scholarly journals Analysis of a Hand-Foot-Mouth Disease Model with Standard Incidence Rate and Estimation for Basic Reproduction Number

2017 ◽  
Vol 22 (2) ◽  
pp. 29
Author(s):  
Chunqing Wu
Keyword(s):  
Incidence Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Disease Model ◽  
Mouth Disease ◽  
Hand Foot Mouth Disease

scholarly journals The Dynamics and Optimal Control of a Hand-Foot-Mouth Disease Model

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Hongwu Tan ◽  
Hui Cao
Keyword(s):  
Optimal Control ◽  
Reproduction Number ◽  
Control Strategies ◽  
Disease Model ◽  
Mouth Disease ◽  
Infected People ◽  
Hand Foot Mouth Disease ◽  
The Cost ◽  
Existence Of Equilibria ◽  
Disease Free

We build and study the transmission dynamics of a hand-foot-mouth disease model with vaccination. The reproduction number is given, the existence of equilibria is obtained, and the global stability of disease-free equilibrium is proved by constructing the Lyapunov function. We also apply optimal control theory to the hand-foot-mouth disease model. The treatment and vaccination interventions are considered in the hand-foot-mouth disease model, and the optimal control strategies based on minimizing the cost of intervention and minimizing the number of the infected people are given. Numerical results show the usefulness of the optimization strategies.

scholarly journals Dynamics Analysis of a Viral Infection Model with a General Standard Incidence Rate

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yu Ji ◽  
Muxuan Zheng
Keyword(s):  
Viral Infection ◽  
Incidence Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Reproduction Numbers ◽  
The Basic Reproduction Number ◽  
General Standard

The basic viral infection models, proposed by Nowak et al. and Perelson et al., respectively, have been widely used to describe viral infection such as HBV and HIV infection. However, the basic reproduction numbers of the two models are proportional to the number of total cells of the host's organ prior to the infection, which seems not to be reasonable. In this paper, we formulate an amended model with a general standard incidence rate. The basic reproduction number of the amended model is independent of total cells of the host’s organ. When the basic reproduction numberR0<1, the infection-free equilibrium is globally asymptotically stable and the virus is cleared. Moreover, ifR0>1, then the endemic equilibrium is globally asymptotically stable and the virus persists in the host.

Analysis of a hand–foot–mouth disease model

2017 ◽  
Vol 10 (02) ◽  
pp. 1750016 ◽  
Author(s):  
Swarnali Sharma ◽  
G. P. Samanta
Keyword(s):  
Epidemic Model ◽  
Equilibrium Points ◽  
Disease Model ◽  
Foot And Mouth Disease ◽  
Cost Effective ◽  
Mouth Disease ◽  
Point Of View ◽  
Existence And Stability ◽  
Hand Foot Mouth Disease ◽  
Asymptomatic Phase

In this paper, we have introduced a six-compartmental epidemic model with hand, foot and mouth disease (HFMD) infection. The total population is divided into six subclasses, namely susceptible, exposed, infective in asymptomatic phase, infective in symptomatic phase, quarantined and recovered class. Some basic properties such as boundedness and non-negativity of solutions are discussed. The basic reproduction number ([Formula: see text]) of the system is obtained using next generation matrix method. Then the deterministic dynamical behaviors of the system are studied. Our study includes the existence and stability analysis of equilibrium points of the system. The sensitivity analysis of our system helps us to find out the parameters of greater interest. Next, we deal with the epidemic model with three controls (two treatment controls with quarantine control). We show that there exists an optimal control, which is effective in controlling the disease outbreak in a cost effective way. Numerical simulation is presented with the help of MATLAB, which shows the reliability of our model from the practical point of view.

scholarly journals Discrete epidemic models with two time scales

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rafael Bravo de la Parra ◽  
Luis Sanz-Lorenzo
Keyword(s):  
Time Scales ◽  
Discrete Time ◽  
Basic Reproduction Number ◽  
First Principles ◽  
Reproduction Number ◽  
Disease Model ◽  
Epidemic Models ◽  
Full Model ◽  
Disease Dynamics ◽  
Spatial Locations

AbstractThe main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could represent movements between spatial locations, changes of individual activities or behaviors, or others.To include a sufficiently general disease model, we first build up from first principles a discrete-time susceptible–exposed–infectious–recovered–susceptible (SEIRS) model and characterize the eradication or endemicity of the disease with the help of its basic reproduction number $\mathcal{R}_{0}$ R 0 .Then, we propose a general full model that includes sequentially the two processes at different time scales and proceed to its analysis through a reduced model. The basic reproduction number $\overline{\mathcal{R}}_{0}$ R ‾ 0 of the reduced system gives a good approximation of $\mathcal{R}_{0}$ R 0 of the full model since it serves at analyzing its asymptotic behavior.As an illustration of the proposed general framework, it is shown that there exist conditions under which a locally endemic disease, considering isolated patches in a metapopulation, can be eradicated globally by establishing the appropriate movements between patches.

scholarly journals Hand, Foot, and Mouth Disease in Thailand: A Comprehensive Modelling of Epidemic Dynamics

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Suraj Verma ◽  
M. A. Razzaque ◽  
U. Sangtongdee ◽  
C. Arpnikanondt ◽  
B. Tassaneetrithep ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Clustering Algorithm ◽  
Reproduction Number ◽  
Foot And Mouth Disease ◽  
Mouth Disease ◽  
Seasonal Effect ◽  
Epidemic Dynamics ◽  
District Hospitals ◽  
Foot And Mouth ◽  
The Basic Reproduction Number

Hand, foot, and mouth disease (HFMD) is a highly contagious disease with several outbreaks in Asian-Pacific countries, including Thailand. With such epidemic characteristics and potential economic impact, HFMD is a significant public health issue in Thailand. Generally, contagious/infectious diseases’ transmission dynamics vary across geolocations due to different socioeconomic situations, demography, and lifestyles. Hence, a nationwide comprehensive model of the disease’s epidemic dynamics can provide information to understand better and predict a potential outbreak of this disease and efficiently and effectively manage its impact. However, there is no nationwide and comprehensive (i.e., the inclusion of reinfections in the model) model of HFDM dynamics for Thailand. This paper has endeavoured to promote nationwide comprehensive modelling of HFMD’s epidemic dynamics and comprehend the reinfection cases. We have formulated the SEIRS epidemiological model with dynamic vitals, including reinfections, to explore this disease’s prevalence. We also introduced periodic seasonality to reproduce the seasonal effect. The pattern of spread of this disease is uneven across the provinces in Thailand, so we used K -means clustering algorithm to cluster those provinces into three groups (i.e., highly, moderately, and least affected levels). We also analysed health records collected from district hospitals, which suggest significant reinfection cases. For example, we found that 11% (approximately) of infectious patients return for repeat treatment within the study period. We also performed sensitivity analysis which indicates that the basic reproduction number ( R 0 ) is sensitive to the rate of transmission ( β ) and the rate at which infected people recover ( γ ). By fitting the model with HFMD confirmed data for the provinces in each cluster, the basic reproduction number ( R 0 ) was estimated to be 2.643, 1.91, and 3.246 which are greater than 1. Based on this high R 0 , this study recommends that this disease will persist in the coming years under identical cultural and environmental conditions.

scholarly journals Global Dynamics of a Periodic SEIRS Model with General Incidence Rate

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Eric Ávila-Vales ◽  
Erika Rivero-Esquivel ◽  
Gerardo Emilio García-Almeida
Keyword(s):  
Numerical Simulations ◽  
Incidence Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Global Dynamics ◽  
Threshold Parameter ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
General Incidence Rate ◽  
The Basic Reproduction Number

We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate of the form Sf(I), and it is shown that the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence of disease. Numerical simulations are performed using a nonlinear incidence rate to estimate the basic reproduction number and illustrate our analytical findings.

scholarly journals Basic Reproduction Number of Enterovirus 71 Coxsackievirus A16 and A6: Evidence from Outbreaks of Hand, Foot and Mouth Disease in China between 2011 and 2018

2020 ◽  
Author(s):  
Zhong Zhang ◽  
Yang Liu ◽  
Fengfeng Liu ◽  
Minrui Ren ◽  
Taoran Nie ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Mainland China ◽  
Enterovirus 71 ◽  
Foot And Mouth Disease ◽  
Mouth Disease ◽  
Initial Growth ◽  
Coxsackievirus A16 ◽  
Foot And Mouth ◽  
Common Serotypes

Abstract Background Enterovirus 71 (EV-A71), Coxsackievirus A16 (CV-A16) and Coxsackievirus A6 (CV-A6) are common serotypes causing hand, foot, and mouth disease (HFMD). Analyses on the basic reproduction number (R0) of common pathogens causing HFMD are limited and there are no related studies using field data from outbreaks in mainland China. Methods We estimated the pathogen-specific basic reproduction number based on laboratory-confirmed HFMD outbreaks (clusters of ≥10 HFMD cases) reported to the national surveillance system between 2011 and 2018. The reproduction numbers were calculated using a mathematical model and the cumulative cases during the initial growth periods. Results This study included 539 outbreaks, of which 198 were caused by EV-A71, 316 by CV-A16, and 25 by CV-A6. All 10417 cases involved were children. Assuming the outbreaks occurred in closed systems and the incubation period is 5 days, the median R0s of EV-A71, CV-A16, and CV-A6 were 5.06 [2.81, 10.20], 4.84 [3.00, 9.00] and 5.94 [3.27, 10.00] (Median [IQR]). After adjusting for seroprevalences, the R0s for EV-A71, CV-A16 (optimistic and conservative scenarios), and CV-A6 were 12.60 [IQR: 7.35, 25.40], 9.29 [IQR: 6.01, 19.20], 15.50 [IQR: 9.77, 30.40], and 25.80 [IQR: 14.20, 43.50], respectively. We did not observe changes in the R0s of EV-A71 after vaccine licensure (p-value = 0.67). Conclusions HFMD is highly transmissible when caused by the three most common serotypes. In mainland China, it primarily affects young children. Although a vaccine became available in 2016, we have not yet observed any related changes in the disease dynamics.

scholarly journals Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
Junyuan Yang ◽  
Xiaoyan Wang
Keyword(s):  
Incidence Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Threshold Dynamics ◽  
Sir Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sir Epidemic ◽  
Age Dependent ◽  
The Basic Reproduction Number

We propose an SIR epidemic model with different susceptibilities and nonlinear incidence rate. First, we obtain the existence and uniqueness of the system and the regularity of the solution semiflow based on some assumptions for the parameters. Then, we calculate the basic reproduction number, which is the spectral radius of the next-generation operator. Second, we investigate the existence and local stability of the steady states. Finally, we construct suitable Lyapunov functionals to strictly prove the global stability of the system, which are determined by the basic reproduction number ℛ0 and some assumptions for the incidence rate.

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