Mass media reports can induce individual behaviour change during a disease outbreak, which has been found to be useful as it reduces the force of infection. We propose a compartmental model by including a new compartment of the intensity of the media reports, which extends existing models by considering a novel media function, which is dependent both on the number of infected individuals and on the intensity of mass media. The existence and stability of the equilibria are analyzed and an optimal control problem of minimizing the total number of cases and total cost is considered, using reduction or enhancement in the media reporting rate as the control. With the help of Pontryagin’s Maximum Principle, we obtain the optimal media reporting intensity. Through parameterization of the model with the 2009 A/H1N1 influenza outbreak data in the 8th Hospital of Xi’an in Shaanxi Province of China, we obtain the basic reproduction number for the formulated model with two particular media functions. The optimal media reporting intensity obtained here indicates that during the early stage of an epidemic we should quickly enhance media reporting intensity, and keep it at a maximum level until it can finally weaken when epidemic cases have decreased significantly. Numerical simulations show that media impact reduces the number of cases during an epidemic, but that the number of cases is further mitigated under the optimal reporting intensity. Sensitivity analysis implies that the outbreak severity is more sensitive to the weight α1 (weight of media effect sensitive to infected individuals) than weight α2 (weight of media effect sensitive to media items).
The global outbreak of COVID-19 has caused worrying concern amongst the public and health authorities. The first and foremost problem that many countries face during the outbreak is a shortage of medical resources. In order to investigate the impact of a shortage of hospital beds on the COVID-19 outbreak, we formulated a piecewise smooth model for describing the limitation of hospital beds. We parameterized the model while using data on the cumulative numbers of confirmed cases, recovered cases, and deaths in Wuhan city from 10 January to 12 April 2020. The results showed that, even with strong prevention and control measures in Wuhan, slowing down the supply rate, reducing the maximum capacity, and delaying the supply time of hospital beds all aggravated the outbreak severity by magnifying the cumulative numbers of confirmed cases and deaths, lengthening the end time of the pandemic, enlarging the value of the effective reproduction number during the outbreak, and postponing the time when the threshold value was reduced to 1. Our results demonstrated that establishment of the Huoshenshan, Leishenshan, and Fangcang shelter hospitals avoided 22,786 people from being infected and saved 6524 lives. Furthermore, the intervention of supplying hospital beds avoided infections in 362,360 people and saved the lives of 274,591 persons. This confirmed that the quick establishment of the Huoshenshan, Leishenshan Hospitals, and Fangcang shelter hospitals, and the designation of other hospitals for COVID-19 patients played important roles in containing the outbreak in Wuhan.
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 numberR0provides 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 approximatelyR0=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.
Highlights• Propose a Filippov model of West Nile Virus with density-dependent culling strategy.• Solutions approach either endemic equilibrium for subsystems or a pseudo-equilibrium.• Results indicate that a previously chosen level of infected birds can be maintained.• Strengthening mosquito culling is beneficial to curbing the spread of WNV. AbstractThis 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 that 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.