Role of media and treatment on an SIR model

n this paper, the impact of awareness programs as well as treatment on an SIR model has been investigated. We assume that the whole population is divided into four compartments, named as susceptible (S), infected (I), aware susceptible (Sa) and recovered (R). Analytical findings and numerical simulations of the model show that if the exposure to the awareness program is high and adequate treatment is available, then the infection can be eliminated. Analysis of the model also depicts that if treatment is not available, then infection is high even if enough awareness is present. But in absence of awareness an infection can not be eliminated inspite of adequate treatment. Effective treatment can led to a diminished level of infection. Stability analysis of the model is investigated by using stability theory of differential equations. Further, numerical simulations are carried out to validate the analytical results

Modeling the dynamics of viral–host interaction during treatment of productively infected cells and free virus involving total immune response

Virus dynamics models are useful in interpreting and predicting the change in viral load over the time and the effect of treatment in emerging viral infections like HIV/AIDS, hepatitis B virus (HBV).We propose a mathematical model involving the role of total immune response (innate, CTL, and humoral) and treatment for productively infected cells and free virus to understand the dynamics of virus–host interactions. A threshold condition for the extinction or persistence of infection, i.e. basic reproductive number, in the presence of immune response (RI ) is established. We study the global stability of virus-free equilibrium and interior equilibrium using LaSalle’s principle and Lyapunov’s direct method. The global stability of virus-free equilibrium ensures the clearance of virus from the body, which is independent of initial status of subpopulations. Central manifold theory is used to study the behavior of equilibrium points at RI = 1, i.e. when the basic reproductive number in the presence of immune response is one. A special case, when the immune response (IR) is not present, has also been discussed. Analysis of special case suggests that the basic reproductive number in the absence of immune response R0 is greater than that of in the presence of immune response RI , i.e. R0> RI . It indicates that infection may be eradicated if RI  < 1. Numerical simulations are performed to illustrate the analytical results using MatLab and Mathematica

Dynamics of an SIR Model with Nonlinear Incidence and Treatment Rate

In this paper, global dynamics of an SIR model are investigated in which the incidence rate is being considered as Beddington-DeAngelis type and the treatment rate as Holling type II (saturated). Analytical study of the model shows that the model has two equilibrium points (diseasefree equilibrium (DFE) and endemic equilibrium (EE)). The disease-free equilibrium (DFE) is locally asymptotically stable when reproduction number is less than one. Some conditions on the model parameters are obtained to show the existence as well as nonexistence of limit cycle. Some sufficient conditions for global stability of the endemic equilibrium using Lyapunov function are obtained. The existence of Hopf bifurcation of model is investigated by using Andronov-Hopf bifurcation theorem. Further, numerical simulations are done to exemplify the analytical studies

Dynamics of prey–predator model with strong and weak Allee effect in the prey with gestation delay

This study proposes two prey–predator models with strong and weak Allee effects in prey population with Crowley–Martin functional response. Further, gestation delay of the predator population is introduced in both the models. We discussed the boundedness, local stability and Hopf-bifurcation of both nondelayed and delayed systems. The stability and direction of Hopfbifurcation is also analyzed by using Normal form theory and Center manifold theory. It is shown that species in the model with strong Allee effect become extinct beyond a threshold value of Allee parameter at low density of prey population, whereas species never become extinct in weak Allee effect if they are initially present. It is also shown that gestation delay is unable to avoiding the status of extinction. Lastly, numerical simulation is conducted to verify the theoretical findings.&nbsp

Optimal management of a renewable resource utilized by a population with taxation as a control variable

A dynamical model is proposed and analyzed to discuss the effect of population on a resource biomass by taking into account the crowding effect. It is assumed that the resource biomass, which has commercial importance, is subjected to harvesting. The harvesting effort is assumed to be a dynamical variable and taxation is being used as a control variable. The optimal harvesting policy is discussed using the Pontryagin’s maximum principle

Optimal harvesting policy of a prey–predator model with Crowley–Martin-type functional response and stage structure in the predator

In this paper, a three-dimensional dynamical model consisting of a prey, a mature predator, and an immature predator is proposed and analysed. The interaction between prey and mature predator is assumed to be of the Crowley–Martin type, and both the prey and mature predator are harvested according to catch-per-unit-effort (CPUE) hypothesis. Steady state of the system is obtained, stability analysis (local and global both) are discussed to explore the long-time behaviour of the system. The optimal harvesting policy is also discussed with the help of Pontryagin's maximum principle. The harvesting effort is taken as an effective control instrument to preserve prey and predator and to maintain them at an optimal level

Acute electrocardiographic changes during smoking: An observational study

Objective To study the temporal relationship of smoking with electrophysiological changes. Design Prospective observational study. Setting Tertiary cardiac center. Participants Male smokers with atypical chest pain were screened with a treadmill exercise test (TMT). A total of 31 such patients aged 49.8±10.5 years, in whom TMT was either negative or mildly positive were included. Heart rate variability (HRV) parameters of smokers were compared to those of 15 healthy non-smoking participants. Interventions All patients underwent a 24 h Holter monitoring to assess ECG changes during smoking periods. Results Heart rate increased acutely during smoking. Mean heart rate increased from 83.8±13.7 bpm 10 min before smoking, to 90.5±16.4 bpm during smoking, (p <0.0001) and returned to baseline after 30 min. Smoking was also associated with increased ectopic beats (mean of 5.3/h prior to smoking to 9.8/h during smoking to 11.3/h during the hour after smoking; p <0.001). Three patients (9.7%) had significant ST–T changes after smoking. HRV index significantly decreased in smokers (15.2±5.3) as compared to non-smoking controls participants (19.4±3.6; p=0.02), but the other spectral HRV parameters were comparable. Conclusions Heart rate and ectopic beats increase acutely following smoking. Ischaemic ST–T changes were also detected during smoking. Spectral parameters of HRV analysis of smokers remained in normal limits, but more importantly geometrical parameter—HRV index—showed significant abnormality

ORIENTAL JOURNAL OF CHEMISTRY Synthesis and Biological Activity of Novel (E)-N'-(Substituted)-3,4,5-trimethoxybenzohydrazide Analogs

ABSTRACT The hydrazide-hydrazone analogs 4a-4l is described via the condensation of 3,4,5-trimethoxybenzohydrazide 3 with various aromatic and hetero aromatic aldehydes a-l. Various spectroscopic techniques viz., ( 1 H NMR, 13 C NMR, IR and MS) were utilized to determine the structures of synthesized compounds. These compounds were evaluated for antibacterial, antifungal screening against S.aureus, S.pyogenes, E.coli, P.aeruginosa, Aspergillus niger and Candida albicans (Fungal strains). The results revealed that most of the hydrazone derivatives exhibited significant antibacterial activity. Furthermore, the synthesized hydrazone derivatives were found to exhibit significant antidiabetic activity when compared to insulin