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This paper studies a nonlinear epidemiological model called susceptible, exposed, asymptomatic infected, infected, and recovered (SEAIR) with a control input (vaccination), which helps to design a sliding mode vaccination strategy by tracking the prevalence of infectious diseases. First, the effective reproduction number is adjusted to the expected value to control infectious disease outbreaks, even with model parameter changes and systematic perturbations. Meanwhile, based on the sliding mode control theory, two control strategies, namely, first‐order sliding mode control and super‐twisting control, are proposed to control the spread of COVID‐19. Besides, an integral sliding surface associated with the effective reproduction number R0(t)$$ {R}_0(t) $$ is constructed to eliminate the chattering problem of the system. Moreover, the sliding mode controller is robust to uncertainties and external perturbations. The stability and finite‐time convergence of the closed‐loop control system are verified by Lyapunov's second method. Also, the effect of the two control strategies on the system performance is evaluated by numerical simulations. Furthermore, this paper presents a practical case simulation based on data from Wuhan. The results indicate that universal vaccination is crucial in the early stage of the COVID‐19 pandemic. As the epidemic progresses, vaccination is still an essential approach for epidemic prevention and control. [ABSTRACT FROM AUTHOR]

A threshold strategy model is proposed to demonstrate the extinction of tumor load and the mobilization of immune cells. Using Filippov system theory, we consider global dynamics and sliding bifurcation analysis. It was found that an effective model of cell targeted therapy captures more complex kinetics and that the kinetic behavior of the Filippov system changes as the threshold is altered, including limit cycle and some of the previously described sliding bifurcations. The analysis showed that abnormal changes in patients' tumor cells could be detected in time by using tumor cell-directed therapy appropriately. Under certain initial conditions, exceeding a certain level of tumor load (depending on the patient) leads to different tumor cell changes, that is, different post-treatment effects. Therefore, the optimal control policy for tumor cell-directed therapy should be individualized by considering individual patient data. [ABSTRACT FROM AUTHOR]

The inappropriate use of insecticides may lead to disastrous pest outbreaks. Aiming at avoiding the outbreak of pests by optimizing the control strategies, we propose a novel mathematical model based on the idea of pulse in this study, namely, a discrete‐time model of pest–natural enemies, which considers the implementation of spraying insecticides within the time interval between two generations of pests. We first investigate the existence and stability of fixed points, and then using the central manifold theory, we proved that the system can exist period‐doubling bifurcation. The main theoretical results are verified by numerical simulations. The experiments show that if the insecticidal time is within a certain range, the lower insecticidal rate stimulates the growth of pests and natural enemies, while the larger insecticidal rate can inhibit the growth of pests and natural enemies. In addition, the effects of pest growth rate, timing of pesticide spraying, and pesticide intensity on the system are comprehensively discussed. The main research provides good reference significance to choose an appropriate time to prevent pest outbreaks. [ABSTRACT FROM AUTHOR]