Modelling epidemics with fractional-dose vaccination in response to limited vaccine supply

Mathematical analysis and optimal control of an epidemic model with vaccination and different infectivity

This paper aims to explore the complex dynamics and impact of vaccinations on controlling epidemic outbreaks. An epidemic transmission model which considers vaccinations and two different infection statuses with different infectivity is developed. In terms of a dynamic analysis, we calculate the basic reproduction number and control reproduction number and discuss the stability of the disease-free equilibrium. Additionally, a numerical simulation is performed to explore the effects of vaccination rate, immune waning rate and vaccine ineffective rate on the epidemic transmission. Finally, a sensitivity analysis revealed three factors that can influence the threshold: transmission rate, vaccination rate, and the hospitalized rate. In terms of optimal control, the following three time-related control variables are introduced to reconstruct the corresponding control problem: reducing social distance, enhancing vaccination rates, and enhancing the hospitalized rates. Moreover, the characteristic expression of optimal control problem. Four different control combinations are designed, and comparative studies on control effectiveness and cost effectiveness are conducted by numerical simulations. The results showed that Strategy C (including all the three controls) is the most effective strategy to reduce the number of symptomatic infections and Strategy A (including reducing social distance and enhancing vaccination rate) is the most cost-effective among the three strategies.

Bifurcations due to different delays of high-order fractional neural networks

This paper expounds the bifurcations of two-delayed fractional-order neural networks (FONNs) with multiple neurons. Leakage delay or communication delay is viewed as a bifurcation parameter, stability zones and bifurcation conditions with respect to them are commendably established, respectively. It declares that both leakage delay and communication delay immensely influence the stability and bifurcation of the developed FONNs. The explored FONNs illustrate superior stability performance if selecting a lesser leakage delay or communication delay, and Hopf bifurcation generates once they overstep their critical values. The verification of the feasibility of the developed analytic results is implemented via numerical experiments.