【摘要】：在理論流行病學(xué)中,SIS (易感者-染病者-易感者)模型提供了研究疾病傳播動(dòng)力學(xué)的基本框架.為研究環(huán)境的非齊次性和種群運(yùn)動(dòng)對(duì)疾病持續(xù)和滅亡的影響,我們研究一類具有零流邊界條件的SIS反應(yīng)擴(kuò)散移流模型,這里我們考慮了易感者的出生率和死亡率以及染病者的死亡率,因此該模型的總?cè)丝跀?shù)可能是不恒定的.首先,本文研究當(dāng)易感者的出生率和死亡率相等,且染病者的死亡率為零時(shí)的SIS傳染病模型.我們給出此時(shí)的基本再生數(shù)R_0的定義,它在決定疾病持續(xù)還是滅亡時(shí)起到關(guān)鍵作用.結(jié)果表明:當(dāng)R_0 1時(shí),無病平衡解是唯一和全局漸近穩(wěn)定的;當(dāng)R_0 1時(shí),無病平衡解不穩(wěn)定.當(dāng)易感者的擴(kuò)散速率和染病者的擴(kuò)散速率相等時(shí),結(jié)果顯示:當(dāng)R_0≤ 1時(shí),無病平衡解是全局穩(wěn)定的;而當(dāng)R_0 1時(shí),地方病平衡解是全局穩(wěn)定的.其次,本文著重考慮了易感者的出生率大于易感者的死亡率,染病者的死亡率為正的情況.本文利用分支理論證明了平衡解的存在性.另外,在一種特殊情形下,本文運(yùn)用上下解方法對(duì)平衡解進(jìn)行估計(jì).結(jié)果表明:當(dāng)初值滿足一定條件時(shí),易感者的數(shù)目最終會(huì)保持有界,而染病者的數(shù)目會(huì)是一個(gè)無界值.
[Abstract]:In theoretical epidemiology, the, SIS (susceptible-infected-susceptible) model provides a basic framework for studying the dynamics of disease transmission. In order to study the inhomogeneity of environment and the effect of population movement on the persistence and extinction of disease, we study a SIS reaction-diffusion model with zero flow boundary condition. Here we consider the birth rate and death rate of the susceptible and the death rate of the infected, so the total population of the model may not be constant. First of all, this paper studies the SIS infectious disease model in which the birth rate and death rate are equal and the mortality rate of infected persons is 00:00. We give the definition of the basic regenerative number R _ S _ 0, which plays a key role in determining whether the disease continues or dies. The results show that the disease-free equilibrium solution is unique and globally asymptotically stable when R _ S _ (0.1) and R _ S _ (0.1) are unstable. When the diffusion rate of susceptible person is equal to that of infected person, the results show that the disease-free equilibrium solution is globally stable when R _ S _ 0 鈮，

本文編號(hào)：2401274