used for construction of different electronic devices. The results of investigation of DNA conducting properties are presented. The method of DNA based nanowires is considered. It is shown that the conducting properties of DNA can be used for making electronic nanobiochips, which have advantages in comparison with optical one due to their miniaturization, execution speed, absence of marking and exactness. It is also demonstrated the possibility of memory and logic devices made from DNA.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"15 1","pages":"115-135"},"PeriodicalIF":0.0,"publicationDate":"2021-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80682584","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}
Y. Fritsler, S. Bartsev, O. Belozor, A. Shuvaev, A. Shuvaev
The influence of ryanodine channels on the cytosole Ca2+ dynamics was studied. We added the equations for ryanodine receptors and voltage-gated calcium channels into the original De Pitta et al. model of Ca2+. The derived model was shown to have significantly wider range of predictions: we derived the frequency of cytosole calcium spontaneous oscillations (which are absent in the original De Pitta et al. model) for various existing models of Ca2+ signalling in astrocytes. Particularly, the initial De Pitta et al. results can be converted to either Lavrentovich and Hemkin model or in the Dupont et al model predictions. The absence of the Ca2+ oscillations in astrocytes with the active ryanodine channels only was recently reported. This behaviour can be achieved in our model predictions for the certain values of parameters, which are supposedly responsible for the bifurcation landscape between the oscillatory and non-oscillatory dynamics of cytosol Ca2+ in astrocytes. We also investigated the interplay between the spontaneous and glutamate-triggered oscillations.
{"title":"Modifying the Models of Calcium Dynamics in Astrocytes by Ryanodine Release","authors":"Y. Fritsler, S. Bartsev, O. Belozor, A. Shuvaev, A. Shuvaev","doi":"10.17537/2021.16.86","DOIUrl":"https://doi.org/10.17537/2021.16.86","url":null,"abstract":"\u0000The influence of ryanodine channels on the cytosole Ca2+ dynamics was studied. We added the equations for ryanodine receptors and voltage-gated calcium channels into the original De Pitta et al. model of Ca2+. The derived model was shown to have significantly wider range of predictions: we derived the frequency of cytosole calcium spontaneous oscillations (which are absent in the original De Pitta et al. model) for various existing models of Ca2+ signalling in astrocytes. Particularly, the initial De Pitta et al. results can be converted to either Lavrentovich and Hemkin model or in the Dupont et al model predictions. The absence of the Ca2+ oscillations in astrocytes with the active ryanodine channels only was recently reported. This behaviour can be achieved in our model predictions for the certain values of parameters, which are supposedly responsible for the bifurcation landscape between the oscillatory and non-oscillatory dynamics of cytosol Ca2+ in astrocytes. We also investigated the interplay between the spontaneous and glutamate-triggered oscillations.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"78 1","pages":"86-100"},"PeriodicalIF":0.0,"publicationDate":"2021-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79672606","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 focuses on the study of light influence mechanisms on microalgae culture growth in the turbidostat. The method of turbidostat culture provides the same light conditions for all cells, stabilization of their biochemical composition, as well as the constancy of all physicochemical factors of the environment. The main approaches and principles of modeling the microalgae culture growth are presented. Modern models are shown to be based on classical concepts of considering cell biomass as the sum of two or more compounds. The use of two-component models for microalgae is due to both photochemical and enzymatic processes of biosynthesis of cell structures from mineral substances due to the energy of high-potential forms of macroergs. The proposed mathematical model is represented by a system of two differential equations describing the synthesis of reserve biomass compounds at the expense of light and biosynthesis of structural components from reserve ones. The model takes into account that a part of the reserve compounds is spent on replenishing the pool of macroergs, and a part of the structural component can be converted into a reserve one. The rates of synthesis of structural and reserve forms of biomass are given by linear splines and expressed in terms of the reduced fluxes of the energy or plastic substrate. The model was verified on the experimental data of the chlorophyllostat culture Tetraselmis viridis. It is shown that the light curve of T. viridis is characterized by a double change in the limiting factor and can be divided into a region of metabolic, light limiting and a region of saturation. A decrease in the specific growth rate is related to a decrease in the efficiency of light energy conversion.
{"title":"Two-Component Model of Microalgae Growth in the Turbidostat","authors":"A. Lelekov, R. P. Trenkenshu","doi":"10.17537/2021.16.101","DOIUrl":"https://doi.org/10.17537/2021.16.101","url":null,"abstract":"\u0000The paper focuses on the study of light influence mechanisms on microalgae culture growth in the turbidostat. The method of turbidostat culture provides the same light conditions for all cells, stabilization of their biochemical composition, as well as the constancy of all physicochemical factors of the environment. The main approaches and principles of modeling the microalgae culture growth are presented. Modern models are shown to be based on classical concepts of considering cell biomass as the sum of two or more compounds. The use of two-component models for microalgae is due to both photochemical and enzymatic processes of biosynthesis of cell structures from mineral substances due to the energy of high-potential forms of macroergs. The proposed mathematical model is represented by a system of two differential equations describing the synthesis of reserve biomass compounds at the expense of light and biosynthesis of structural components from reserve ones. The model takes into account that a part of the reserve compounds is spent on replenishing the pool of macroergs, and a part of the structural component can be converted into a reserve one. The rates of synthesis of structural and reserve forms of biomass are given by linear splines and expressed in terms of the reduced fluxes of the energy or plastic substrate. The model was verified on the experimental data of the chlorophyllostat culture Tetraselmis viridis. It is shown that the light curve of T. viridis is characterized by a double change in the limiting factor and can be divided into a region of metabolic, light limiting and a region of saturation. A decrease in the specific growth rate is related to a decrease in the efficiency of light energy conversion.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"86 1","pages":"101-114"},"PeriodicalIF":0.0,"publicationDate":"2021-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76269372","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}
In this manuscript, we design a fractional order delay differential equation model for HIV transmission with the implementation of three distinct therapies for three different infectious stages. We investigate the positivity of solutions, analyze the stability properties, followed by Hopf bifurcation analysis. To probe the parameters that expedite the spread of infection, uncertainty and sensitivity analysis were performed. The numerical review was carried out to substantiate our theoretical results. Our proposed model parameters have been calibrated to fit yearly data from Afghanistan, Australia, France, Italy, Netherlands and New Zealand.
{"title":"An Investigation on Analytical Properties of Delayed Fractional Order HIV Model: A Case Study","authors":"M. Pitchaimani, A. Devi","doi":"10.17537/2021.16.57","DOIUrl":"https://doi.org/10.17537/2021.16.57","url":null,"abstract":"\u0000In this manuscript, we design a fractional order delay differential equation model for HIV transmission with the implementation of three distinct therapies for three different infectious stages. We investigate the positivity of solutions, analyze the stability properties, followed by Hopf bifurcation analysis. To probe the parameters that expedite the spread of infection, uncertainty and sensitivity analysis were performed. The numerical review was carried out to substantiate our theoretical results. Our proposed model parameters have been calibrated to fit yearly data from Afghanistan, Australia, France, Italy, Netherlands and New Zealand.\u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"1 1","pages":"57-85"},"PeriodicalIF":0.0,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89222596","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 aim is to explore a COVID-19 SEIR model involving Atangana-Baleanu Caputo type (ABC) fractional derivatives. Existence, uniqueness, positivity, and boundedness of the solutions for the model are established. Some stability results of the proposed system are also presented. Numerical simulations results obtained in this paper, according to the real data, show that the model is more suitable for the disease evolution.
{"title":"A Fractional Epidemic Model with Mittag-Leffler Kernel for COVID-19","authors":"Hassan Aghdaoui, M. Tilioua, K. Nisar, I. Khan","doi":"10.17537/2021.16.39","DOIUrl":"https://doi.org/10.17537/2021.16.39","url":null,"abstract":"\u0000The aim is to explore a COVID-19 SEIR model involving Atangana-Baleanu Caputo type (ABC) fractional derivatives. Existence, uniqueness, positivity, and boundedness of the solutions for the model are established. Some stability results of the proposed system are also presented. Numerical simulations results obtained in this paper, according to the real data, show that the model is more suitable for the disease evolution. \u0000","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73301705","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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