A reaction-advection-diffusion model of cholera epidemics with seasonality and human behavior change

Threshold dynamics of a reaction-advection-diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity

Most water-borne disease models ignore the advection of water flows in order to simplify the mathematical analysis and numerical computation. However, advection can play an important role in determining the disease transmission dynamics. In this paper, we investigate the long-term dynamics of a periodic reaction-advection-diffusion schistosomiasis model and explore the joint impact of advection, seasonality and spatial heterogeneity on the transmission of the disease. We derive the basic reproduction number R 0 and show that the disease-free periodic solution is globally attractive whenR 0 < 1 whereas there is a positive endemic periodic solution and the system is uniformly persistent in a special case whenR 0 > 1 . Moreover, we find that R 0 is a decreasing function of the advection coefficients which offers insights into why schistosomiasis is more serious in regions with slow water flows.

Mechanistic movement models to predict geographic range expansions of ticks and tick-borne pathogens: Case studies with Ixodes scapularis and Amblyomma americanum in eastern North America

The geographic range of the blacklegged tick, Ixodes scapularis, is expanding northward from the United States into southern Canada, and studies suggest that the lone star tick, Amblyomma americanum, will follow suit. These tick species are vectors for many zoonotic pathogens, and their northward range expansion presents a serious threat to public health. Climate change (particularly increasing temperature) has been identified as an important driver permitting northward range expansion of blacklegged ticks, but the impacts of host movement, which is essential to tick dispersal into new climatically suitable regions, have received limited investigation. Here, a mechanistic movement model was applied to landscapes of eastern North America to explore 1) relationships between multiple ecological drivers and the speed of the northward invasion of blacklegged ticks infected with the causative agent of Lyme disease, Borrelia burgdorferi sensu stricto, and 2) its capacity to simulate the northward range expansion of infected blacklegged ticks and uninfected lone star ticks under theoretical scenarios of increasing temperature. Our results suggest that the attraction of migratory birds (long-distance tick dispersal hosts) to resource-rich areas during their spring migration and the mate-finding Allee effect in tick population dynamics are key drivers for the spread of infected blacklegged ticks. The modeled increases in temperature extended the climatically suitable areas of Canada for infected blacklegged ticks and uninfected lone star ticks towards higher latitudes by up to 31% and 1%, respectively, and with an average predicted speed of the range expansion reaching 61 km/year and 23 km/year, respectively. Differences in the projected spatial distribution patterns of these tick species were due to differences in climate envelopes of tick populations, as well as the availability and attractiveness of suitable habitats for migratory birds. Our results indicate that the northward invasion process of lone star ticks is primarily driven by local dispersal of resident terrestrial hosts, whereas that of blacklegged ticks is governed by long-distance migratory bird dispersal. The results also suggest that mechanistic movement models provide a powerful approach for predicting tick-borne disease risk patterns under complex scenarios of climate, socioeconomic and land use/land cover changes.

Mathematical Models for Cholera Dynamics-A Review

Cholera remains a significant public health burden in many countries and regions of the world, highlighting the need for a deeper understanding of the mechanisms associated with its transmission, spread, and control. Mathematical modeling offers a valuable research tool to investigate cholera dynamics and explore effective intervention strategies. In this article, we provide a review of the current state in the modeling studies of cholera. Starting from an introduction of basic cholera transmission models and their applications, we survey model extensions in several directions that include spatial and temporal heterogeneities, effects of disease control, impacts of human behavior, and multi-scale infection dynamics. We discuss some challenges and opportunities for future modeling efforts on cholera dynamics, and emphasize the importance of collaborations between different modeling groups and different disciplines in advancing this research area.