scholarly journals Complexities and Bifurcations Induced by Drug Responses in a Pulsed Tumour-Immune Model

2020 ◽  
Vol 30 (07) ◽  
pp. 2050104 ◽  
Author(s):  
Jin Yang ◽  
Yuanshun Tan ◽  
Robert A. Cheke
Keyword(s):  
Complex Dynamics ◽  
Accumulation Rate ◽  
Tumour Size ◽  
Drug Dosage ◽  
Effector Cells ◽  
Therapeutic Protocol ◽  
Threshold Conditions ◽  
Depletion Rate ◽  
Transcritical Bifurcations ◽  
Globally Stable

Responses to drugs play key roles in exploring how drug toxicity affects the evolution of tumour cells. We model pulsed comprehensive therapies using an impulsive tumour-immune model, in which the application of comprehensive therapies is dependent on a threshold tumour size. By employing the definitions and properties of the Poincaré map, we show that the effector cell eradication periodic solution is globally stable under threshold conditions. In the light of bifurcation theorems, it is shown that transcritical bifurcations can occur with respect to many treatment parameters including depletion rate, chemotherapeutic drug concentration, a medicine toxicity coefficient and the accumulation rate of effector cells. Then we provide conditions for the existence of order-[Formula: see text] [Formula: see text] periodic solutions. The results indicate that the threshold [Formula: see text] is sensitive to treatment parameters and the proposed system exists with very complex dynamics when treatment parameters are chosen as bifurcation parameters. Moreover, a therapeutic protocol with a smaller chemotherapy drug dosage and more frequent applications is more effective for maintaining a high tumour cell depletion rate.

scholarly journals Insight of COVID-19/ SARS-CoV-2 and its Probable Treatment - A Mathematical Approach

2020 ◽  
Author(s):  
Amar Nath Chatterjee ◽  
Shubhankar Saha ◽  
Priti Kumar Roy ◽  
Fahad Al Basir ◽  
Evgenii Khailov ◽  
...  
Keyword(s):  
Drug Therapy ◽  
Side Effects ◽  
Complex Dynamics ◽  
Medical Science ◽  
Threshold Value ◽  
Drug Dosage ◽  
Equilibrium Analysis ◽  
Combination Drug ◽  
Drug Dosing ◽  
Novel Coronavirus

Abstract The novel coronavirus disease (COVID19) emerged in Wuhan, China in December 2019. In a matter of weeks, the disease had spread well outside China, and now reaching countries in all parts of the globe. Its treatment and recovery are the two most primary concerns for every country. Recently, medical science has shown some studies that reveal post-infection Hydroxychloroquine (HCQ) treatment followed by lipopeptide EK1C4 could be an effective interference in prevention of the disease COVID19, spreaded by SARS-CoV-2. However, there are some side effects of these drugs, especially for aged persons, but this is yet to be explored by rescaling the drug dosage with a proper dosing time interval.We propose a mathematical model that explains combination drug therapy on the dynamics of SARSCoV-2/COVID19. We apply the method of impulsive differential equation in our model and it is useful for elucidating insights into regular drug dosing. Systematic approach of this combination of drug therapy allows us to gain more fruitful results.In this model, we first investigate the chaotic nature of the system induced by SARS-CoV-2 with and without any treatment. Then we enquire how drug therapy reduces the threshold value of infection and observe its complex dynamics. We perform equilibrium analysis, local and global stability analysis and find the region of safe dosing so that there occurs no side-effects during treatment and afterwards. Our results suggest that only proper treatment enhances the stability in a SARS-CoV-2 infected system.

scholarly journals NONLINEAR AND COMPLEX DYNAMICS IN ECONOMICS

2014 ◽  
Vol 19 (8) ◽  
pp. 1749-1779 ◽  
Author(s):  
William A. Barnett ◽  
Apostolos Serletis ◽  
Demitre Serletis
Keyword(s):  
Dynamical Systems ◽  
Complex Dynamics ◽  
State Of The Art ◽  
Geometric Approach ◽  
Stable Region ◽  
Physical Sciences ◽  
Dynamical Complexity ◽  
Policy Relevance ◽  
Potential Applications ◽  
Transcritical Bifurcations

This paper is an up-to-date survey of the state of the art in dynamical systems theory relevant to high levels of dynamical complexity, characterizing chaos and near-chaos, as commonly found in the physical sciences. The paper also surveys applications in economics and finance. This survey does not include bifurcation analyses at lower levels of dynamical complexity, such as Hopf and transcritical bifurcations, which arise closer to the stable region of the parameter space. We discuss the geometric approach (based on the theory of differential/difference equations) to dynamical systems and make the basic notions of complexity, chaos, and other related concepts precise, having in mind their (actual or potential) applications to economically motivated questions. We also introduce specific applications in microeconomics, macroeconomics, and finance and discuss the policy relevance of chaos.

The Onset of Chaos via Asymptotically Period-Doubling Cascade in Fractional Order Lorenz System

2017 ◽  
Vol 27 (13) ◽  
pp. 1750207 ◽  
Author(s):  
Xiaofang Lin ◽  
Binghui Liao ◽  
Caibin Zeng
Keyword(s):  
Fractional Order ◽  
Periodic System ◽  
Lorenz System ◽  
Complex Dynamics ◽  
Period Doubling ◽  
Onset Of Chaos ◽  
Asymptotically Periodic ◽  
Stable Periodic ◽  
Negative Damping ◽  
Globally Stable

Little seems to be known about the chaotification problem in the framework of fractional order nonlinear systems. Based on the negative damping instability mechanism and fractional calculus technique, this paper reports the onset of chaos in fractional order Lorenz system with periodic system parameters via asymptotically period-doubling cascade. To further understand the complex dynamics of the system, some basic properties such as the largest Lyapunov exponents, bifurcation diagram, routes to chaos, asymptotically periodic windows, possible chaotic and asymptotically periodic window parameter regions, and the compound structure of the system are analyzed and demonstrated with careful numerical simulations. Of particular interest is a striking finding that fractional derivative can chaotify the globally stable periodic system without feedback control.

scholarly journals Chemical Control for Host-Parasitoid Model within the Parasitism Season and Its Complex Dynamics

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Tao Wang ◽  
Youtang Zhang
Keyword(s):  
Pest Control ◽  
Chemical Control ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Pesticide Application ◽  
Multiple Attractors ◽  
Threshold Conditions ◽  
Existence And Stability ◽  
Numerical Bifurcation ◽  
Type Ii Functional Response

In the present paper, we develop a host-parasitoid model with Holling type II functional response function and chemical control, which can be applied at any time of each parasitism season or pest generation, and focus on addressing the importance of the timing of application pesticide during the parasitism season or pest generation in successful pest control. Firstly, the existence and stability of both the host and parasitoid populations extinction equilibrium and parasitoid-free equilibrium have been investigated. Secondly, the effects of key parameters on the threshold conditions have been discussed in more detail, which shows the importance of pesticide application times on the pest control. Thirdly, the complex dynamics including multiple attractors coexistence, chaotic behavior, and initial sensitivity have been studied by using numerical bifurcation analyses. Finally, the uncertainty and sensitivity of all the parameters on the solutions of both the host and parasitoid populations are investigated, which can help us to determine the key parameters in designing the pest control strategy. The present research can help us to further understand the importance of timings of pesticide application in the pest control and to improve the classical chemical control and to make management decisions.

Periodic Solution Bifurcation and Spiking Dynamics of Impacting Predator–Prey Dynamical Model

2018 ◽  
Vol 28 (12) ◽  
pp. 1850147 ◽  
Author(s):  
Sanyi Tang ◽  
Xuewen Tan ◽  
Jin Yang ◽  
Juhua Liang
Keyword(s):  
Periodic Solution ◽  
Poincaré Map ◽  
Complex Dynamics ◽  
Poincare Map ◽  
Predator Prey ◽  
Threshold Conditions ◽  
Existence And Stability ◽  
The Stability ◽  
Nonmonotonic Functional Response ◽  
Solution Bifurcation

A planar predator–prey impacting system model with a nonmonotonic functional response function is proposed and analyzed. The existence and stability of a boundary order-1 periodic solution were investigated and the threshold conditions for a transcritical bifurcation and stable switching were obtained, and also the definition and properties of the Poincaré map are discussed. The main results indicate that multiple discontinuous points of the Poincaré map could induce the coexistence of multiple order-1 periodic solutions. Numerical analyses reveal the complex dynamics of the model including periodic adding and halving bifurcations, which could result in multiple active phases, among them rapid spiking and quiescence phases which can switch from one to another and consequently create complex bursting patterns. The main results reveal that it is beneficial to restore the stability and balance of a ecosystem for species with group defence by moderately reducing population densities and the group defence capacity.

Russia in International Capital Movement: Comparative Analysis

2011 ◽  
pp. 66-76 ◽  
Author(s):  
A. Bulatov
Keyword(s):  
Comparative Analysis ◽  
Emerging Markets ◽  
Economic Model ◽  
Accumulation Rate ◽  
Capital Movement ◽  
International Capital ◽  
International Capital Movement

The article tries to reveal specific features of Russias participation in international capital movement in comparison with other emerging markets. Peculiarities of outflow and inflow of capital in Russia are considered as consequences of specifics of its economic model. Proposals on using international capital movement for the increase of accumulation rate in Russia are put forward.

ANALYSIS OF THE BIPHASIC ACTION OF GROWTH HORMONE IN VITRO ON THE RAT DIAPHRAGM

1968 ◽  
Vol 57 (3_Suppl) ◽  
pp. S19-S35 ◽  
Author(s):  
Å. Hjalmarson
Keyword(s):  
Growth Hormone ◽  
Actinomycin D ◽  
Accumulation Rate ◽  
Inhibitory Effect ◽  
Bovine Growth Hormone ◽  
Rat Diaphragm ◽  
Dual Nature ◽  
Hypophysectomized Rats ◽  
D 20

ABSTRACT In vitro addition of bovine growth hormone (GH) to intact hemidiaphragms from hypophysectomized rats has previously been found to produce both an early stimulatory effect lasting for 2—3 hours and a subsequent late inhibitory effect during which the muscle is insensitive to further addition of GH (Hjalmarson 1968). These effects on the accumulation rate of α-aminoisobutyric acid (AIB) and D-xylose have been further studied. In presence of actinomycin D (20 μg/ml) or puromycin (100 μg/ml) the duration of the stimulatory effect of GH (25 μg/ml) was prolonged to last for at least 4—5 hours and the late inhibitory effect was prevented. Similar results were obtained when glucose-free incubation medium was used. Preincubation of the diaphragm at different glucose concentrations (0—5 mg/ml) for 3 hours did not change the GH sensitivity. Addition of insulin at start of incubation could not prevent GH from inducing its late inhibitory effect, while dexamethasone seemed to potentiate this effect of GH. Furthermore, adrenaline was found to decrease the uptake of AIB-14C and D-xylose-14C in the diaphragm, but not to change the sensitivity of the muscle to GH. Preincubation of the diaphragm for 3 hours with puromycin in a concentration of 200 μg/ml markedly decreased the subsequent basal uptake of both AIB-14C and D-xylose-14C, in the presence of puromycin, and abolished the stimulatory effect of GH on the accumulation of AIB-14C. However, the effect of GH on the accumulation of D-xylose-14C was unchanged. The present observations are discussed and evaluated in relation to various mechanisms of GH action proposed to explain the dual nature of the hormone.

Intraoperative, postoperative and long-term oncosurgical safety of therapeutic mammaplasty

2013 ◽  
Vol 154 (33) ◽  
pp. 1291-1296 ◽  
Author(s):  
László Romics Jr. ◽  
Sophie Barrett ◽  
Sheila Stallard ◽  
Eva Weiler-Mithoff
Keyword(s):  
Recurrence Rate ◽  
Tumour Size ◽  
Breast Conservation ◽  
Malignant Lesion ◽  
Surgical Techniques ◽  
Incomplete Resection ◽  
Immediate Reconstruction ◽  
Oncological Safety

Introduction: (Pre)malignant lesion in the breast requiring mastectomy conventionally may be treated with breast conservation by using oncoplastic breast surgical techniques, which is called therapeutic mammaplasty. However, no reliable data has been published so far as regards the oncological safety of this method. Aim: The aim of the authors was to analyse the oncological safety of therapeutic mammaplasty in a series of patients. Method: 99 patients were treated with therapeutic mammaplasty and data were collected in a breast surgical database prospectively. Results were analysed with respect to intraoperative, postoperative and long-term oncological safety. Results: Incomplete resection rate was 14.1%, which correlated with tumour size (p = 0.023), and multifocality (p = 0.012). Time between surgery (therapeutic mammaplasty) and chemotherapy was similar to time between conventional breast surgeries (wide excision, mastectomy, mastectomy with immediate reconstruction) and chemotherapy (mean 29–31 days; p<0.05). Overall recurrence rate was 6.1%, locoregional recurrence rate was 2% during 27 month (1–88) mean follow-up. Conclusions: Since literature data are based on relatively short follow-up and low patient number, it is highly important that all data on therapeutic mammaplasty is collected in a prospectively maintained breast surgical database in order to determine true recurrence after long-follow-up. Orv. Hetil., 2013, 154, 1291–1296.

Sign in / Sign up

Export Citation Format

Share Document