Otunuga Olusegun Michael
Department of Mathematics, Marshall University, One John Marshall Drive, Huntington, WV, USA.
Chaos Solitons Fractals. 2021 Jun;147:110983. doi: 10.1016/j.chaos.2021.110983. Epub 2021 Apr 24.
We derive the time-dependent probability distribution for the number of infected individuals at a given time in a stochastic Susceptible-Infected-Susceptible (SIS) epidemic model. The mean, variance, skewness, and kurtosis of the distribution are obtained as a function of time. We study the effect of noise intensity on the distribution and later derive and analyze the effect of changes in the transmission and recovery rates of the disease. Our analysis reveals that the time-dependent probability density function exists if the basic reproduction number is greater than one. It converges to the Dirac delta function on the long run (entirely concentrated on zero) as the basic reproduction number tends to one from above. The result is applied using published COVID-19 parameters and also applied to analyze the probability distribution of the aggregate number of COVID-19 cases in the United States for the period: January 22, 2020-March 23, 2021. Findings show that the distribution shifts concentration to the right until it concentrates entirely on the carrying infection capacity as the infection growth rate increases or the recovery rate reduces. The disease eradication and disease persistence thresholds are calculated.
我们推导了随机易感-感染-易感(SIS)传染病模型中给定时间感染个体数量的时间依赖概率分布。该分布的均值、方差、偏度和峰度作为时间的函数被得出。我们研究了噪声强度对该分布的影响,随后推导并分析了疾病传播率和恢复率变化的影响。我们的分析表明,如果基本再生数大于1,则存在时间依赖概率密度函数。当基本再生数从上方趋于1时,从长远来看它会收敛到狄拉克δ函数(完全集中在零处)。该结果使用已公布的COVID-19参数进行应用,并且还用于分析2020年1月22日至2021年3月23日期间美国COVID-19病例总数的概率分布。研究结果表明,随着感染增长率增加或恢复率降低,分布的集中度向右移动,直到完全集中在承载感染能力上。计算了疾病根除和疾病持续阈值。