Multiple attractors of host-parasitoid models with integrated pest management strategies: eradication, persistence and outbreak

Host-parasitoid models including integrated pest management (IPM) interventions with impulsive effects at both fixed and unfixed times were analyzed with regard to host-eradication, host-parasitoid persistence and host-outbreak solutions. The host-eradication periodic solution with fixed moments is globally stable if the host's intrinsic growth rate is less than the summation of the mean host-killing rate and the mean parasitization rate during the impulsive period. Solutions for all three categories can coexist, with switch-like transitions among their attractors showing that varying dosages and frequencies of insecticide applications and the numbers of parasitoids released are crucial. Periodic solutions also exist for models with unfixed moments for which the maximum amplitude of the host is less than the economic threshold. The dosages and frequencies of IPM interventions for these solutions are much reduced in comparison with the pest-eradication periodic solution. Our results, which are robust to inclusion of stochastic effects and with a wide range of parameter values, confirm that IPM is more effective than any single control tactic

A threshold policy to interrupt transmission of West Nile Virus to birds

This paper proposes a model of West Nile Virus (WNV) with a Filippov-type control strategy of culling mosquitoes implemented once the number of infected birds exceeds a threshold level. The long-term dynamical behaviour of the proposed non-smooth system is investigated. It is shown hat as the threshold value varies, model solutions ultimately approach either one of two endemic equilibria for two subsystems or a pseudo-equilibrium on the switching surface, which is a novel steady state. The results indicate that a previously chosen level of infected birds can be maintained when the threshold policy and other parameters are chosen properly. Numerical studies show that under the threshold policy, strengthening mosquito culling together with protecting bird population is beneficial to curbing the spread of WNV

Models of impulsive culling of mosquitoes to interrupt transmission of West Nile Virus to birds

A mathematical model describing the transmission of West Nile virus (WNV) between vector mosquitoes and birds, incorporating a control strategy of culling mosquitoes and defined by impulsive differential equations is presented and its properties investigated. First, we consider a strategy of periodic impulsive culling of the mosquitoes. Theoretical results indicate that if the threshold R 0 is greater than unity the disease uniformly persists, but, if not, the disease does not necessarily become extinct. The explicit conditions determining the backward or forward bifurcation were obtained. The culling rate has a major effect on the occurrence of backward bifurcation. Analysis shows that the disease is most sensitive to mosquito-bird contacts, mosquito-culling rate and intervals between culls. The dependence of the outcomes of the culling strategy on mosquito biting rate is discussed. When the complete elimination of disease is impossible, mosquito culls are implemented once the infected birds reach a predefined but adjustable threshold value. Numerical analysis shows that the period of mosquito culling finally stabilizes at a fixed value. In addition, variations of mean prevalence of \{WNV\} in birds and the culling period are simulated

Global dynamics of a piece-wise epidemic model with switching vaccination strategy

A piece-wise epidemic model of a switching vaccination program, implemented once the number of people exposed to a disease-causing virus reaches a critical level, is proposed. In addition, variation or uncertainties in interventions are examined with a perturbed system version of the model. We also analyzed the global dynamic behaviors of both the original piece-wise system and the perturbed version theoretically, using generalized Jacobian theory, Lyapunov constants for a non-smooth vector field and a generalization of Dulac's criterion. The main results show that, as the critical value varies, there are three possibilities for stabilization of the piece-wise system: (i) at the disease-free equilibrium; (ii) at the endemic states for the two subsystems or (iii) at a generalized equilibrium which is a novel global attractor for non-smooth systems. The perturbed system exhibits new global attractors including a pseudo-focus of parabolic-parabolic (PP) type, a pseudo-equilibrium and a crossing cycle surrounding a sliding mode region. Our findings demonstrate that an infectious disease can be eradicated either by increasing the vaccination rate or by stabilizing the number of infected individuals at a previously given level, conditional upon a suitable critical level and the parameter values

Global Dynamics and Applications of an Epidemiological Model for Hepatitis C Virus Transmission in China

An epidemiological model is proposed and studied to understand the transmission dynamics and prevalence of HCV infection in China. Theoretical analysis indicates that the basic reproduction number R0 provides a threshold value determining whether the disease dies out or not. Two Lyapunov functions are constructed to prove the global asymptotic stability of the disease-free and the endemic equilibria, respectively. Based on data reported by the National Health and Family Planning Commission of China, the basic reproduction number is estimated as approximately R0=1.9897, which is much less than that for the model when a treatment strategy is not considered. An ever-increasing HCV infection is predicted in the near future. Numerical simulations, performed to investigate the potential effect of antiviral treatment, show that increasing the treatment cure rate and enlarging the treatment rate for patients at the chronic stage remain effective in reducing the number of new infections and the equilibrium prevalence. The finding suggests that treatment measures are significantly beneficial for disease control in terms of reducing new infections and, in particular, more attention should be paid to treatment for patients at the chronic stage

General practitioners' knowledge of ageing and attitudes towards older people in China

Author version made available in accordance with Publisher copyright. 12 month embargo from date of publication [Oct 9 2013]. This is the accepted version of the following article: [Yang, Y., Xiao, L. D., Ullah, S. and Deng, L. (2013), General practitioners' knowledge of ageing and attitudes towards older people in China. Australasian Journal on Ageing. ], which has been published in final form at [doi: 10.1111/ajag.12105]. In addition, authors may also transmit, print and share copies with colleagues, provided that there is no systematic distribution of the submitted version, e.g. posting on a listserve, network or automated delivery.Aim To explore general practitioners (GPs)' knowledge of ageing, attitudes towards older people and factors affecting their knowledge and attitudes in a Chinese context. Methods Four hundred GPs were surveyed using the Chinese version of the Aging Semantic Differential (CASD) and the Chinese version of the Facts on Aging Quiz (CFAQ1) scale. Results The CASD scores indicated that GPs had a neutral attitude towards older people. The CFAQ1 scores indicated a low level of knowledge about ageing. GPs' awareness of the mental and social facts of ageing was poorer compared to that of physical facts. Male GPs had a significantly higher negative bias score than female GPs. No other variables had a statistically significant influence on knowledge and attitudes. Conclusions The findings suggest the need for education interventions for GPs regarding knowledge of ageing and also provide evidence to guide future development of continuing medical programs for this group of medical doctors

Modeling Saturated Diagnosis and Vaccination in Reducing HIV/AIDS Infection

A mathematical model is proposed to consider the effects of saturated diagnosis and vaccination on HIV/AIDS infection. By employing center manifold theory, we prove that there exists a backward bifurcation which suggests that the disease cannot be eradicated even if the basic reproduction number is less than unity. Global stability of the disease-free equilibrium is investigated for appropriate conditions. When the basic reproduction number is greater than unity, the system is uniformly persistent. The proposed model is applied to describe HIV infection among injecting drug users (IDUs) in Yunnan province, China. Numerical studies indicate that new cases and prevalence are sensitive to transmission rate, vaccination rate, and vaccine efficacy. The findings suggest that increasing vaccination rate and vaccine efficacy and enhancing interventions like reducing share injectors can greatly reduce the transmission of HIV among IDUs in Yunnan province, China

Linking key intervention timing to rapid decline of the COVID-19 effective reproductive number to quantify lessons from mainland China

Effective reproductive numbers (Rt) were calculated from data on the COVID-19 outbreak in China and linked to dates in 2020 when different interventions were enacted. From a maximum of 3.98 before the lockdown in Wuhan City, the values of Rt declined to below 1 by the second week of February, after the construction of hospitals dedicated to COVID-19 patients. The Rt continued to decline following additional measures in line with the policy of “early detection, early report, early quarantine, and early treatment.” The results provide quantitative evaluations of how intervention measures and their timings succeeded, from which lessons can be learned by other countries dealing with future outbreaks

Modelling the effects of contaminated environments in mainland China on seasonal HFMD infections and the potential benefit of a pulse vaccination strategy

Substantial and increasing outbreaks of EV71-related hand, foot and mouth disease (HFMD) have occurred recently in mainland China with serious consequences for child health. The HFMD pathogens can survive for long periods outside the host in suitable conditions, and hence indirect transmission via free-living pathogens in the environment cannot be ignored. We propose a novel mathematical model of both periodic direct transmission and indirect transmission followed by incorporation of an impulsive vaccination strategy. By applying Floquet theory and the comparison theorem of impulsive differential equations, we obtained a threshold parameter which governs the extinction or the uniform persistence of the disease. The rate, frequency and timing of pulse vaccination were found to affect the basic reproduction number and the number of infected individuals significantly. In particular, frequent vaccination with a high coverage rate leads to declines in the basic reproduction number. Moreover, for a given rate of vaccination or frequency, numerical studies suggested that there was an optimal time (September, just before the start of new school terms) when the basic reproduction number and hence new HFMD infections could be minimised. Frequent high intensity vaccinations at a suitable time (e.g. September) and regular cleaning of the environment are effective measures for controlling HFMD infections

Modelling the effects of contaminated environments on HFMD infections in mainland China

Hand-foot-mouth disease (HFMD) has spread widely in mainland China increasing in prevalence in most years with serious consequences for child health. The HFMD virus can survive for a long period outside the host in suitable conditions, and hence contaminated environments may play important roles in HFMD infection. A new mathematical model was proposed and used to investigate the roles that asymptomatic individuals and contaminated environments played in HFMD dynamics. The model includes both direct transmission between susceptible and infected individuals and indirect transmission via free-living infectious unites in the environment. Theoretical analysis shows that the disease goes to extinction if the basic reproduction number is less than unity, whilst otherwise the disease persists. By fitting the proposed model to surveillance data we estimated the basic reproduction number as 1.509. Numerical simulations show that increasing the rate of virus clearance and decreasing transmission rates can delay epidemic outbreaks and weaken the severity of HFMD. Sensitivity analysis indicated that the basic reproduction number is sensitive to the transmission rate induced by asymptomatic infectious individuals and parameters associated with contaminated environments such as the indirect transmission rate, the rate of clearance and the virus shedding rates. This implies that asymptomatic infectious individuals and contaminated environments contribute substantially to new HFMD infections, and so would be targets for effective control measures