论文标题
具有季节性和矢量偏置的两晶型反应扩散疟疾模型
A two-strain reaction-diffusion malaria model with seasonality and vector-bias
论文作者
论文摘要
为了研究耐药性，季节性和矢量偏置的综合作用，我们制定了一个定期的两型晶体反应扩散模型。它是一种具有抗性和敏感性菌株的竞争系统，但单元子系统是合作的。我们得出了基本的复制号$ \ MATHCAL {R} _i $和入侵复制号$ \ Mathcal {\ hat {r}} _ I $，用于应变$ i〜（i = 1,2）$，并根据以下四个数量建立传输动态。更准确地说，（i）如果$ \ nathcal {r} _1 <1 $和$ \ nathcal {r} _2 <1 $，则该疾病已灭绝； （ii）如果$ \ MATHCAL {R} _1> 1> \ MATHCAL {R} _2 $（$ \ Mathcal {r} _2> 1> 1> \ Mathcal {r} _1 $），则敏感（抵抗）应变持续，而抵抗力（敏感）（敏感）strains strains strains trainains trains ex ex ex ex ex ex ex ex ex ex ex ex ex ex ex ex ex ex ex ex ex ex ex ex ex ex ex ex ex die die die die; （iii）如果$ \ MATHCAL {R} _i> 1 $和$ \ MATHCAL {\ HAT {r}} _ I> 1〜（i = 1,2）$，则观察到两个菌株是共存的，并且观察到周期性的振荡现象。我们还研究了基本繁殖数的渐近行为，相对于小和大扩散系数。从数值上讲，我们证明了两种菌株的共存和竞争排斥现象，并探讨了季节性和矢量偏见对疾病扩散的影响。
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.
