利用渐近传播速度理论研究了一类带分布时滞的时间周期\S-I型反应扩散传染病模型具有紧支集初值的解的演化性质,由此可以解释新发传染病的地理传播现象.首先,对于疾病已入侵区域,利用一致持久性思想结合比较技巧分三步验证了模型系统的一致持久性,在此过程中,通过构造截断区间初边值问题解决了模型系数的周期性和时滞共同导致的关键困难.其次,通过构造单调方程并利用单调系统的传播速度理论和比较原理分析了宿主种群在疾病未入侵区域的演化性质.
Abstract
This work is devoted to study the evolution properties of the solutions with compactly supported initial data of a time-periodic S-I reaction-diffusion epidemic model with distributed delays by using the theory of asymptotic spreading speed, by which we can explain the geographic spreading phenomena of newly introduced diseases. Firstly, by applying the uniform persistence idea and comparison skill, and taking three steps, we prove the uniform persistence of the model system in the region where the disease has invaded. Along the way, the main difficulty caused by delay and the periodicity of the coefficients is solved by constructing initial boundary value problems posed on truncated intervals. Secondly, we analyze the evolution properties of the host population in the disease-free region by constructing monotone equation and further employing the spreading speed theory of monotone systems combining with the comparison principle.
关键词
时间周期 /
分布时滞 /
渐近传播速度 /
一致持久 /
比较原理
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Key words
time-periodic /
distributed delays /
asymptotic spreading speed /
uniform persistence /
comparison principle
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参考文献
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脚注
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基金
国家自然科学基金(批准号:12171214), 甘肃省科技计划(批准号: 21JR7RA549), 兰州财经大学科研创新团队支持计划(批准号:202002)资助.
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