Pulse vaccination is a repeated vaccination policy, which plays a tremendous role in the global fight against communicable diseases in terms of saving medical resources and decreasing the economic burden. In this article, we propose a dynamic model of dengue infection with periodic transmission functions and seasonality in vector population. Furthermore, we introduce a pulse vaccination strategy in the susceptible host population to examine how frequency and intensity of implementation of this strategy affect the dynamics of dengue infection. We successfully obtained the threshold dynamics by defining the basic reproduction number R0, which is the spectral radius of the next generation operator and governs whether the disease dies out or not. It has been established that the infection-free periodic solution of the proposed impulsive system is globally asymptotically stable if $\mbox{R}_{0}<1$
 and is unstable otherwise. Moreover, we found that the dengue infection is uniformly persistent for the proposed system if $\mbox{R}_{0}>1$
 . Finally, we execute the system numerically to illustrate the piecewise solutions of the proposed system with impulsive vaccination measure and to investigate the influence of different control parameters on the basic reproduction. The finding indicates that a frequent implementation of the vaccination strategy with great intensity and the use of mosquito nets can essentially lead to a decline of new infections.

/pdf/effect-of-pulse-vaccination-on-dynamics-of-dengue-with-22cad4ww6k.pdf

Effect of pulse vaccination on dynamics of dengue with periodic transmission functions

We are concerned with a reaction–diffusion–advection SIS epidemic model with mass action infection mechanism in a one dimensional bounded domain. We first prove the existence of endemic equilibrium (EE) whenever the basic reproduction number is greater than unity. We then focus on the asymptotic behavior of EE in three cases: large advection; small diffusion of the susceptible population; small diffusion of the infected population. Our main results show that the asymptotic profiles of the susceptible and infected populations obtained here are very different from that of the corresponding system without advection and that of the system with standard incidence infection mechanism. Thus, the effects of advection and different infection mechanisms are substantial on the spatial distribution of infectious disease; our findings bring novel insight into the disease control strategy.

Concentration behavior of endemic equilibrium for a reaction–diffusion–advection SIS epidemic model with mass action infection mechanism

This paper provides an analysis on global dynamics of a diffusive cholera model. We formulate the model by a reaction–diffusion system with space-dependent parameters and bacterial hyperinfectivity, where susceptible and infectious humans disperse with distinct dispersal rates and the hyper-infectious and lower-infectious vibrios in contaminated water are assumed to be immobile in the domain. We first establish the well-posedness of the model. To cope with the lack of compactness of solution semiflow, we verify the asymptotic smoothness of semiflow implied with $$\kappa $$
 -contraction condition. The basic reproduction number, $$\mathfrak {R}_0$$
 , is identified as a threshold, predicting whether or not the disease extinction and persistence will occur. $$\mathfrak {R}_0$$
 is also equivalently characterized by some principle spectral conditions of an associated elliptic eigenvalue problem. The asymptotic profiles of the positive steady state are investigated for the cases when the dispersal rate of the susceptible humans is small and large. Our theoretical results indicate that: (1) cholera epidemics will be extinct through restricting the flow of susceptible humans within some extend; (2) the risk of infection will be underestimated if hyperinfectivity is not considered. In a homogeneous case, we also confirm the global attractivity of a unique positive equilibrium by utilizing the technique of Lyapunov function.

Dynamics and Profiles of a Diffusive Cholera Model with Bacterial Hyperinfectivity and Distinct Dispersal Rates

We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction-diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially heterogeneous environments. Topics include Lokta-Volterra competition models, river models, evolution of biased movement, phytoplankton growth, and spatial spread of epidemic disease. Open problems and conjectures are presented.

https://ojs.lib.uwo.ca/index.php/mase/article/download/10644/8576

Selected Topics on Reaction-Diffusion-Advection Models from Spatial Ecology

We show that the basic reproduction number of an SIS patch model with standard incidence is either strictly decreasing and strictly convex with respect to the diffusion coefficient of infected subpopulation if the patch reproduction numbers of at least two patches in isolation are distinct or constant otherwise. Biologically, it means that fast diffusion of the infected people reduces the risk of infection. This completely solves and generalizes a conjecture by Allen et al. ({\it SIAM J Appl Math}, 67: 1283-1309, 2007). Furthermore, a substantially improved lower bound on the multipatch reproduction number, a generalized monotone result on the spectral bound the Jacobian matrix of the model system at the disease-free equilibrium, and the limiting endemic equilibrium are obtained. The approach and results can be applied to a class of epidemic patch models where only one class of infected compartments migrate between patches and one transmission route is involved.

/pdf/fast-diffusion-inhibits-disease-outbreaks-4lejn4lb9g.pdf

Yanni Xiao

Papers

A spatial SEIRS reaction-diffusion model in heterogeneous environment