Pub Date : 2021-05-15DOI: 10.1504/IJDSDE.2021.10037984
Samhita Das, P. Das, P. Das
In this paper, we have considered a nonautonomous susceptible, infected, removed (SIR) model with saturation incidence rate for disease transmission. The global dynamical properties like permanence and global stability of the system as well as extinction of disease are analytically and numerically studied. The impact of behavioural patterns of individuals on disease control is validated along with possible applications. Furthermore, Pontryagin's Maximum Principle is used to characterise optimal level of the two controls, treatment and awareness level. Our objective is to minimise the infected population as well as the cost of applied control. The controls at optimal level are found to achieve different levels of impact on infection. It is observed that the combined impact of treatment and awareness exhibits more effective result in disease control compared to their single application. Based on observation, the strategy regarding the implementation of awareness and treatment is suggested.
{"title":"Optimal control of behaviour and treatment in a nonautonomous SIR model","authors":"Samhita Das, P. Das, P. Das","doi":"10.1504/IJDSDE.2021.10037984","DOIUrl":"https://doi.org/10.1504/IJDSDE.2021.10037984","url":null,"abstract":"In this paper, we have considered a nonautonomous susceptible, infected, removed (SIR) model with saturation incidence rate for disease transmission. The global dynamical properties like permanence and global stability of the system as well as extinction of disease are analytically and numerically studied. The impact of behavioural patterns of individuals on disease control is validated along with possible applications. Furthermore, Pontryagin's Maximum Principle is used to characterise optimal level of the two controls, treatment and awareness level. Our objective is to minimise the infected population as well as the cost of applied control. The controls at optimal level are found to achieve different levels of impact on infection. It is observed that the combined impact of treatment and awareness exhibits more effective result in disease control compared to their single application. Based on observation, the strategy regarding the implementation of awareness and treatment is suggested.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49632956","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 : 2021-05-15DOI: 10.1504/IJDSDE.2021.10037983
V. Muthulakshmi, R. Manjuram
The purpose of this paper is to investigate the oscillatory behaviour of certain types of damped second-order forced delay differential equations with nonlinearities given by Riemann-Stieltjes integral. By using the Riccati transformation, some inequalities and integral averaging technique, interval oscillation criteria of both El-Sayed type and Kong type are established. Finally, two examples are presented to illustrate the theoretical results.
{"title":"Interval oscillation criteria for damped second-order delay differential equations with nonlinearities given by Riemann-Stieltjes integral","authors":"V. Muthulakshmi, R. Manjuram","doi":"10.1504/IJDSDE.2021.10037983","DOIUrl":"https://doi.org/10.1504/IJDSDE.2021.10037983","url":null,"abstract":"The purpose of this paper is to investigate the oscillatory behaviour of certain types of damped second-order forced delay differential equations with nonlinearities given by Riemann-Stieltjes integral. By using the Riccati transformation, some inequalities and integral averaging technique, interval oscillation criteria of both El-Sayed type and Kong type are established. Finally, two examples are presented to illustrate the theoretical results.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47578252","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 : 2021-03-21DOI: 10.1504/IJDSDE.2021.10036610
R. Zeghdane
In this paper, we give a new method for solving stochastic nonlinear Volterra integral equations by using shifted Legendre operational matrix. It is discussed that how the stochastic differential equations (SDE) could numerically be solved as matrix problems. By using this new operational matrix of integration and the so-called collocation method, nonlinear Volterra integral equations is reduced to systems of algebraic equations with unknown Legendre coefficients. Finally, the high accuracy of approximated solutions are illustrated by several experiment.
{"title":"Numerical approach for solving nonlinear stochastic Itô-Volterra integral equations using shifted Legendre polynomials","authors":"R. Zeghdane","doi":"10.1504/IJDSDE.2021.10036610","DOIUrl":"https://doi.org/10.1504/IJDSDE.2021.10036610","url":null,"abstract":"In this paper, we give a new method for solving stochastic nonlinear Volterra integral equations by using shifted Legendre operational matrix. It is discussed that how the stochastic differential equations (SDE) could numerically be solved as matrix problems. By using this new operational matrix of integration and the so-called collocation method, nonlinear Volterra integral equations is reduced to systems of algebraic equations with unknown Legendre coefficients. Finally, the high accuracy of approximated solutions are illustrated by several experiment.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41673098","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 : 2021-01-01DOI: 10.1504/ijdsde.2021.10040324
Tom Cuchta, S. Georgiev
{"title":"Analysis of the bilateral Laplace transform on time scales with applications","authors":"Tom Cuchta, S. Georgiev","doi":"10.1504/ijdsde.2021.10040324","DOIUrl":"https://doi.org/10.1504/ijdsde.2021.10040324","url":null,"abstract":"","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66733684","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 : 2021-01-01DOI: 10.1504/ijdsde.2021.10043529
M. Marudai, V. Anbukkarasi, M. S. Narayanan
{"title":"Convergence results of K iteration process for nonexpansive mappings with an application","authors":"M. Marudai, V. Anbukkarasi, M. S. Narayanan","doi":"10.1504/ijdsde.2021.10043529","DOIUrl":"https://doi.org/10.1504/ijdsde.2021.10043529","url":null,"abstract":"","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66734164","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 : 2021-01-01DOI: 10.1504/ijdsde.2021.10043537
K. Dhanalakshmi, P. Balasubramaniam
{"title":"Stability result for fractional neutral stochastic differential system driven by mixed fractional Brownian motion","authors":"K. Dhanalakshmi, P. Balasubramaniam","doi":"10.1504/ijdsde.2021.10043537","DOIUrl":"https://doi.org/10.1504/ijdsde.2021.10043537","url":null,"abstract":"","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66734276","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 : 2021-01-01DOI: 10.1504/ijdsde.2021.10043541
R. Krishnasamy, R. K. George
{"title":"Mean-square asymptotic stability of stochastic inertial neural networks with time-delay and Markovian jump parameters","authors":"R. Krishnasamy, R. K. George","doi":"10.1504/ijdsde.2021.10043541","DOIUrl":"https://doi.org/10.1504/ijdsde.2021.10043541","url":null,"abstract":"","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66734300","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 : 2021-01-01DOI: 10.1504/ijdsde.2021.10043581
G. Mahadevan, V. Vijayalakshmi
{"title":"Analysing of complementary perfect hop domination numeral of corona products of graphs","authors":"G. Mahadevan, V. Vijayalakshmi","doi":"10.1504/ijdsde.2021.10043581","DOIUrl":"https://doi.org/10.1504/ijdsde.2021.10043581","url":null,"abstract":"","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66734349","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 : 2021-01-01DOI: 10.1504/ijdsde.2021.10040326
Sokea Luey, H. Usami
{"title":"Application of generalised Riccati equations to analysis of asymptotic forms of solutions of perturbed half-linear ordinary differential equations","authors":"Sokea Luey, H. Usami","doi":"10.1504/ijdsde.2021.10040326","DOIUrl":"https://doi.org/10.1504/ijdsde.2021.10040326","url":null,"abstract":"","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66733902","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 : 2021-01-01DOI: 10.1504/ijdsde.2021.10043534
K. Erandi, S. Perera, A. Mahasinghe
{"title":"Dengue outbreak prediction model for urban Colombo using meteorological data","authors":"K. Erandi, S. Perera, A. Mahasinghe","doi":"10.1504/ijdsde.2021.10043534","DOIUrl":"https://doi.org/10.1504/ijdsde.2021.10043534","url":null,"abstract":"","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66734210","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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