Global Stability of a Time-delayed Malaria Model with Standard Incidence Rate.

A four-dimensional delay differential equations (DDEs) model of malaria with standard incidence rate is proposed. By utilizing the limiting system of the model and Lyapunov direct method, the global stability of equilibria of the model is obtained with respect to the basic reproduction number R 0. Specifically, it shows that the disease-free equilibrium E 0 is globally asymptotically stable (GAS) for R 0 < 1, and globally attractive (GA) for R 0 = 1, while the endemic equilibrium E* is GAS and E 0 is unstable for R 0 > 1. Especially, to obtain the global stability of the equilibrium E* for R 0 > 1, the weak persistence of the model is proved by some analysis techniques.

Global Stability of a Mumps Transmission Model with Quarantine Measure.

In this paper, a model of mumps transmission with quarantine measure is proposed and then the control reproduction number ℛ c of the model is obtained. This model admits a unique endemic equilibrium P* if and only if R c > 1, while the disease-free equilibrium P 0 always exists. By using the technique of constructing Lyapunov functions and the generalized Lyapunov-LaSalle theorem, we first show that the equilibrium P 0 is globally asymptotically stable (GAS) if R c ≤ 1; second, we prove that the equilibrium P* is GAS if R c > 1. Our results reveal that mumps can be eliminated from the community for ℛ c ≤ 1 and it will be persistent for ℛ c > 1 , and quarantine measure can also effectively control the mumps transmission.

Epidemiological Characteristics and Transmissibility of Human Immunodeficiency Virus in Nanning City, China, 2001-2020.

Background: Human immunodeficiency virus (HIV) is a single-stranded RNA virus that can weaken the body's cellular and humoral immunity and is a serious disease without specific drug management and vaccine. This study aimed to evaluate the epidemiologic characteristics and transmissibility of HIV. Methods: Data on HIV follow-up were collected in Nanning City, Guangxi Zhuang Autonomous, China. An HIV transmission dynamics model was built to simulate the transmission of HIV and estimate its transmissibility by comparing the effective reproduction number (Reff ) at different stages: the rapid growth period from January 2001 to March 2005, slow growth period from April 2005 to April 2011, and the plateau from May 2011 to December 2019 of HIV in Nanning City. Results: High-risk areas of HIV prevalence in Nanning City were mainly concentrated in suburbs. Furthermore, high-risk groups were those of older age, with lower income, and lower education levels. The Reff in each stage (rapid growth, slow growth, and plateau) were 2.74, 1.62, and 1.15, respectively, which suggests the transmissibility of HIV in Nanning City has declined and prevention and control measures have achieved significant results. Conclusion: Over the past 20 years, the HIV incidence in Nanning has remained at a relatively high level, but its development trend has been curbed. Transmissibility was reduced from 2.74 to 1.15. Therefore, the prevention and treatment measures in Nanning City have achieved significant improvement.

Influence of asymptomatic infections for the effectiveness of facemasks during pandemic influenza.

In this paper, the SEIR model is generalized by introducing an asymptomatic class to quantify the influence of wearing N95 facemasks in reducing the spread of influenza H1N1. What's more, we explain the control reproduction number Rc according to the biological meaning reasonably. Without any intervention, the basic reproduction number R0=1.83 and there will be a large outbreak of infectious diseases. If N95 facemasks are 50% effective in reducing susceptibility and infectivity, 50% of population wear them on the first day, the basic reproduction number will be decreased from 1.83 to 1.17 and the final size reduced from 73% to 2%.

Influence of media intervention on AIDS transmission in MSM groups.

To explore the effects of propaganda and education on the prevention and control of AIDS infection, a model of AIDS transmission in MSM population is proposed and theoretically analyzed by introducing media impact factors. The basic reproduction number of AIDS transmission in MSM group without media intervention R0 = 1.5447 is obtained. Based on the comparison of the implementation of three different detection and treatment measures, it can be concluded that the promotion of condom use is more effective than other strategies, and using condoms with a fixed partner can reduce the value of R0 more quickly.