We study traveling wavefront solutions for two reaction-diffusion systems, which are derived respectively as diffusion approximations to two nonlocal spatial SIRS models. These solutions characterize the propagating progress and speed of the spatial spread of underlying epidemic waves. For the first diffusion system, we find a lower bound for wave speeds and prove that the traveling waves exist for all speeds bigger than this bound. For the second diffusion system, we find the minimal wave speed and show that the traveling waves exist for all speeds bigger than or equal to the minimal speed. We further prove the uniqueness (up to translation) of these solutions for sufficiently large wave speeds. The existence of these solutions are proved by a shooting argument combining with LaSalle's invariance principle, and their uniqueness by a geometric singular perturbation argument.

This study aimed to assess the association between exposures to outdoor environmental factors and autism spectrum disorder (ASD) prevalence in a diverse and spatially distributed population of 8-year-old children from the USA (n = 2,097,188) using the air quality index (AQI) of the US Environmental Protection Agency as well as satellite-derived data of PM concentrations, sunlight, and maximum heat index. Multivariable logistic regression analyses were performed to determine whether the unhealthy AQI, PM, sunlight, and maximum heat index were related to the odds of ASD prevalence based on gender and race and taking into consideration the confounding factors of smoking and socioeconomic status. The logistic regression odds ratios for ASD per 10% increase in the unhealthy AQI were greater than 1 for all categories, indicating that unhealthy AQI is related to the odds of ASD prevalence. The odds ratio of ASD due to the exposure to the unhealthy AQI was higher for Asians (OR = 2.96, 95% CI = 1.11-7.88) than that for Hispanics (OR = 1.308, 95% CI = 0.607-2.820), and it was higher for Blacks (OR = 1.398, 95% CI = 0.827-2.364) than that for Whites (OR = 1.219, 95% CI = 0.760-1.954). The odds ratio of ASD due to the unhealthy AQI was slightly higher for males (OR = 1.123, 95% CI = 0.771-1.635) than that for females (OR = 1.117, 95% CI = 0.789-1.581). The effects of the unhealthy environmental exposures on the odds ratios of ASD of this study were inconclusive (i.e., statically insignificant; p value > 0.05) for all categories except for Asians. The odds ratios of ASD for Asians were increased by 5, 12, and 14% with increased levels of the environmental exposures of 10 μg/m of PM, 1000 kJ/m of sunlight, and 1 °F of maximum heat index, respectively. The odds ratios of ASD prevalence for all categories, except for Asians, were increased with the inclusion of the smoking covariate, reflecting the effect of smoking on ASD prevalence besides the unhealthy environmental factors.

This study aimed to assess the association between exposure to fine particulate matter (PM) and respiratory system cancer incidence in the US population (n = 295,404,580) using a satellite-derived estimate of PM concentrations. Linear and logistic regression analyses were performed to determine whether PM was related to the odds of respiratory system cancer (RSC) incidence based on gender and race. Positive linear regressions were found between PM concentrations and the age-adjusted RSC incidence rates for all groups (Males, Females, Whites, and Blacks) except for Asians and American Indians. The linear relationships between PM and RSC incidence rate per 1 μg/m PM increase for Males, Females, Whites, Blacks, and all categories combined had slopes of, respectively, 7.02 (R = 0.36), 2.14 (R = 0.14), 3.92 (R = 0.23), 5.02 (R = 0.21), and 4.15 (R = 0.28). Similarly, the logistic regression odds ratios per 10 μg/m increase of PM were greater than one for all categories except for Asians and American Indians, indicating that PM is related to the odds of RSC incidence. The age-adjusted odds ratio for males (OR = 2.16, 95% CI = 1.56-3.01) was higher than that for females (OR = 1.50, 95% CI = 1.09-2.06), and it was higher for Blacks (OR = 2.12, 95% CI = 1.43-3.14) than for Whites (OR = 1.72, 95% CI = 1.23-2.42). The odds ratios for all categories were attenuated with the inclusion of the smoking covariate, reflecting the effect of smoking on RSC incidence besides PM.

This ecological study aimed to assess the association between long-term exposures to outdoor environmental factors and mortality rate from cardiovascular disease (CVD) in a diverse and spatially distributed population from 3,094 counties within the U.S. (n > 3,780,000 CVD deaths) using satellite-derived data of PM concentrations, sunlight, and maximum heat index. Multivariable logistic regression analyses were conducted to determine whether PM, sunlight and maximum heat index were related to the odds of the total CVD death rate based on gender, race, and age taking into consideration the confounding risk factors of diabetes, obesity, leisure- time physical inactivity, smoking and socioeconomic status. The study has shown that elevated levels of PM, sunlight and heat long-term exposures are significantly associated with an increase in the odds ratio of the total CVD mortality. The results suggest a 9.8% (95% CI = 6.3% - 13.4%), 0.9% (95% CI = 0.5% - 1.2%), and 0.7% (95% CI = 0.5% - 11.2%) increase in total CVD mortality associated with 10 μg/m increase in PM concentrations, 1,000 kJ/m increases in sunlight, and 1 F increase in heat index, respectively. The odds ratios for the CVD death rate due to long-term exposures of PM, sunlight, and heat index were significantly greater than 1.0 for all categories except for Asians, Hispanics, and American Indians, indicating that the effect of long-term exposures to particulate matter, sunlight radiation, and maximum heat on CVD mortality is trivial for Asians, Hispanics, and American Indians. Among the categories of age, the group of 65 years and older had the highest odds ratios, suggesting that the age group of 65 years and older are the most vulnerable group to the environmental exposures of PM (OR = 1.179, 95% CI = 1.124 - 1.237), sunlight (OR = 1.047, 95% CI = 1.041 - 1.053), and maximum heat (OR = 1.014, 95% CI = 1.011 - 1.016). The odds ratios of CVD mortality due to the environmental exposures were higher for Blacks than those for Whites. The odds ratios for all categories were attenuated with the inclusion of diabetes, obesity, leisure-time physical inactivity, smoking, and income covariates, reflecting the effect of other medical conditions, lifestyle, behavioral and socioeconomic factors on the CVD death rate besides the environmental factors.