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Chakraborty S, Li XZ, Roy PK. How can HPV-induced cervical cancer be controlled by a combination of drug therapy? A mathematical study. INT J BIOMATH 2019. [DOI: 10.1142/s1793524519500700] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This paper deals with a control strategy through impulsive drug treatment to study the effect of Chemotherapy and CTL activator drug to eradicate the cervical cancer. CTL kills the HPV infected cells and helps to prevent cervical cancer. Dendritic cell (DC) plays a crucial role in this disease dynamics in enhancing the activity of CTL. To explore these effects, we have formulated a mathematical model consisting of six compartments to describe the interactions between HPV and three classes of cervical cells (susceptible, infected, cancerous), with DC and CTL. Calculating the basic reproduction ratio, we find that there exists a disease-free equilibrium point and an endemic equilibrium point. In our study, we have shown that though DC enhances the activity of CTL, it is not sufficient to eradicate the disease totally. How we could restrict the cancer development by using double drug in an impulsive way with particular drug doses is being reflected in the results. To illustrate our results, numerical simulations are also presented.
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Affiliation(s)
- Sudip Chakraborty
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - Xue-Zhi Li
- College of Mathematics and Information Science, Henan Normal University, Xinxiang 45300, P. R. China
| | - Priti Kumar Roy
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
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Cheng Y, Wang X, Shi B. Consensus of a two-agent opinion dynamical system with processing delay. INT J BIOMATH 2018. [DOI: 10.1142/s179352451850081x] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
A sufficient condition is obtained for a two-agent opinion dynamical system with processing delay to experience unconditional consensus. To this end, the dynamics proposed is transformed into a general class of delay differential equation and asymptotic stability of the origin is then analyzed. It is also shown that increasing delay can prolong the time needed for the system to realize consensus and even induce a Hopf bifurcation.
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Affiliation(s)
- Ye Cheng
- School of Basic Sciences for Aviation, Naval Aviation University, Yantai 264001, P. R. China
| | - Xiao Wang
- College of Science, National University of Defense Technology, Changsha 410073, P. R. China
| | - Bao Shi
- School of Basic Sciences for Aviation, Naval Aviation University, Yantai 264001, P. R. China
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