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• The various optimal control problems of a coupled SIS model for respiratory disease with air pollution are proposed. • The optimal control solutions for the deterministic and stochastic models are theoretically analyzed respectively. • Data fitting results identify unknown parameters of the models and reveal the effect of actual control measures. • The cost values for different combinations of control measures reveal air pollution reduction is the most effective. Respiratory diseases caused by inhalation of air pollutants are affected by seasonal changes and mitigated by air pollution control, resulting in complex dynamics. In order to investigate the effects of various factors such as random noise and air pollution control on respiratory diseases, we developed deterministic and stochastic two-dimensional coupled SIS models with multiple control measures. The proposed models and parameter estimation methods, including determinations of unknown parameter values, were used to fit the Air Quality Index (AQI) data for Xi'an city in recent 10 years. The existence of the optimal solutions for the deterministic and stochastic models were analyzed theoretically and provided to compare the parameter fitting solutions with the optimal solutions, and give theoretical support for seeking a more reasonable air pollution optimization prevention and control scheme. To show this, we conducted numerical simulations of the optimal control solution and state evolution trajectories under different weight coefficient ratios and control objectives. The results show that the stochastic optimal control problem is more consistent with the practical scenario. We also formulate the optimal control problem assuming that the control variable depends on the concentration of air pollutants. The optimal control solution reflected the periodic variation of the air pollution control strategy well. A comparison of cost values for different combinations of the three control measures illustrated that air pollution reduction is the most effective control measure. [ABSTRACT FROM AUTHOR]

A Filippov crop-pest-natural enemy ecological system with threshold switching surface related to the pest control is developed, which has been completely analyzed by employing the qualitative techniques of non-smooth dynamical systems. The main results reveal that the proposed switching model can have multiple pseudo-equilibria in the sliding region, which result in rich bifurcations in the sliding region including saddle-node, Hopf, Bogdanov-Takens and Hopf-like boundary equilibrium bifurcations. Moreover, the pseudo-periodic solution (or pseudo-homoclinic loop) can be generated in the sliding region through a Hopf bifurcation (or a homoclinic bifurcation), which can collide with the tangential lines at the cusp singularities and finally disappears as parameter varies. This reveals that although the system can stabilize on the sliding region to achieve the purpose of pest control, there are complex dynamical behaviors and sliding bifurcations within the sliding region. Furthermore, as the threshold level varies, the model exhibits the interesting global sliding bifurcations including grazing bifurcation, buckling bifurcation, crossing bifurcation, homoclinic bifurcation to a pseudo-saddle, period-halving bifurcation and chaotic dynamics. This implies that control outcomes are sensitive to the threshold level, and hence it is crucial to choose the threshold level to initiate control strategy. [ABSTRACT FROM AUTHOR]

The mass vaccination program has been actively promoted since the end of 2020. However, waning immunity, antibody-dependent enhancement (ADE), and increased transmissibility of variants make the herd immunity untenable and the implementation of dynamic zero-COVID policy challenging in China. To explore how long the vaccination program can prevent China at low resurgence risk, and how these factors affect the long-term trajectory of the COVID-19 epidemics, we developed a dynamic transmission model of COVID-19 incorporating vaccination and waning immunity, calibrated using the data of accumulative vaccine doses administered and the COVID-19 epidemic in 2020 in mainland China. The prediction suggests that the vaccination coverage with at least one dose reach 95.87%, and two doses reach 77.92% on 31 August 2021. However, despite the mass vaccination, randomly introducing infected cases in the post-vaccination period causes large outbreaks quickly with waning immunity, particularly for SARS-CoV-2 variants with higher transmissibility. The results showed that with the current vaccination program and 50% of the population wearing masks, mainland China can be protected at low resurgence risk until 8 January 2023. However, ADE and higher transmissibility for variants would significantly shorten the low-risk period by over 1 year. Furthermore, intermittent outbreaks can occur while the peak values of the subsequent outbreaks decrease, indicating that subsequent outbreaks boosted immunity in the population level, further indicating that follow-up vaccination programs can help mitigate or avoid the possible outbreaks. The findings revealed that the integrated effects of multiple factors: waning immunity, ADE, relaxed interventions, and higher variant transmissibility, make controlling COVID-19 challenging. We should prepare for a long struggle with COVID-19, and not entirely rely on the COVID-19 vaccine. [ABSTRACT FROM AUTHOR]

We develop a stochastic HIV model by integrating drug adherence into a pharmacokinetic model and by coupling a pharmacodynamic model with a viral dynamic model. Numerical simulations show that the proposed model can generate viral blips, which have been observed in HIV patients receiving suppressive antiretroviral therapy. We calculate the probability density function of infected CD 4 + T cells by developing the generalized density evolution equation. We fit the model to the clinical data of four HIV patients exhibiting viral blips. The results demonstrate that poor drug adherence can be a reason explaining the occurrence of viral blips in treated HIV patients. We also find that viral dynamics are sensitive to drug-adherence parameters, which have a significant impact on the frequency and amplitude of viral blips. The modeling and methods can be applied to the study of long-term therapy of other chronic diseases in which drug adherence might also be an issue. [ABSTRACT FROM AUTHOR]