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Uttam Ghosh

Bio: Uttam Ghosh is an academic researcher from University of Calcutta. The author has contributed to research in topic(s): Fractional calculus & Differential equation. The author has an hindex of 12, co-authored 77 publication(s) receiving 370 citation(s).
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Journal ArticleDOI
Abstract: This manuscript describes a mathematical epidemiological model of COVID-19 to investigate the dynamics of this pandemic disease and we have fitted this model to the current COVID-19 cases in Italy. We have obtained the basic reproduction number which plays a crucial role on the stability of disease free equilibrium point. Backward bifurcation with respect to the cure rate of treatment occurs conditionally. It is clear from the sensitivity analysis that the developments of self immunities with proper maintaining of social distancing of the exposed and asymptomatic individuals play key role for controlling the disease. We have validated the model by considering the COVID-19 cases of Italy and the future situations of epidemicity in Italy have been predicted from the model. We have estimated the basic reproduction number for the COVID-19 outbreak in Italy and effective reproduction number has also been studied. Finally, an optimal control model has been formulated and solved to realize the positive impacts of adapting lock down by many countries for maintaining social distancing.

Journal ArticleDOI
Bapin Mondal1, Uttam Ghosh1, Sadikur Rahman2, Pritam Saha1  +1 moreInstitutions (2)
TL;DR: The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population.
Abstract: Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences.

Journal ArticleDOI
Abstract: Isolation and quarantine play important role to control dengue outbreak but much attention has not yet been paid to develop dengue models with these control factors. In this paper, we have developed a $$SEIQR-SEI$$ type compartmental dengue model with the effect of isolation. The model has one locally asymptotically stable disease free equilibrium (DFE) point when the basic reproduction number is less than unity. The model without dengue induced death has a globally asymptotically stable DFE point when the corresponding basic reproduction number is less than unity and a globally asymptotically stable endemic equilibrium point when the basic reproduction number is greater than unity. The model exhibits backward bifurcation when the basic production number is equal to one and the first bifurcation coefficient is greater than zero. The key model parameters have been estimated by fitting the model to the dengue outbreak data reported from Singapore during the period 18th week to 53th week,2014. The findings suggest that the total outbreak size reduces by 32.87%, 27.02% and 35.96% respectively when the isolation rate increases from 0 to 0.5, the mosquito biting rate reduces from 1.235 to 1.00 and the vector control rate increases from 0.038 to 0.090. Using sensitivity analysis, we have determined the most sensitive model parameters.

Posted ContentDOI
TL;DR: A tri-topic food web model with Beddington-DeAngelis functional response between interacting species is considered, incorporating the reduction of prey and intermediate predator growth because of the fear of intermediate and top predator respectively.
Abstract: The most important fact in the field of theoretical ecology and evolutionary biology is the strategy of predation for predators and avoidance of prey from predator attack. A lot of experimental works suggest that the reduction of prey depends on both direct predation and fear of predation. We explore the impact of fear effect and mutual interference among predators into a three-species food chain model. In this manuscript, we have considered a tri-topic food chain model with Beddington–DeAngelis functional response between interacting species, incorporating the reduction of prey and intermediate predator growth due to the fear of intermediate and top predator, respectively. We have provided parametric conditions for existence of biologically feasible equilibria as well as their local and global stability. We have established conditions of transcritical, saddle-node and Hopf bifurcation about different equilibria. Finally, we have performed some numerical investigations to justify analytical findings.

Journal ArticleDOI
TL;DR: A new concept of interval representation named as linear parametric representation is introduced by which a biological system in an uncertain situation can be formulated mathematically in a precise way.
Abstract: Currently, proper modeling of a biological system in an uncertain situation is a challenging task for researchers. Facing this challenge, in this article, a new concept of interval representation named as linear parametric representation is introduced by which a biological system in an uncertain situation can be formulated mathematically in a precise way. The aim of this work is to formulate a three species imprecise food chain model with one prey and two competing predators in an interval environment. Here, all the biological parameters except the conversion efficiency of the species are considered interval-valued. And interactions among the species are taken as Holling Type I functional response. Using the linear parametric representation of interval, a system in the interval form has been converted in the parametric form. Positivity and boundedness of the solutions of the proposed imprecise system are verified. Then, conditions of local stability, global stability and transcritical bifurcation of equilibrium points of the proposed system are established. Thereafter, all the theoretical results of this work are validated by a numerical example with interval-valued parametric data and results are presented pictorially. Finally, some biological implications of the obtained results are discussed and a fruitful conclusion has been made.

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Journal ArticleDOI
Abstract: This manuscript describes a mathematical epidemiological model of COVID-19 to investigate the dynamics of this pandemic disease and we have fitted this model to the current COVID-19 cases in Italy. We have obtained the basic reproduction number which plays a crucial role on the stability of disease free equilibrium point. Backward bifurcation with respect to the cure rate of treatment occurs conditionally. It is clear from the sensitivity analysis that the developments of self immunities with proper maintaining of social distancing of the exposed and asymptomatic individuals play key role for controlling the disease. We have validated the model by considering the COVID-19 cases of Italy and the future situations of epidemicity in Italy have been predicted from the model. We have estimated the basic reproduction number for the COVID-19 outbreak in Italy and effective reproduction number has also been studied. Finally, an optimal control model has been formulated and solved to realize the positive impacts of adapting lock down by many countries for maintaining social distancing.

Journal ArticleDOI
Liwei Tang1, Min Liu1, Bingyu Ren1, Jinghong Chen1  +4 moreInstitutions (3)
Abstract: India has suffered from the second wave of COVID-19 pandemic since March 2021. This wave of the outbreak has been more serious than the first wave pandemic in 2020, which suggests that some new transmission characteristics may exist. COVID-19 is transmitted through droplets, aerosols, and contact with infected surfaces. Air pollutants are also considered to be associated with COVID-19 transmission. However, the roles of indoor transmission in the COVID-19 pandemic and the effects of these factors in indoor environments are still poorly understood. Our study focused on reveal the role of indoor transmission in the second wave of COVID-19 pandemic in India. Our results indicated that human mobility in the home environment had the highest relative influence on COVID-19 daily growth rate in the country. The COVID-19 daily growth rate was significantly positively correlated with the residential percent rate in most state-level areas in India. A significant positive nonlinear relationship was found when the residential percent ratio ranged from 100 to 120%. Further, epidemic dynamics modelling indicated that a higher proportion of indoor transmission in the home environment was able to intensify the severity of the second wave of COVID-19 pandemic in India. Our findings suggested that more attention should be paid to the indoor transmission in home environment. The public health strategies to reduce indoor transmission such as ventilation and centralized isolation will be beneficial to the prevention and control of COVID-19.

Journal ArticleDOI
Abstract: A discrete fractional order model is proposed to analyze the behaviour of an epidemic process with indirect transmission. This model is based on a discrete version of the Grunwald-Letnikov fractional derivative operator. Some properties of this operator are shown and used to derive a truncated version of the operator, which is used to propose a model with short-term memory. Based on the biological meaning of the problem, some bounds have been obtained to assure the nonnegativity of the model solution. The ( α , k ) -Basic Reproduction Number has been introduced and used to analyze the stability of the solution around its equilibrium points. Moreover, the influence of the fractional order, α , and the memory steps, k , on the behaviour of the solution has been analyzed. Finally, the results obtained have been clarified by means of numerical simulations of a model for the evolution of an infection by Salmonella in a hens farm.

Journal ArticleDOI
Bapin Mondal1, Uttam Ghosh1, Sadikur Rahman2, Pritam Saha1  +1 moreInstitutions (2)
TL;DR: The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population.
Abstract: Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences.

Journal ArticleDOI
Abstract: We analyse the time-series evolution of the cumulative number of confirmed cases of COVID-19, the novel coronavirus disease, for some African countries. We propose a mathematical model, incorporating non-pharmaceutical interventions to unravel the disease transmission dynamics. Analysis of the stability of the model's steady states was carried out, and the reproduction number R 0 , a vital key for flattening the time-evolution of COVID-19 cases, was obtained by means of the next generation matrix technique. By dividing the time evolution of the pandemic for the cumulative number of confirmed infected cases into different regimes or intervals, hereafter referred to as phases, numerical simulations were performed to fit the proposed model to the cumulative number of confirmed infections for different phases of COVID-19 during its first wave. The estimated R 0 declined from 2.452-9.179 during the first phase of the infection to 1.374-2.417 in the last phase. Using the Atangana-Baleanu fractional derivative, a fractional COVID-19 model is proposed and numerical simulations performed to establish the dependence of the disease dynamics on the order of the fractional derivatives. An elasticity and sensitivity analysis of R 0 was carried out to determine the most significant parameters for combating the disease outbreak. These were found to be the effective disease transmission rate, the disease diagnosis or case detection rate, the proportion of susceptible individuals taking precautions, and the disease infection rate. Our results show that if the disease infection rate is less than 0.082/day, then R 0 is always less than 1; and if at least 55.29% of the susceptible population take precautions such as regular hand washing with soap, use of sanitizers, and the wearing of face masks, then the reproduction number R 0 remains below unity irrespective of the disease infection rate. Keeping R 0 values below unity leads to a decrease in COVID-19 prevalence.

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Author's H-index: 12

No. of papers from the Author in previous years
YearPapers
20222
202114
202016
20199
20189
20179