Pub Date : 2021-03-14DOI: 10.11145/J.BIOMATH.2020.01.067
Yaya Youssouf Yaya, D. Ngom, Mamadou Sy
Qualitative study of higher order non linear dynamical systems? is a rewarding experience and a great challenge. This reflective paper is an attempt to deeply analyze interaction features between nutrients, phytoplanktons and zooplanktons by building a so-called NPZ-Model. We used classical methods (of Lyapunov, Hopf, etc.) to examine existence, positivity, boundedness and stability of solutions. Our main contribution is the implementation of a meaningful space parameter that simultaneously guarantees instability of equilibria at the border and? stability of the internal equilibrium. In the case of internal equilibrium instability, we observed the emergence of limit cycle which means the existence of periodical solutions.
{"title":"Qualitative features of a NPZ-Model.","authors":"Yaya Youssouf Yaya, D. Ngom, Mamadou Sy","doi":"10.11145/J.BIOMATH.2020.01.067","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2020.01.067","url":null,"abstract":"Qualitative study of higher order non linear dynamical systems? is a rewarding experience and a great challenge. This reflective paper is an attempt to deeply analyze interaction features between nutrients, phytoplanktons and zooplanktons by building a so-called NPZ-Model. We used classical methods (of Lyapunov, Hopf, etc.) to examine existence, positivity, boundedness and stability of solutions. Our main contribution is the implementation of a meaningful space parameter that simultaneously guarantees instability of equilibria at the border and? stability of the internal equilibrium. In the case of internal equilibrium instability, we observed the emergence of limit cycle which means the existence of periodical solutions.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41751265","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}
Pub Date : 2020-12-31DOI: 10.11145/j.biomath.2020.12.297
D. Adak, N. Bairagi, R. Hakl
Biological models inherently contain delay. Mathematical analysis of a delay-induced model is, however, more difficult compare to its non-delayed counterpart. Difficulties multiply if the model contains multiple delays. In this paper, we analyze a realistic HIV-1 infection model in the presence and absence of multiple delays. We consider self-proliferation of CD4+T cells, nonlinear saturated infection rate and recovery of infected cells due to incomplete reverse transcription in a basic HIV-1 in-host model and incorporate multiple delays to account for successful viral entry and subsequent virus reproduction from the infected cell. Both of delayed and non-delayed system becomes disease-free if the basic reproduction number is less than unity. In the absence of delays, the infected equilibrium is shown to be locally asymptotically stable under some parametric space and unstable otherwise. The system may show unstable oscillatory behaviour in the presence of either delay even when the non-delayed system is stable. The second delay further enhances the instability of the endemic equilibrium which is otherwise stable in the presence of a single delay. Numerical results are shown to be in agreement with the analytical results and reflect quite realistic dynamics observed in HIV-1 infected individuals.
{"title":"Accounting for multi-delay effects in an HIV-1 infection model with saturated infection rate, recovery and proliferation of host cells","authors":"D. Adak, N. Bairagi, R. Hakl","doi":"10.11145/j.biomath.2020.12.297","DOIUrl":"https://doi.org/10.11145/j.biomath.2020.12.297","url":null,"abstract":"Biological models inherently contain delay. Mathematical analysis of a delay-induced model is, however, more difficult compare to its non-delayed counterpart. Difficulties multiply if the model contains multiple delays. In this paper, we analyze a realistic HIV-1 infection model in the presence and absence of multiple delays. We consider self-proliferation of CD4+T cells, nonlinear saturated infection rate and recovery of infected cells due to incomplete reverse transcription in a basic HIV-1 in-host model and incorporate multiple delays to account for successful viral entry and subsequent virus reproduction from the infected cell. Both of delayed and non-delayed system becomes disease-free if the basic reproduction number is less than unity. In the absence of delays, the infected equilibrium is shown to be locally asymptotically stable under some parametric space and unstable otherwise. The system may show unstable oscillatory behaviour in the presence of either delay even when the non-delayed system is stable. The second delay further enhances the instability of the endemic equilibrium which is otherwise stable in the presence of a single delay. Numerical results are shown to be in agreement with the analytical results and reflect quite realistic dynamics observed in HIV-1 infected individuals.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41469056","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}
Pub Date : 2020-10-26DOI: 10.11145/j.biomath.2020.09.107
J. Ndam
A model describing the dynamics of COVID-19 is formulated and examined. The model is meant to address the impacts of lockdown and social isolation as strategies for the eradication of the pandemic. Local stability analysis indicate that the equilibria are locally-asymptotically stable for R0<1 and R_0>1 for the disease-free equilibrium and the endemic equilibrium respectively. Numerical simulations of the model equations show that lockdown is a more effective strategy in the eradication of the disease than social isolation. However, strict enforcement of both strategies is the most effective means that could end the disease within a shorter period of time.
{"title":"Modelling the impacts of lockdown and isolation on the eradication of COVID-19","authors":"J. Ndam","doi":"10.11145/j.biomath.2020.09.107","DOIUrl":"https://doi.org/10.11145/j.biomath.2020.09.107","url":null,"abstract":"A model describing the dynamics of COVID-19 is formulated and examined. The model is meant to address the impacts of lockdown and social isolation as strategies for the eradication of the pandemic. Local stability analysis indicate that the equilibria are locally-asymptotically stable for R0<1 and R_0>1 for the disease-free equilibrium and the endemic equilibrium respectively. Numerical simulations of the model equations show that lockdown is a more effective strategy in the eradication of the disease than social isolation. However, strict enforcement of both strategies is the most effective means that could end the disease within a shorter period of time.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48723446","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}
Pub Date : 2020-09-12DOI: 10.11145/J.BIOMATH.2020.08.173
Anuraag Bukkuri
We consider a mathematical model of human immunodeficiency virus (HIV) infection dynamics of T lymphocyte (T cell), infected T cell, and viral populations under reverse transcriptase inhibitor (RTI) andprotease inhibitor (PI) treatment. Existence, uniqueness, and characterization of optimal treatment profiles which minimize total amount of drug used, viral, and infected T cell populations, while maximizing levels of T cells are determined analytically. Numerical optimal control experiments are also performed to illustrate how burst rate of infected T cells and shedding rate of virions impact optimal treatment profiles. Finally, a sensitivity analysis is performed to detect how model input parameters contribute to output variance.
{"title":"The impact of infected T lymphocyte burst rate and viral shedding rate on optimal treatment scheduling in a human immunodeficiency virus infection","authors":"Anuraag Bukkuri","doi":"10.11145/J.BIOMATH.2020.08.173","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2020.08.173","url":null,"abstract":"We consider a mathematical model of human immunodeficiency virus (HIV) infection dynamics of T lymphocyte (T cell), infected T cell, and viral populations under reverse transcriptase inhibitor (RTI) andprotease inhibitor (PI) treatment. Existence, uniqueness, and characterization of optimal treatment profiles which minimize total amount of drug used, viral, and infected T cell populations, while maximizing levels of T cells are determined analytically. Numerical optimal control experiments are also performed to illustrate how burst rate of infected T cells and shedding rate of virions impact optimal treatment profiles. Finally, a sensitivity analysis is performed to detect how model input parameters contribute to output variance.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48134007","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}
Pub Date : 2020-09-12DOI: 10.11145/J.BIOMATH.2020.08.227
John J. H. Miller, E. O'Riordan
A system of two coupled nonlinear initial value equations, arising in the mathematical modelling of enzyme kinetics, is examined. The system is singularly perturbed and one of the components will contain steep gradients. A priori parameter explicit bounds on the two components are established. A numerical method incorporating a specially constructed piecewise-uniform mesh is used to generate numerical approximations, which are shown to converge pointwise to the continuous solution irrespective of the size of the singular perturbation parameter. Numerical results are presented to illustrate the computational performance of the numerical method. The numerical method is also remarkably simple to implement.
{"title":"Robust numerical method for a singularly perturbed problem arising in the modelling of enzyme kinetics","authors":"John J. H. Miller, E. O'Riordan","doi":"10.11145/J.BIOMATH.2020.08.227","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2020.08.227","url":null,"abstract":"A system of two coupled nonlinear initial value equations, arising in the mathematical modelling of enzyme kinetics, is examined. The system is singularly perturbed and one of the components will contain steep gradients. A priori parameter explicit bounds on the two components are established. A numerical method incorporating a specially constructed piecewise-uniform mesh is used to generate numerical approximations, which are shown to converge pointwise to the continuous solution irrespective of the size of the singular perturbation parameter. Numerical results are presented to illustrate the computational performance of the numerical method. The numerical method is also remarkably simple to implement. ","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41738225","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}
Pub Date : 2020-08-08DOI: 10.11145/j.biomath.2020.06.143
Musa Rabiu, R. Willie, N. Parumasur
We develop a virus-resistant HIV-1 mathematical model with behavioural change in HIV-1 resistant non-progressors. The model has both disease-free and endemic equilibrium points that are proved to be locally asymptotically stable depending on the value of the associated reproduction numbers. In both models, a non-linear Goh{Volterra Lyapunov function was used to prove that the endemic equilibrium point is globally asymptotically stable for special case while the method of Castillo-Chavez was used to prove the global asymptotic stability of the disease-free equilibrium point. In both the analytic and numerical results, this study shows that in the context of resistance to HIV/AIDS, total abstinence can also play an important role in protection against this notorious infectious disease.
{"title":"Analysis of a virus-resistant HIV-1 model with behavior change in non-progressors","authors":"Musa Rabiu, R. Willie, N. Parumasur","doi":"10.11145/j.biomath.2020.06.143","DOIUrl":"https://doi.org/10.11145/j.biomath.2020.06.143","url":null,"abstract":"We develop a virus-resistant HIV-1 mathematical model with behavioural change in HIV-1 resistant non-progressors. The model has both disease-free and endemic equilibrium points that are proved to be locally asymptotically stable depending on the value of the associated reproduction numbers. In both models, a non-linear Goh{Volterra Lyapunov function was used to prove that the endemic equilibrium point is globally asymptotically stable for special case while the method of Castillo-Chavez was used to prove the global asymptotic stability of the disease-free equilibrium point. In both the analytic and numerical results, this study shows that in the context of resistance to HIV/AIDS, total abstinence can also play an important role in protection against this notorious infectious disease.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43150684","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}
Pub Date : 2020-06-18DOI: 10.20944/preprints202006.0224.v1
Mouhamadou Diaby, Oumar Diop, A. Konté, A. Sène
The outburst of the COVID-19 pandemic has raised several questions leading to a complex system in terms of modeling. Indeed, the modeling of the epidemic, at the level of a country, needs considering each of the different sources of contamination as well as the public health authorities strategy, in a specific way. With this in mind, in the present paper, we develop a mathematical model of the COVID-19 epidemic in Senegal. In the model, the population is subdivided into five compartments: susceptible, infected but asymptomatic, symptomatic, quarantined, and recovered immune people. In addition, due to its important impact on the propagation of the disease, we add one more variable: the number of infected objects. Therefore, the model corresponds to a system of six non-linear ordinary differential equations we submit to an analytical study to prove the relevancy of the model, simulate the evolution of the epidemic, and retrieve epidemiological parameters, namely the infection rate and the basic reproduction number. Based on the senegalese territory COVID-19 data, we simulate various scenarios as for the evolution of the epidemic in the country, in order to predict the peak and its magnitude with regard to the application of barrier measures. We also explore the option of collective immunity with special protection for vulnerable people. In doing so, non-available parameters are identified using some mathematical identification technics.
{"title":"COVID-19 propagation mathematical modeling: the case of Senegal","authors":"Mouhamadou Diaby, Oumar Diop, A. Konté, A. Sène","doi":"10.20944/preprints202006.0224.v1","DOIUrl":"https://doi.org/10.20944/preprints202006.0224.v1","url":null,"abstract":"The outburst of the COVID-19 pandemic has raised several questions leading to a complex system in terms of modeling. Indeed, the modeling of the epidemic, at the level of a country, needs considering each of the different sources of contamination as well as the public health authorities strategy, in a specific way. With this in mind, in the present paper, we develop a mathematical model of the COVID-19 epidemic in Senegal. In the model, the population is subdivided into five compartments: susceptible, infected but asymptomatic, symptomatic, quarantined, and recovered immune people. In addition, due to its important impact on the propagation of the disease, we add one more variable: the number of infected objects. Therefore, the model corresponds to a system of six non-linear ordinary differential equations we submit to an analytical study to prove the relevancy of the model, simulate the evolution of the epidemic, and retrieve epidemiological parameters, namely the infection rate and the basic reproduction number. Based on the senegalese territory COVID-19 data, we simulate various scenarios as for the evolution of the epidemic in the country, in order to predict the peak and its magnitude with regard to the application of barrier measures. We also explore the option of collective immunity with special protection for vulnerable people. In doing so, non-available parameters are identified using some mathematical identification technics.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43522519","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}
Pub Date : 2020-05-17DOI: 10.11145/j.biomath.2020.05.033
N. Kyurkchiev
The cumulative distribution function (cdf) of the discrete two--parameter bathtub hazard distribution has important role in the fields of population dynamics, reliability analysis and life testing experiments. Also of interest to the specialists is the task of approximating the Heaviside function by new (cdf) in Hausdorff sense. We define new activation function and family of new recurrence generated functions and study the ''saturation'' by these families. In this paper we analyze some intrinsic properties of the new Topp-Leone-G-Family with baseline ''deterministic-type'' (cdf) - (NTLG-DT). Some numerical examples with real data from Biostatistics, Population dynamics and Signal theory, illustrating our results are given. It is shown that the study of the two characteristics - "confidential curves" and ''super saturation'' is a must when choosing the right model. Some related problems are discussed, as an example to the Approximation Theory.
{"title":"A new class of activation functions. Some related problems and applications","authors":"N. Kyurkchiev","doi":"10.11145/j.biomath.2020.05.033","DOIUrl":"https://doi.org/10.11145/j.biomath.2020.05.033","url":null,"abstract":"The cumulative distribution function (cdf) of the discrete two--parameter bathtub hazard distribution has important role in the fields of population dynamics, reliability analysis and life testing experiments. Also of interest to the specialists is the task of approximating the Heaviside function by new (cdf) in Hausdorff sense. We define new activation function and family of new recurrence generated functions and study the ''saturation'' by these families. In this paper we analyze some intrinsic properties of the new Topp-Leone-G-Family with baseline ''deterministic-type'' (cdf) - (NTLG-DT). Some numerical examples with real data from Biostatistics, Population dynamics and Signal theory, illustrating our results are given. It is shown that the study of the two characteristics - \"confidential curves\" and ''super saturation'' is a must when choosing the right model. Some related problems are discussed, as an example to the Approximation Theory.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43679747","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}
Pub Date : 2020-05-11DOI: 10.11145/j.biomath.2020.05.103
R. Anguelov, J. Banasiak, C. Bright, J. Lubuma, R. Ouifki
The paper draws attention to the asymptomatic and mildly symptomatic cases of COVID-19, which, according to some reports, may constitute a large fraction of the infected individuals. These cases are often unreported and are not captured in the total number of confirmed cases communicated daily. On the one hand, this group may play a significant role in the spread of the infection, as asymptomatic cases are seldom detected and quarantined. On the other hand, it may play a significant role in disease extinction by contributing to the development of sufficient herd immunity.
{"title":"The big unknown: The asymptomatic spread of COVID-19","authors":"R. Anguelov, J. Banasiak, C. Bright, J. Lubuma, R. Ouifki","doi":"10.11145/j.biomath.2020.05.103","DOIUrl":"https://doi.org/10.11145/j.biomath.2020.05.103","url":null,"abstract":"The paper draws attention to the asymptomatic and mildly symptomatic cases of COVID-19, which, according to some reports, may constitute a large fraction of the infected individuals. These cases are often unreported and are not captured in the total number of confirmed cases communicated daily. On the one hand, this group may play a significant role in the spread of the infection, as asymptomatic cases are seldom detected and quarantined. On the other hand, it may play a significant role in disease extinction by contributing to the development of sufficient herd immunity.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43684078","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}
Pub Date : 2020-05-04DOI: 10.11145/j.biomath.2020.05.047
H. Kojouharov
The goal of the series is to provide a platform for rapid communication and exchange of ideas concerning the COVID-19 epidemic. It is new and unlike the known virus-induced diseases. There is a significant research effort, including mathematical modelling, to understand the characteristics of the virus SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) and the epidemiological dynamics of COVID-19, the disease caused by it. Due to their novelty, the research is often likely to produce results only on specific aspects of the disease, provide just partial answers to research questions, or collect evidence for formulating hypothesis yet to be tested. We believe, however, that the significance of the pandemic for the human population makes it essential to share even such partial results as soon as they are available to facilitate the advancement of the research on this disease. While eventually, a more comprehensive picture of both the virus and the disease will emerge, even incomplete but timely and scientifically-based information will help the authorities to make sound decisions on the course of action during the epidemic. For the series, we invite publications on any aspect of the COVID-19 epidemic. Specifically, the series aims to cover • the biological research, providing an understanding of the relevant structures and causal relationships in the epidemiological environment, which can facilitate mathematical or statistical modelling, • mathematical models of the structures, causal interactions and epidemiological data, and their analysis, • mathematical models and analysis of the socio-economic aspects of the pandemic, • any new mathematical methods, applicable to the study of any of the mentioned topics. All submissions to the series will be prioritised for a fast peer-review.
{"title":"COVID-19 Research Communications (Editorial)","authors":"H. Kojouharov","doi":"10.11145/j.biomath.2020.05.047","DOIUrl":"https://doi.org/10.11145/j.biomath.2020.05.047","url":null,"abstract":"The goal of the series is to provide a platform for rapid communication and exchange of ideas concerning the COVID-19 epidemic. It is new and unlike the known virus-induced diseases. There is a significant research effort, including mathematical modelling, to understand the characteristics of the virus SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) and the epidemiological dynamics of COVID-19, the disease caused by it. Due to their novelty, the research is often likely to produce results only on specific aspects of the disease, provide just partial answers to research questions, or collect evidence for formulating hypothesis yet to be tested. We believe, however, that the significance of the pandemic for the human population makes it essential to share even such partial results as soon as they are available to facilitate the advancement of the research on this disease. While eventually, a more comprehensive picture of both the virus and the disease will emerge, even incomplete but timely and scientifically-based information will help the authorities to make sound decisions on the course of action during the epidemic. For the series, we invite publications on any aspect of the COVID-19 epidemic. Specifically, the series aims to cover • the biological research, providing an understanding of the relevant structures and causal relationships in the epidemiological environment, which can facilitate mathematical or statistical modelling, • mathematical models of the structures, causal interactions and epidemiological data, and their analysis, • mathematical models and analysis of the socio-economic aspects of the pandemic, • any new mathematical methods, applicable to the study of any of the mentioned topics. All submissions to the series will be prioritised for a fast peer-review.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49135068","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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