具有季节性和向量偏差的两种群反应扩散疟疾模型
A two-strain reaction-diffusion malaria model with seasonality and vector-bias
摘要：
为了研究抗药性、季节性和矢量偏差的综合影响，我们建立了一个周期性的两菌株反应扩散模型。抗性菌株和敏感菌株是一个竞争系统，但单菌株亚系统是合作的。我们推导出菌株$i~(i=1,2)$的基本繁殖数$\mathcal {R}_i$和侵入繁殖数$\mathcal {\hat{R}}_i$，并根据这四个量建立传播动力学。更确切地说，（i）如果是$\mathcal {R}_1<1$和$\mathcal{R}_2<1$，则疾病灭绝;（ii）如果是$\mathcal {R}_1>1>\mathcal{R}_2$（$\mathcal {R}_2>1>\mathcal{R}_1$），则敏感（抗性）菌株持续存在，而抗性（敏感）菌株消亡;（iii）如果是$\mathcal {R}_i>1$和$\mathcal {\hat{R}}_i>1~(i=1,2)$，则两种菌株共存，并观察到周期性振荡现象。我们还研究了基本再生数关于小扩散系数和大扩散系数的渐近行为。在数值上，我们证明了两种菌株的共存和竞争排斥现象，并探讨了季节性和媒介偏倚对疾病传播的影响。
英文摘要：
To investigate the combined effects of drug resistance, seasonality and vector-bias, we formulate a periodic two-strain reaction-diffusion model. It is a competitive system for resistant and sensitive strains, but the single-strain subsystem is cooperative. We derive the basic reproduction number $\mathcal {R}_i$ and the invasion reproduction number $\mathcal {\hat{R}}_i$ for strain $i~(i=1,2)$, and establish the transmission dynamics in terms of these four quantities. More precisely, (i) if $\mathcal {R}_1<1$ and $\mathcal{R}_2<1$, then the disease is extinct; (ii) if $\mathcal {R}_1>1>\mathcal{R}_2$ ($\mathcal {R}_2>1>\mathcal{R}_1$), then the sensitive (resistant) strains are persistent, while the resistant (sensitive) strains die out; (iii) if $\mathcal {R}_i>1$ and $\mathcal {\hat{R}}_i>1~(i=1,2)$, then two strains are coexistent and periodic oscillation phenomenon is observed. We also study the asymptotic behavior of the basic reproduction number with respect to small and large diffusion coefficients. Numerically, we demonstrate the phenomena of coexistence and competitive exclusion for two strains and explore the influences of seasonality and vector-bias on disease spreading.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
