scholarly journals Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Peilin Shi ◽  
Lingzhen Dong
Keyword(s):  
Infectious Diseases ◽  
Global Stability ◽  
Periodic Solutions ◽  
Dynamical Models ◽  
Bifurcation Theorem ◽  
Time Period ◽  
Population Sizes ◽  
Variable Population ◽  
Disease Free ◽  
Varying Population

We formulate and discuss models for the spread of infectious diseases with variable population sizes and vaccinations on the susceptible individuals. First, we assume that the susceptible individuals are vaccinated continuously. We establish the threshold-like results for the existence and global stability of the disease-free and the endemic equilibriums for these systems. Especially, we prove the global stability of the endemic equilibriums by converting the systems into integrodifferential equations. Second, we suppose that vaccinations occur once per time period. We obtain the existence and global stability of the disease-free periodic solutions for such systems with impulsive effects. By a useful bifurcation theorem, we acquire the existence of the endemic periodic solutions when the disease-related deaths do not occur. At last, we compare the results with vaccinations and without vaccinations and illustrate our results by numerical simulations.

scholarly journals Global Stability of Vector-Host Disease with Variable Population Size

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Saeed Islam ◽  
Sher Afzal Khan ◽  
Gul Zaman
Keyword(s):  
Global Stability ◽  
Population Size ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Host Disease ◽  
Variable Population ◽  
Globally Stable ◽  
Disease Free ◽  
Disease Persistence ◽  
Variable Population Size

The paper presents the vector-host disease with a variability in population. We assume, the disease is fatal and for some cases the infected individuals become susceptible. We first show the local and global stability of the disease-free equilibrium, for the case when, the disease free-equilibrium of the model is both locally as well as globally stable. For , the disease persistence occurs. The endemic equilibrium is locally as well as globally asymptotically stable for . Numerical results are presented for the justifications of theoratical results.

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

Graphical Hopf Bifurcation of a Filippov HTLV-1 Model With Delay in Cytotoxic T Cells Response

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Elham Shamsara ◽  
Zahra Afsharnezhad ◽  
Elham Javidmanesh
Keyword(s):  
T Cells ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Bifurcation Theory ◽  
Cytotoxic T Cells ◽  
Dynamical Behavior ◽  
Bifurcation Theorem ◽  
Nyquist Criterion ◽  
The Stability ◽  
Frequency Domain Approach

In this paper, we present a discontinuous cytotoxic T cells (CTLs) response for HTLV-1. Moreover, a delay parameter for the activation of CTLs is considered. In fact, a system of differential equation with discontinuous right-hand side with delay is defined for HTLV-1. For analyzing the dynamical behavior of the system, graphical Hopf bifurcation is used. In general, Hopf bifurcation theory will help to obtain the periodic solutions of a system as parameter varies. Therefore, by applying the frequency domain approach and analyzing the associated characteristic equation, the existence of Hopf bifurcation by using delay immune response as a bifurcation parameter is determined. The stability of Hopf bifurcation periodic solutions is obtained by the Nyquist criterion and the graphical Hopf bifurcation theorem. At the end, numerical simulations demonstrated our results for the system of HTLV-1.

scholarly journals Impact of daily versus weekly service of infectious diseases consultation on hospital antimicrobial consumption: a retrospective study

2020 ◽  
Vol 20 (1) ◽  
Author(s):  
Andrea Cona ◽  
Lidia Gazzola ◽  
Ottavia Viganò ◽  
Teresa Bini ◽  
Giulia Carla Marchetti ◽  
...  
Keyword(s):  
Infectious Diseases ◽  
Hospital Setting ◽  
Patient Characteristics ◽  
Wilcoxon Test ◽  
Defined Daily Dose ◽  
Paired Data ◽  
Comprehensive Management ◽  
Time Period ◽  
Infectious Diseases Consultation ◽  
The Impact

Abstract Background To verify whether a daily service of Infectious Diseases consultation (ID-cons) is more effective than a weekly service in reducing antibiotic (ATB) consumption without worsening of clinical outcomes. Methods Two-year observational analysis of the ID-cons provided in a hospital setting in Milan, Italy. ID-cons resulted in: start-of-ATB; no-ATB; confirmation; modification-of-ATB. The impact of a weekly (September 1, 2016 - August 31, 2017 versus a daily (September 1, 2017 – September 30, 2018) service of ID-cons was evaluated in terms of: time-from-admission-to-first-ID-cons, type of ATB-intervention and number-of-ID-cons per 100 bed-days (bd). Primary outcomes: reduction of hospital ATB consumption overall and by department and classes expressed as Defined Daily Dose (DDD)/100bd (by Wilcoxon test for paired data). Secondary outcomes: overall and sepsis-related in-hospital annual mortality rates (as death/patient’s admissions). Results Overall 2552 ID-cons in 1111 patients (mean, 2.3 ID-cons per patient) were performed (18.6% weekly vs 81.4% daily). No differences in patient characteristics were observed. In the daily-service, compared to the weekly-service, patients were seen by the ID-consultant earlier (time-from-admission-to-ID-cons: 6 days (IQR 2–13) vs 10 days (IQR 6–19), p < 0.001) and ATB was more often started by the ID-consultant (Start-of-ATB: 11.6% vs 8%, p = 0.02), rather than treating physicians. After switching to daily-service, the number-of-ID-cons increased from 0.4/100bd to 1.5/100bd (p = 0.01), with the greatest increase in the emergency department (1.5/100bd vs 6.7/100bd, p < 0.001). Total ATB consumption decreased from 64 to 60 DDD/100bd. As for the number-of-cons, the consumption of ATB decreased mainly in the emergency area. According to ATB classes, glycopeptides consumption was reduced from 3.1 to 2.1 DDD/100bd (p = 0.02) while carbapenem use decreased from 3.7 to 3.1 DDD/100bd (p = 0.07). No changes in overall mortality (5.2% vs 5.2%) and sepsis-related mortality (19.3% vs 20.9%; p = 0.7) were observed among the two time-period. Conclusions Daily-ID-cons resulted in a more comprehensive management of the infected patient by the ID-consultant, especially in the emergency area where we also observed the highest rate of reduction of ATB-usage. No change in mortality was observed.

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