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Cholera is a water- and food-borne infectious disease caused by V. cholerae. To investigate multiple effects of human behavior change, seasonality and spatial heterogeneity on cholera spread, we propose a reaction-advection-diffusion model that incorporates human hosts and aquatic reservoir of V. cholerae. We derive the basic reproduction number [Formula: see text] for this system and then establish a threshold type result on its global dynamics in terms of [Formula: see text]. Further, we show that the bacterial loss at the downstream end of the river due to water flux can reduce the disease risk, and describe the asymptotic behavior of [Formula: see text] for small and large diffusion in a special case (where the diffusion rates of infected human and the pathogen are constant). We also study the transmission dynamics at the early stage of cholera outbreak numerically, and find that human behavior change may lower the infection level and delay the disease peak. Moreover, the relative rate of bacterial loss, together with convection rate, plays an important role in identifying the severely infected areas. Meanwhile spatial heterogeneity may dilute or amplify cholera infection, which in turn would increase the complexity of disease spread.

West Nile virus (WNv) is a mosquito-borne disease caused by Flavivirus. To investigate the combined effects of vertical transmission, temperature-dependent incubation periods and seasonality on the...

A vector-borne disease is caused by a range of pathogens and transmitted to hosts through vectors. To investigate the multiple effects of the spatial heterogeneity, the temperature sensitivity of extrinsic incubation period and intrinsic incubation period, and the seasonality on disease transmission, we propose a nonlocal reaction–diffusion model of vector-borne disease with periodic delays. We introduce the basic reproduction number $$\mathfrak {R}_0$$ for this model and then establish a threshold-type result on its global dynamics in terms of $$\mathfrak {R}_0$$ . In the case where all the coefficients are constants, we also prove the global attractivity of the positive constant steady state when $$\mathfrak {R}_0>1$$ . Numerically, we study the malaria transmission in Maputo Province, Mozambique.

Bat-borne rabies is a viral infection caused by lyssaviruses. To explore the complex interaction between bats and cattle, we develop a periodic compartment system with seasonality, temperature-dependent incubation period and different control measures. We derive the basic reproduction number R 0 and show it determines the global dynamics. In particular, we prove the non-existence of positive periodic solutions in the critical case where R 0 = 1 . Numerically, we observe that sufficient long time-varying incubation periods could potentially increase the disease outbreak risk.