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In this paper, we propose a deterministic model to study the transmission dynamics of anthrax disease, which includes live animals, carcasses, spores in the environment and vectors. We derive three biologically plausible and insightful quantities (reproduction numbers) that determine the stability of the equilibria. We carry out rigorous mathematical analysis on the model dynamics, the global stability of the disease-free and vector-free equilibrium, the disease-free equilibrium and the vector-free disease equilibrium is proved. The global stability of the endemic equilibrium as the basic reproduction number is greater than one is derived in the special case in which the disease-related death rate is zero. The possibility of backward bifurcation is briefly discussed. Numerical analyses are carried out to understand the transmission dynamics of anthrax and investigate effective control strategies for the outbreaks of the disease. Our studies suggest that the larval vector control measure should be taken as early as possible to control the vector population size, a vaccination policy and an animal carcass removal policy are useful methods to control the prevalence of the diseases in infected animal populations, the adult vector control measure is also necessary to prevent the transmission of anthrax. [ABSTRACT FROM AUTHOR]

Schistosomiasis is a parasitic disease caused by Schistosoma Japonicum that is transmitted by freshwater snails. Humans and some mammals are hosts of Schistosoma Japonicum. In this paper, we propose a multi-host (human-snail-bovine) schistosomiasis model with seasonality and temperature-dependent delays. We first introduce the basic reproduction number $ \mathcal R_0 $ for the whole system and the basic reproduction number $ \mathcal {\hat R}_0 $ for the system in the absence of bovines, respectively. Then we determine the extinction and persistence of the disease in terms of $ \mathcal R_0 $ and $ \mathcal {\hat R}_0 $. In the presence of susceptible humans, snails and bovines, we show that the disease persists if $ \mathcal R_0>1 $ and dies out if $ \mathcal R_0<1 $. As an application of our model, we study the transmission tendency of the schistosomiasis in Hubei province, China. Our numerical simulations indicate that the schistosomiasis incidences in both humans and bovines decline in an oscillatory way, but cannot disappear completely in the near future. A sensitivity analysis suggests that enhancing environmental disinfection, increasing treatment rate for both infected humans and bovines, replacing cattle with machine, and controlling the growth of snail population should be the effective measures for the prevention and control of schistosomiasis. [ABSTRACT FROM AUTHOR]

This paper discusses the existence of traveling wave solutions of delayed reaction-dif-fusion systems with partial quasi-monotonicity. By using the Schauder's fixed point theorem, the existence of traveling wave solutions is obtained by the existence of a pair of upper-lower solutions. We study the existence of traveling wave solutions in a delayed prey-predator system. [ABSTRACT FROM AUTHOR]

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