An SIRS model with nonmonotone incidence and saturated treatment in a changing environment.

Nonmonotone incidence and saturated treatment are incorporated into an SIRS model under constant and changing environments. The nonmonotone incidence rate describes the psychological or inhibitory effect: when the number of the infected individuals exceeds a certain level, the infection function decreases. The saturated treatment function describes the effect of infected individuals being delayed for treatment due to the limitation of medical resources. In a constant environment, the model undergoes a sequence of bifurcations including backward bifurcation, degenerate Bogdanov-Takens bifurcation of codimension 3, degenerate Hopf bifurcation as the parameters vary, and the model exhibits rich dynamics such as bistability, tristability, multiple periodic orbits, and homoclinic orbits. Moreover, we provide some sufficient conditions to guarantee the global asymptotical stability of the disease-free equilibrium or the unique positive equilibrium. Our results indicate that there exist three critical values [Formula: see text] and [Formula: see text] for the treatment rate r: (i) when [Formula: see text], the disease will disappear; (ii) when [Formula: see text], the disease will persist. In a changing environment, the infective population starts along the stable disease-free state (or an endemic state) and surprisingly continues tracking the unstable disease-free state (or a limit cycle) when the system crosses a bifurcation point, and eventually tends to the stable endemic state (or the stable disease-free state). This transient tracking of the unstable disease-free state when [Formula: see text] predicts regime shifts that cause the delayed disease outbreak in a changing environment. Furthermore, the disease can disappear in advance (or belatedly) if the rate of environmental change is negative and large (or small). The transient dynamics of an infectious disease heavily depend on the initial infection number and rate or the speed of environmental change.

SARS-CoV-2 vaccine research and development: Conventional vaccines and biomimetic nanotechnology strategies.

The development of a massively producible vaccine against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), a novel coronavirus, is essential for stopping the current coronavirus disease (COVID-19) pandemic. A vaccine must stimulate effective antibody and T cell responses in vivo to induce long-term protection. Scientific researchers have been developing vaccine candidates for the severe acute respiratory syndrome (SARS) and Middle East respiratory syndrome (MERS) since the outbreaks of these diseases. The prevalence of new biotechnologies such as genetic engineering has shed light on the generation of vaccines against novel viruses. In this review, we present the status of the development of coronavirus vaccines, focusing particularly on the biomimetic nanoparticle technology platform, which is likely to have a major role in future developments of personalized medicine.