A delayed hand–foot–mouth disease model with pulse vaccination strategy

Stability Analysis of a Delayed Rumor Propagation Model with Nonlinear Incidence Incorporating Impulsive Vaccination

The presence of information asymmetry can hinder the public's ability to make well-informed decisions, resulting in unwarranted suspicion and the widespread dissemination of rumors. Therefore, it is crucial to provide individuals with consistent and dependable scientific education. Regular popular science education is considered a periodic impulsive intervention to mitigate the impact of information asymmetry and promote a more informed and discerning public. Drawing on these findings, this paper proposes a susceptible-hesitant-infected-refuting-recovered (SHIDR) rumor-spreading model to explain the spread of rumors. The model incorporates elements such as time delay, nonlinear incidence, and refuting individuals. Firstly, by applying the comparison theorem of an impulsive differential equation, we calculate two thresholds for rumor propagation. Additionally, we analyze the conditions of global attractiveness of the rumor-free periodic solution. Furthermore, we consider the condition for the rumor's permanence. Finally, numerical simulations are conducted to validate the accuracy of our findings. The results suggest that increasing the proportion of impulsive vaccination, reducing the impulsive period, or prolonging the delay time can effectively suppress rumors.

The risk factor assessment of the spread of foot-and-mouth disease in mainland China

In China, foot-and-mouth disease (FMD) serotype O remains prevalent, and its main host is pigs. Infected but undiscovered pigs can carry foot-and-mouth disease virus (FMDV) for a longtime. And, the virus can spread among farms through pig trade. Although individual vaccination at least 2 times a year and monthly monitoring disease and culling all individual in same group for pigs are adopted vigorously in China, the epidemic remains prevalent. Therefore, in this paper, based on these propagation characteristics and control measures of the epidemic in China, we take the pig farms as research individuals, the trade among farms as transmission routes to establish a dynamic model with nonlinear incidence. In addition, we use this model to assess the impact of trade and transport of pigs among farms on the spread of foot-and-mouth disease virus (FMDV), and to assess the effect of the immunization, monitoring and culling adopted presently in China on the control of the epidemic. By the dynamical analysis of the model, it is found that there will appear backward branching under some conditions, which means that there are two spreading thresholds for the disease, and the disease development trend is also related to the current epidemic situation. Besides, we give the threshold conditions of key parameters to control the spread of FMD. By carrying out data fitting and parameter estimation, we confirm the model rationality, and give four evaluation indexes: the basic reproduction number R₀ of FMD serotype O in China, the value of the infected farms at the equilibria, annual probability of a susceptible farm being infected and annual transmission intensity of an infected farm. By carrying out the sensitivity analysis of key parameters on four evaluation indexes, the effect of parameters on the spread of the disease can be intuitively observed. All these can provide a theoretical basis for understanding of the trading-based transmission mechanism, control and prevention of foot-and-mouth disease in pigs in China.

Epidemiological and clinical characteristics of severe hand-foot-and-mouth disease (HFMD) among children: a 6-year population-based study

Background

Hand-foot-and-mouth disease (HFMD) is considered to be self-limited, however, severe HFMD is a deadly threat for children worldwide, therefore, it is essential to define the clinical and epidemiologic characteristics of children with severe HFMD and identify the risk factors of death.

Methods

Between 2013 and 2018, children who diagnosed with severe HFMD from Chongqing, China were enrolled in this population-based study. A total of 459 severe HFMD children cases were identified during the study period, including 415 survivors and 44 fatal cases. Demographic, geographical, epidemiological and clinical data of the cases were acquired and analyzed.

Results

Risk factors of the death because of severe HFMD children included female, aged 1 ~ 3 years, enterovirus 71 infection, falling ill in winter, more than one children in home, being taken care of by grandparents, the caregivers’ education not more than 9 years, having fever more than 3 days, consciousness disorders, general weakness, vomiting, general weakness, abnormal pupillary light reflex, repeated cough, tachypnea, moist rales, white frothy sputum, pink frothy sputum, and cyanosis on lips or the whole body, tachycardia, arrhythmia, cold limbs, pale complexion, weakened pulse. (all p < 0.05). Spatial-temporal analysis detected high-value clusters, the most likely cluster located at rural countries in the northern parts of Chongqing, from January, 2015 to July, 2017. (p < 0.01). Besides, some urban districts were also found high incidence of severe HFMD cases according to the incidence maps.

Conclusions

The detection of clinical risk factors and the temporal, spatial and socio-demographic distribution epidemiological characteristics of severe HFMD contribute to the timely diagnosis and intervention, the results of this study can be the reference of further clinical and public health practice.

On a New Discrete SEIADR Model with Mixed Controls: Study of Its Properties

A new discrete SEIADR epidemic model is built based on previous continuous models. The model considers two extra subpopulation, namely, asymptomatic and lying corpses on the usual SEIR models. It can be of potential interest for diseases where infected corpses are infectious like, for instance, Ebola. The model includes two types of vaccinations, a constant one and another proportional to the susceptible subpopulation, as well as a treatment control applied to the infected subpopulation. We study the positivity of the controlled model and the stability of the equilibrium points. Simulations are made in order to provide allocation and examples to the different possible conditions. The equilibrium point with no infection and its stability is related, via the reproduction number values, to the reachability of the endemic equilibrium point.

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

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.

Analysis of a hand–foot–mouth disease model

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.