Mathematical modeling the dynamics of SARS-CoV-2 infection with antibody-dependent enhancement

The advent and swift global spread of the novel coronavirus (COVID-19) transmitted by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have caused massive deaths and economic devastation worldwide. Antibody-dependent enhancement (ADE) is a common phenomenon in virology that directly affects the effectiveness of the vaccine, and there is no fully effective vaccine for diseases. In order to study the potential role of ADE on SARS-CoV-2 infection, we establish the SARS-CoV-2 infection dynamics model with ADE. The basic reproduction number is computed. We prove that when R 0 < 1 , the infection-free equilibrium is globally asymptotically stable, and the system is uniformly persistent when R 0 > 1 . We carry out the sensitivity analysis by the partial rank correlation coefficients and the extended version of the Fourier amplitude sensitivity test. Numerical simulations are implemented to illustrate the theoretical results. The potential impact of ADE on SARS-CoV-2 infection is also assessed. Our results show that ADE may accelerate SARS-CoV-2 infection. Furthermore, our findings suggest that increasing antibody titers can have the ability to control SARS-CoV-2 infection with ADE, but enhancing the neutralizing power of antibodies may be ineffective to control SARS-CoV-2 infection with ADE. Our study presumably contributes to a better understanding of the dynamics of SARS-CoV-2 infection with ADE.

Modelling and stability analysis of ASFV with swill and the virus in the environment

African swine fever (ASF) is an acute, hemorrhagic and severe infectious disease caused by the African swine fever virus (ASFV), and leads to a serious threat to the pig industry in China. Yet the impact of the virus in the environment and contaminated swill on the ASFV transmission is unclear in China. Then we build the ASFV transmission model with the virus in the environment and swill. We compute the basic reproduction number, and prove that the disease-free equilibrium is globally asymptotically stable when $ R_0 < 1 $ and the unique endemic equilibrium is globally asymptotically stable when $ R_0 > 1 $. Using the public information, parameter values are evaluated. PRCCs and eFAST sensitivity analysis reveal that the release rate of ASFV from asymptomatic and symptomatic infectious pigs and the proportion of pig products from infectious pigs to swill have a significant impact on the ASFV transmission. Our findings suggest that the virus in the environment and contaminated swill contribute to the ASFV transmission. Our results may help animal health to prevent and control the ASFV transmission.

Estimation of COVID-19 outbreak size in Harbin, China

Since the first level response to public health emergencies was launched on January 25, 2020, in Heilongjiang province, China, the outbreak of COVID-19 seems to be under control. However, an outbreak of COVID-19 caused by imported cases developed in Harbin during April 2020. A mathematical model is established to investigate the transmission of COVID-19 in Harbin. Based on the dynamical analysis and data fitting, the research investigates the outbreak of COVID-19 in Harbin and estimates the outbreak size of COVID-19 in Harbin. The outbreak size estimated of COVID-19 in Harbin reaches 174, where 54% of infected cases were identified while 46% of infected cases were not found out. We should maintain vigilance against unfound infected people. Our findings suggest that the effective reproduction number decreased drastically in contrast with the value of 3.6 on April 9; after that the effective interventions were implemented by the Heilongjiang province government. Finally, the effective reproduction number arrived at the value of 0.04 which is immensely below the threshold value 1, which means that the Heilongjiang province government got the outbreak of COVID-19 in Harbin under control.

A series of population models for Hyphantria cunea with delay and seasonality

In this paper, we establish and study a basic stage-structured model for the population of Hyphantria cunea, a delay differential equation model and a model incorporating the resource and seasonality. By introducing the population reproduction number R₀, we show that R₀ acts as a threshold parameter for the existence and stability of equilibria. The trivial equilibria of the above models are all globally asymptotically stable when R₀<1; the basic model and the delay-differential model have a unique positive equilibrium respectively, and they are both locally asymptotically stable when R₀>1; the model with periodic season is uniformly persistent and admits a positive periodic solution if R₀>1. Numerical simulations are carried out to illustrate the theoretical results. In addition, we consider the effect of temperature and season on the population of Hyphantria cunea.