Threshold dynamics of an almost periodic vector-borne disease model.

Many infectious diseases cannot be transmitted from human to human directly, and the transmission needs to be done via a vector. It is well known that vectors' life cycles are highly dependent on their living environment. In order to investigate dynamics of vector-borne diseases under environment influence, we propose a vector-borne disease model with almost periodic coefficients. We derive the basic reproductive number [Formula: see text] for this model and establish a threshold type result on its global dynamics in terms of [Formula: see text]. As an illustrative example, we consider an almost periodic model of malaria transmission. Our numerical simulation results show that the basic reproductive number may be underestimated if almost periodic coefficients are replaced by their average values . Finally, we use our model to study the dengue fever transmission in Guangdong, China. The parameters are chosen to fit the reported data available for Guangdong. Numerical simulations indicate that the annual dengue fever case in Guangdong will increase steadily in the near future unless more effective control measures are implemented. Sensitivity analysis implies that the parameters with strong impact on the outcome are recovery rate, mosquito recruitment rate, mosquito mortality rate, baseline transmission rates between mosquito and human. This suggests that the effective control strategies may include intensive treatment, mosquito control, decreasing human contact number with mosquitoes (e.g., using bed nets and preventing mosquito bites), and environmental modification.

Analysis of a COVID-19 Epidemic Model with Seasonality.

The statistics of COVID-19 cases exhibits seasonal fluctuations in many countries. In this paper, we propose a COVID-19 epidemic model with seasonality and define the basic reproduction number [Formula: see text] for the disease transmission. It is proved that the disease-free equilibrium is globally asymptotically stable when [Formula: see text], while the disease is uniformly persistent and there exists at least one positive periodic solution when [Formula: see text]. Numerically, we observe that there is a globally asymptotically stable positive periodic solution in the case of [Formula: see text]. Further, we conduct a case study of the COVID-19 transmission in the USA by using statistical data.

Preliminary prediction of the control reproduction number of COVID-19 in Shaanxi Province, China.

OBJECTIVES: Firstly, according to the characteristics of COVID-19 epidemic and the control measures of the government of Shaanxi Province, a general population epidemic model is established. Then, the control reproduction number of general population epidemic model is obtained. Based on the epidemic model of general population, the epidemic model of general population and college population is further established, and the control reproduction number is also obtained. METHODS: For the established epidemic model, firstly, the expression of the control reproduction number is obtained by using the next generation matrix. Secondly, the real-time reported data of COVID-19 in Shaanxi Province is used to fit the epidemic model, and the parameters in the model are estimated by least square method and MCMC. Thirdly, the Latin hypercube sampling method and partial rank correlation coefficient (PRCC) are adopted to analyze the sensitivity of the model. CONCLUSIONS: The control reproduction number remained at 3 from January 23 to January 31, then gradually decreased from 3 to slightly greater than 0.2 by using the real-time reports on the number of COVID-19 infected cases from Health Committee of Shaanxi Province in China. In order to further control the spread of the epidemic, the following measures can be taken: (i) reducing infection by wearing masks, paying attention to personal hygiene and limiting travel; (ii) improving isolation of suspected patients and treatment of symptomatic individuals. In particular, the epidemic model of the college population and the general population is established, and the control reproduction number is given, which will provide theoretical basis for the prevention and control of the epidemic in the colleges.

A periodic two-patch SIS model with time delay and transport-related infection.

In this paper, we propose a periodic SIS epidemic model with time delay and transport-related infection in a patchy environment. The basic reproduction number R0 is derived which determines the global dynamics of the model system: if R0 < 1, the disease-free periodic state is globally attractive while there exists at least one positive periodic state and the disease persists if R0 > 1. Numerical simulations are performed to confirm the analytical results and to explore the dependence of R0 on the transport-related infection parameters and the amplitude of fluctuations.

Modeling and Analyzing the Transmission Dynamics of HBV Epidemic in Xinjiang, China.

Hepatitis B is an infectious disease caused by the hepatitis B virus (HBV) which affects livers. In this paper, we formulate a hepatitis B model to study the transmission dynamics of hepatitis B in Xinjiang, China. The epidemic model involves an exponential birth rate and vertical transmission. For a better understanding of HBV transmission dynamics, we analyze the dynamic behavior of the model. The modified reproductive number σ is obtained. When σ < 1, the disease-free equilibrium is locally asymptotically stable, when σ > 1, the disease-free equilibrium is unstable and the disease is uniformly persistent. In the simulation, parameters are chosen to fit public data in Xinjiang. The simulation indicates that the cumulated HBV infection number in Xinjiang will attain about 600,000 cases unless there are stronger or more effective control measures by the end of 2017. Sensitive analysis results show that enhancing the vaccination rate for newborns in Xinjiang is very effective to stop the transmission of HBV. Hence, we recommend that all infants in Xinjiang receive the hepatitis B vaccine as soon as possible after birth.

An impulsive delayed SEIRS epidemic model with saturation incidence.

A delayed SEIRS epidemic model with pulse vaccination and saturation incidence rate is investigated. Using Krasnoselskii's fixed-point theorem, we obtain the existence of infection-free periodic solution of the impulsive delayed epidemic system. We define some new threshold values R(1), R(2) and R(3). Further, using the comparison theorem, we obtain the explicit formulae of R(1) and R(2). Under the condition R(1) < 1, the infection-free periodic solution is globally attractive, and that R(2) > 1 implies that the disease is permanent. Theoretical results show that the disease will be extinct if the vaccination rate is larger than θ* and the disease is uniformly persistent if the vaccination rate is less than θ(*). Our results indicate that a long latent period of the disease or a large pulse vaccination rate will lead to eradication of the disease. Moreover, we prove that the disease will be permanent as R(3) > 1.

An SIRVS epidemic model with pulse vaccination strategy.

The aim of this paper is to analyze an SIRVS epidemic model in which pulse vaccination strategy (PVS) is included. We are interested in finding the basic reproductive number of the model which determine whether or not the disease dies out. The global attractivity of the disease-free periodic solution (DFPS for short) is obtained when the basic reproductive number is less than unity. The disease is permanent when the basic reproductive number is greater than unity, i.e., the epidemic will turn out to endemic. Our results indicate that the disease will go to extinction when the vaccination rate reaches some critical value.

On a nonautonomous SEIRS model in epidemiology.

In this paper, we derive some threshold conditions for permanence and extinction of diseases that can be described by a nonautonomous SEIRS epidemic model. Under the quite weak assumptions, we establish some sufficient conditions to prove the permanence and extinction of disease. Some new threshold values are determined.