We look at the SQIRP mathematical model for new coronavirus transmission in Bangladesh and India ... more We look at the SQIRP mathematical model for new coronavirus transmission in Bangladesh and India in this study. The basic reproduction number of the SQIRP system is designed using the next cohort matrix process. The SQIRP system has asymptotically stable locally at an infection-free equilibrium point when the basic reproduction number is not more than unity and unsteady when the value is greater than unity. The SQIRP system is found to go through a backward bifurcation, which is a novel perspective for Coronavirus infection transmission. The infection-free equilibrium and endemic equilibrium are shown to be asymptotically stable globally using the Lyapunov function hypothesis and the invariance principle of Lasalle. A SQIRP system with backward bifurcation is explored using stochastic analysis. The ecological stochasticity in the appearance of white noise best describes the system's value. To verify the results, more numerical simulations are run.
International Review on Modelling and Simulations, 2022
In this study, a modern technique dealing with a specific 4−dimensional genetic network has been ... more In this study, a modern technique dealing with a specific 4−dimensional genetic network has been introduced. Theoretically, the analysis has been performed and validated geo- metrically under the ambient hypercube. Both synchronized and asynchronous switching dynamics have been investigated for discrete time steps. We have obtained cycles that share the same vertex by presenting its dynamics on a hypercube. It is known as nothing but a weak condition of chaotic dynamics which is proven for the proposed problem of this article. Moreover, only one gene can reach the threshold due to no self-input condition. For the rest of the genes, to terminate the integration, a value of 6.7 is placed; this will expedite the process of starting the new integration for the next approach of the threshold. Eigenvalues with negative real parts are obtained, which means the system is stable. Based on that, its behavioral dynamics are predicted. Finally, the results have been investigated in Matlab and express its behavior through figures. From those figures, the stability of its dynamics has been concluded. The numerical calculation of Poincare ́ maps addresses new evidence of dynamics, pointing to a new research direction. To the best of our knowledge, such numerical results were not studied before
General relativity predicts that two freely counter-revolving test particles in the exterior fiel... more General relativity predicts that two freely counter-revolving test particles in the exterior field of a central rotating mass take different periods of time to complete the same full orbit; this time difference leads to the gravitomagnetic clock effect. The effect has been derived for circular equatorial orbits; moreover, it has been extended via azimuthal closure to spherical orbits around a slowly rotating mass. In this work, a general formula is derived for the main gravitomagnetic clock effect in the case of slow motion along an arbitrary elliptical orbit in the exterior field of a slowly rotating mass. Some of the implications of this result are briefly discussed.
In this article, we introduce a compartmental mathematical model, which is attempted to understan... more In this article, we introduce a compartmental mathematical model, which is attempted to understand the dynamics of poverty and drug addiction. In the model, we have an addicted compartment, which allows for an approach of government and non-government interventions. The stability analysis in this model holds for an addiction free equilibrium. We instated that, the equilibrium is locally asymptotically stable when the reproduction number is less than 1 and unstable when it is greater than 1. Numerical simulations of the systems have been presented to show the variations of the population in different situations. We also find out that, the high rate of interventions will reduce poverty and drug addiction and snatching faster. Our aim is to reduce poverty and addiction to their barest minimum. Data that have been used for simulations are based on the addiction happens in the district of Sylhet in Bangladesh. Some of the data we used are actually based on estimations from the results of...
Amit Kumar Chakraborty Department of Mathematics, Shahjalal University of Science and Technology,... more Amit Kumar Chakraborty Department of Mathematics, Shahjalal University of Science and Technology, Sylhet-3114, Bangladesh [email protected] Dr. Pabel Shahrear* Department of Mathematics, Shahjalal University of Science and Technology, Sylhet-3114, Bangladesh [email protected] Dr. Md. Anowarul Islam Department of Mathematics, Shahjalal University of Science and Technology, Sylhet-3114, Bangladesh [email protected]
Computer viruses pose a considerable problem for users of personal computers. In order to effecti... more Computer viruses pose a considerable problem for users of personal computers. In order to effectively defend against a virus, this paper proposes a compartmental model SAEIQRS (Susceptible – Antidotal – Exposed - Infected – Quarantine - Recovered - Susceptible) of virus transmission in a computer network. The differential transformation method (DTM) is applied to obtain an improved solution of each compartment. We have achieved an accuracy of order O(h 6 ) and validated the results of DTM with fourth-order Runge-Kutta (RK4) method. Based on the basic reproduction number, we analyzed the local stability of the model for virus free and endemic equilibria. Using a Lyapunov function, we demonstrated the global stability of virus free equilibria. Numerically the eigenvalues are computed using two different sets of parameter values and the corresponding dominant eigenvalues are determined by means of power method. Finally, we simulate the system in MATLAB. Based on the analysis, aspects o...
Members of the Camellia genus of plants may be affected by many of the diseases, pathogens and pe... more Members of the Camellia genus of plants may be affected by many of the diseases, pathogens and pests that mainly affect the tea plant (Camellia sinensis). One of the most common diseases which are found in tea garden is known as Branch Canker (BC) [1]. Recent outbreaks of these diseases is not only hampering the production of tea, but also stupendously hampering our national economy. In this paper, a simple SEIR model has been used to analyze the dynamics of Branch Canker in the tea garden. The stability of the system is analyzed for the existence of the disease free equilibrium. We established that there exists a disease free equilibrium point that is locally asymptotically stable when the reproduction number R o < 1 and unstable when R o > 1. Theoretically, we analyze the BC model. Finally, we numerically tested the theoretical results in MATLAB.
General relativity predicts that two freely counter-revolving test particles in the exterior fiel... more General relativity predicts that two freely counter-revolving test particles in the exterior field of a central rotating mass take different periods of time to complete the same full orbit; this time difference leads to the gravitomagnetic clock effect. The effect has been derived for circular equatorial orbits; moreover, it has been extended via azimuthal closure to spherical orbits around a slowly rotating mass. In this work, a general formula is derived for the main gravitomagnetic clock effect in the case of slow motion along an arbitrary elliptical orbit in the exterior field of a slowly rotating mass. Some of the implications of this result are briefly discussed.
In this study, we have introduced a modern technique that can deal with a specific 4−dimensional ... more In this study, we have introduced a modern technique that can deal with a specific 4−dimensional network. In my opinion, this is not studied before. Such an approach will be feasible to address gene networks and answer the relevant biological questions. Theoretically, the analysis has been made and validated geometrically under the ambient of hypercube. A continuous ho- molog gives us information and based on that we can predict its behavioral dynamics. Moreover, we investigate the results in Matlab and express its behavior through figures. Numerical calculation of Poincar ́e maps is used to address new evidence of dynamics pointing to a new direction of research.
Genetic networks play a fundamental role in the regulation and control of the development and fun... more Genetic networks play a fundamental role in the regulation and control of the development and function of organisms. A simple model of gene networks assumes that a gene can be switched on or off as regulatory inputs to the gene cross critical thresholds. In studies of dynamics of such networks, we found unusual behavior in which phase plane trajectories display irregular dynamics that shrink over long times. This observation leads us to identify a type of dynamics that can be described as collapsing chaos, in which the Lyapunov exponent is positive, but points on the trajectory approach the origin in the long time limit.
A compartmental mathematical model is established to study the dynamics of poverty, drug addictio... more A compartmental mathematical model is established to study the dynamics of poverty, drug addiction and snatching. In the model, we have compartments, which allow for an approach of government and nongovernment interventions. The stability analysis in this model holds for an addiction and snatching free equilibrium. We constituted that, the equilibrium is locally asymptotically stable when the reproduction number is less than 1 and unstable when it is greater than 1. Numerical simulations of the systems have been presented to show the variations of the population in different situations. We figured out that, the high rate of interventions will reduce poverty, drug addiction and snatching faster towards their barest minimum. Data that have been used for simulations are based on the addiction and snatching happens in the district of Sylhet in Bangladesh. But we believe that, our model is applicable for the whole country and even for the whole world.
In this paper, generating formulae for the existing (e.g. Trapezoidal, Simpson’s and Weddle’s) an... more In this paper, generating formulae for the existing (e.g. Trapezoidal, Simpson’s and Weddle’s) and non-existing numerical integration formulae are derived by use of shape functions widely used in Finite Element Method (FEM). The technique, so presented for the derivation of Numerical Integration Formulae (NIF) is new as well as very simple. For the first time, NIF up to 10-th order and their generating formulae are presented. Further, based on the presented generating formulae a convenient computer code is developed. Efficiency and suitability of the derived formulae are demonstrated through several practical application examples.
This paper presents a technique to evaluate the integrals over the triangular surfaces using read... more This paper presents a technique to evaluate the integrals over the triangular surfaces using readily available Gaussian quadrature for the square domain integrals. As the technique suitably can employ higher order Gaussian quadrature and have higher degree of accuracy of the integrals is possible to achieve without resorting to inefficient quadrature for triangles.
Considering a gravitational coupling between the spin and the orbital angular momentum of a spinn... more Considering a gravitational coupling between the spin and the orbital angular momentum of a spinning test particle orbiting a central massive body, we derive two particular consequences: (1) the influence of the coupling on the location of the innermost stable circular orbit and (2) the gravitomagnetic clock effect due to this coupling. The previous result does not seem to exist for the former, while for the latter we arrive at a result that coincides with what we think is the most accurate.
Genetic interactions are often modeled by logical networks in which time is discrete and all gene... more Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sens...
General relativity predicts that two freely counter-revolving test particles in the exterior fiel... more General relativity predicts that two freely counter-revolving test particles in the exterior field of a central rotating mass take different periods of time to complete the same full orbit; this time difference leads to the gravitomagnetic clock effect. The effect has been derived for circular equatorial orbits; moreover, it has been extended via azimuthal closure to spherical orbits around a slowly rotating mass. In this Letter, a general formula is derived for the main gravitomagnetic clock effect in the case of slow motion along an arbitrary elliptical orbit in the exterior field of a slowly rotating mass. Some of the implications of this result are briefly discussed.
We look at the SQIRP mathematical model for new coronavirus transmission in Bangladesh and India ... more We look at the SQIRP mathematical model for new coronavirus transmission in Bangladesh and India in this study. The basic reproduction number of the SQIRP system is designed using the next cohort matrix process. The SQIRP system has asymptotically stable locally at an infection-free equilibrium point when the basic reproduction number is not more than unity and unsteady when the value is greater than unity. The SQIRP system is found to go through a backward bifurcation, which is a novel perspective for Coronavirus infection transmission. The infection-free equilibrium and endemic equilibrium are shown to be asymptotically stable globally using the Lyapunov function hypothesis and the invariance principle of Lasalle. A SQIRP system with backward bifurcation is explored using stochastic analysis. The ecological stochasticity in the appearance of white noise best describes the system's value. To verify the results, more numerical simulations are run.
International Review on Modelling and Simulations, 2022
In this study, a modern technique dealing with a specific 4−dimensional genetic network has been ... more In this study, a modern technique dealing with a specific 4−dimensional genetic network has been introduced. Theoretically, the analysis has been performed and validated geo- metrically under the ambient hypercube. Both synchronized and asynchronous switching dynamics have been investigated for discrete time steps. We have obtained cycles that share the same vertex by presenting its dynamics on a hypercube. It is known as nothing but a weak condition of chaotic dynamics which is proven for the proposed problem of this article. Moreover, only one gene can reach the threshold due to no self-input condition. For the rest of the genes, to terminate the integration, a value of 6.7 is placed; this will expedite the process of starting the new integration for the next approach of the threshold. Eigenvalues with negative real parts are obtained, which means the system is stable. Based on that, its behavioral dynamics are predicted. Finally, the results have been investigated in Matlab and express its behavior through figures. From those figures, the stability of its dynamics has been concluded. The numerical calculation of Poincare ́ maps addresses new evidence of dynamics, pointing to a new research direction. To the best of our knowledge, such numerical results were not studied before
General relativity predicts that two freely counter-revolving test particles in the exterior fiel... more General relativity predicts that two freely counter-revolving test particles in the exterior field of a central rotating mass take different periods of time to complete the same full orbit; this time difference leads to the gravitomagnetic clock effect. The effect has been derived for circular equatorial orbits; moreover, it has been extended via azimuthal closure to spherical orbits around a slowly rotating mass. In this work, a general formula is derived for the main gravitomagnetic clock effect in the case of slow motion along an arbitrary elliptical orbit in the exterior field of a slowly rotating mass. Some of the implications of this result are briefly discussed.
In this article, we introduce a compartmental mathematical model, which is attempted to understan... more In this article, we introduce a compartmental mathematical model, which is attempted to understand the dynamics of poverty and drug addiction. In the model, we have an addicted compartment, which allows for an approach of government and non-government interventions. The stability analysis in this model holds for an addiction free equilibrium. We instated that, the equilibrium is locally asymptotically stable when the reproduction number is less than 1 and unstable when it is greater than 1. Numerical simulations of the systems have been presented to show the variations of the population in different situations. We also find out that, the high rate of interventions will reduce poverty and drug addiction and snatching faster. Our aim is to reduce poverty and addiction to their barest minimum. Data that have been used for simulations are based on the addiction happens in the district of Sylhet in Bangladesh. Some of the data we used are actually based on estimations from the results of...
Amit Kumar Chakraborty Department of Mathematics, Shahjalal University of Science and Technology,... more Amit Kumar Chakraborty Department of Mathematics, Shahjalal University of Science and Technology, Sylhet-3114, Bangladesh [email protected] Dr. Pabel Shahrear* Department of Mathematics, Shahjalal University of Science and Technology, Sylhet-3114, Bangladesh [email protected] Dr. Md. Anowarul Islam Department of Mathematics, Shahjalal University of Science and Technology, Sylhet-3114, Bangladesh [email protected]
Computer viruses pose a considerable problem for users of personal computers. In order to effecti... more Computer viruses pose a considerable problem for users of personal computers. In order to effectively defend against a virus, this paper proposes a compartmental model SAEIQRS (Susceptible – Antidotal – Exposed - Infected – Quarantine - Recovered - Susceptible) of virus transmission in a computer network. The differential transformation method (DTM) is applied to obtain an improved solution of each compartment. We have achieved an accuracy of order O(h 6 ) and validated the results of DTM with fourth-order Runge-Kutta (RK4) method. Based on the basic reproduction number, we analyzed the local stability of the model for virus free and endemic equilibria. Using a Lyapunov function, we demonstrated the global stability of virus free equilibria. Numerically the eigenvalues are computed using two different sets of parameter values and the corresponding dominant eigenvalues are determined by means of power method. Finally, we simulate the system in MATLAB. Based on the analysis, aspects o...
Members of the Camellia genus of plants may be affected by many of the diseases, pathogens and pe... more Members of the Camellia genus of plants may be affected by many of the diseases, pathogens and pests that mainly affect the tea plant (Camellia sinensis). One of the most common diseases which are found in tea garden is known as Branch Canker (BC) [1]. Recent outbreaks of these diseases is not only hampering the production of tea, but also stupendously hampering our national economy. In this paper, a simple SEIR model has been used to analyze the dynamics of Branch Canker in the tea garden. The stability of the system is analyzed for the existence of the disease free equilibrium. We established that there exists a disease free equilibrium point that is locally asymptotically stable when the reproduction number R o < 1 and unstable when R o > 1. Theoretically, we analyze the BC model. Finally, we numerically tested the theoretical results in MATLAB.
General relativity predicts that two freely counter-revolving test particles in the exterior fiel... more General relativity predicts that two freely counter-revolving test particles in the exterior field of a central rotating mass take different periods of time to complete the same full orbit; this time difference leads to the gravitomagnetic clock effect. The effect has been derived for circular equatorial orbits; moreover, it has been extended via azimuthal closure to spherical orbits around a slowly rotating mass. In this work, a general formula is derived for the main gravitomagnetic clock effect in the case of slow motion along an arbitrary elliptical orbit in the exterior field of a slowly rotating mass. Some of the implications of this result are briefly discussed.
In this study, we have introduced a modern technique that can deal with a specific 4−dimensional ... more In this study, we have introduced a modern technique that can deal with a specific 4−dimensional network. In my opinion, this is not studied before. Such an approach will be feasible to address gene networks and answer the relevant biological questions. Theoretically, the analysis has been made and validated geometrically under the ambient of hypercube. A continuous ho- molog gives us information and based on that we can predict its behavioral dynamics. Moreover, we investigate the results in Matlab and express its behavior through figures. Numerical calculation of Poincar ́e maps is used to address new evidence of dynamics pointing to a new direction of research.
Genetic networks play a fundamental role in the regulation and control of the development and fun... more Genetic networks play a fundamental role in the regulation and control of the development and function of organisms. A simple model of gene networks assumes that a gene can be switched on or off as regulatory inputs to the gene cross critical thresholds. In studies of dynamics of such networks, we found unusual behavior in which phase plane trajectories display irregular dynamics that shrink over long times. This observation leads us to identify a type of dynamics that can be described as collapsing chaos, in which the Lyapunov exponent is positive, but points on the trajectory approach the origin in the long time limit.
A compartmental mathematical model is established to study the dynamics of poverty, drug addictio... more A compartmental mathematical model is established to study the dynamics of poverty, drug addiction and snatching. In the model, we have compartments, which allow for an approach of government and nongovernment interventions. The stability analysis in this model holds for an addiction and snatching free equilibrium. We constituted that, the equilibrium is locally asymptotically stable when the reproduction number is less than 1 and unstable when it is greater than 1. Numerical simulations of the systems have been presented to show the variations of the population in different situations. We figured out that, the high rate of interventions will reduce poverty, drug addiction and snatching faster towards their barest minimum. Data that have been used for simulations are based on the addiction and snatching happens in the district of Sylhet in Bangladesh. But we believe that, our model is applicable for the whole country and even for the whole world.
In this paper, generating formulae for the existing (e.g. Trapezoidal, Simpson’s and Weddle’s) an... more In this paper, generating formulae for the existing (e.g. Trapezoidal, Simpson’s and Weddle’s) and non-existing numerical integration formulae are derived by use of shape functions widely used in Finite Element Method (FEM). The technique, so presented for the derivation of Numerical Integration Formulae (NIF) is new as well as very simple. For the first time, NIF up to 10-th order and their generating formulae are presented. Further, based on the presented generating formulae a convenient computer code is developed. Efficiency and suitability of the derived formulae are demonstrated through several practical application examples.
This paper presents a technique to evaluate the integrals over the triangular surfaces using read... more This paper presents a technique to evaluate the integrals over the triangular surfaces using readily available Gaussian quadrature for the square domain integrals. As the technique suitably can employ higher order Gaussian quadrature and have higher degree of accuracy of the integrals is possible to achieve without resorting to inefficient quadrature for triangles.
Considering a gravitational coupling between the spin and the orbital angular momentum of a spinn... more Considering a gravitational coupling between the spin and the orbital angular momentum of a spinning test particle orbiting a central massive body, we derive two particular consequences: (1) the influence of the coupling on the location of the innermost stable circular orbit and (2) the gravitomagnetic clock effect due to this coupling. The previous result does not seem to exist for the former, while for the latter we arrive at a result that coincides with what we think is the most accurate.
Genetic interactions are often modeled by logical networks in which time is discrete and all gene... more Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sens...
General relativity predicts that two freely counter-revolving test particles in the exterior fiel... more General relativity predicts that two freely counter-revolving test particles in the exterior field of a central rotating mass take different periods of time to complete the same full orbit; this time difference leads to the gravitomagnetic clock effect. The effect has been derived for circular equatorial orbits; moreover, it has been extended via azimuthal closure to spherical orbits around a slowly rotating mass. In this Letter, a general formula is derived for the main gravitomagnetic clock effect in the case of slow motion along an arbitrary elliptical orbit in the exterior field of a slowly rotating mass. Some of the implications of this result are briefly discussed.
Uploads
Papers by Pabel Shahrear