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We conducted a comparative study of the COVID-19 epidemic in three different settings: mainland China, the Guangdong province of China and South Korea, by formulating two disease transmission dynamics models which incorporate epidemic characteristics and setting-specific interventions, and fitting the models to multi-source data to identify initial and effective reproduction numbers and evaluate effectiveness of interventions. We estimated the initial basic reproduction number for South Korea, the Guangdong province and mainland China as 2.6 (95% confidence interval (CI): (2.5, 2.7)), 3.0 (95%CI: (2.6, 3.3)) and 3.8 (95%CI: (3.5,4.2)), respectively, given a serial interval with mean of 5 days with standard deviation of 3 days. We found that the effective reproduction number for the Guangdong province and mainland China has fallen below the threshold 1 since February 8th and 18th respectively, while the effective reproduction number for South Korea remains high until March 2nd Moreover our model-based analysis shows that the COVID-19 epidemics in South Korean is almost under control with the cumulative confirmed cases tending to be stable as of April 14th. Through sensitivity analysis, we show that a coherent and integrated approach with stringent public health interventions is the key to the success of containing the epidemic in China and especially its provinces outside its epicenter. In comparison, we find that the extremely high detection rate is the key factor determining the success in controlling the COVID-19 epidemics in South Korea. The experience of outbreak control in mainland China and South Korea should be a guiding reference for the rest of the world. • We conducted a comparative study of the COVID-19 epidemic in three different settings: mainland China, the Guangdong province of China and South Korea. • We estimated the initial basic reproduction number for South Korea, the Guangdong province and mainland China as 2.6 (95% confidence interval (CI): (2.5, 2.7)), 3.0 (95%CI: (2.6, 3.3)) and 3.8 (95%CI: (3.5,4.2)). • A coherent and integrated approach with stringent public health interventions is the key to the success of containing the epidemic in China and especially its provinces outside its epicenter. • The extremely high detection rate of infected individuals is the key to the success in controlling the epidemics in South Korea. [ABSTRACT FROM AUTHOR]

• 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]

China is now experiencing major public health challenges caused by air pollution. Few studies have quantified the dynamics of air pollution and its impact on the risk of respiratory infection. We conducted an integrated data analysis to quantify the association among air quality index (AQI), meteorological variables and respiratory infection risk in Shaanxi province of China in the period of November 15th, 2010 to November 14th, 2016. Our analysis illustrated a statistically significantly positive correlation between the number of influenza-like illness (ILI) cases and AQI, and the respiratory infection risk has increased progressively with increased AQI with a time lag of 0–3 days. We also developed mathematical models for the AQI trend and respiratory infection dynamics, incorporating AQI-dependent incidence and AQI-based behaviour change interventions. Our combined data and modelling analysis estimated the basic reproduction number for the respiratory infection during the studying period to be 2.4076, higher than the basic reproduction number of the 2009 pandemic influenza in the same province. Our modelling-based simulations concluded that, in terms of respiratory infection risk reduction, the persistent control of emission in the China's blue-sky programme is much more effective than substantial social-economic interventions implemented only during the smog days. [ABSTRACT FROM AUTHOR]

In reality, the outbreak of emerging infectious diseases including SARS, A/H1N1 and Ebola are accompanied by the common cold and flu. The selective treatment measure for mitigating and controlling the emerging infectious diseases should be implemented due to limited medical resources. However, how to determine the threshold infected cases and when to implement the selective treatment tactics are crucial for disease control. To address this, we derive a non-smooth Filippov system induced by selective treatment measure. The dynamic behaviors of two subsystems have been discussed completely, and the existence conditions for sliding segment, sliding mode dynamics and different types of equilibria such as regular equilibrium, pseudo-equilibrium, boundary equilibrium and tangent point have been provided. Further, numerical sliding bifurcation analyses show that the proposed Filippov system has rich sliding bifurcations. Especially, the most interesting results are those for the fixed parameter set as the bifurcation parameter varies, the sliding bifurcations occur sequentially: crossing → buckling → real/virtual equilibrium → buckling → crossing. The key factors which affect the selective treatment measures and the threshold value of infected cases for emerging infectious disease have been discussed in more detail. [ABSTRACT FROM AUTHOR]

With the evolution of pest resistance to Bt-corn, farmers’ economic losses are increasing. However, a planting strategy with Bt-corn mixed with non-Bt-corn to fight the development of pest resistance can be efficient. Nevertheless, this mixed strategy poses questions such as (1) what is the optimal ratio of Bt-corn to non-Bt-corn that should be planted in a field? And (2) what is the main factor affecting the farmers’ net present value? To address these questions, we propose and investigate a discrete pest growth model with pest resistance to Bt-corn. According to the model’s economic functions, the main factors affecting the farmers’ net present value are presented and discussed. By comparing the net present values of a pure Bt-corn planting strategy with the mixed planting strategy, an optimal planting strategy was devised. Moreover, the optimal ratio of Bt-corn to non-Bt-corn to be planted when the mixed planting strategy is implemented in the field was also investigated. [ABSTRACT FROM AUTHOR]

How to use chemical and biological control in sensible combinations has been a concern of many agriculture departments and ecologists. To address this problem, a pest-natural enemy model with disease in the pest and with different frequencies of pesticide sprays and of releases of both infected pests and natural enemies is proposed and analyzed by using impulsive differential equations. The threshold conditions for susceptible pest (or total pest) eradication periodic solution are provided for different scenarios. In particular, two different natural enemy release strategies and two different pest control tactics are investigated and compared in detail. Furthermore, the effects of the frequency of pesticide applications and the frequency of natural enemy and infected pest releases on the threshold values are discussed. The results indicate that there exists an optimal frequency of pesticide application or an optimal releasing period which minimizes the threshold value. This information may help pest control experts to decide on the optimum timing for spray applications and optimum rates for releases. [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]

Abstract: In a prey–predator model, an effective management strategy called the threshold policy control (TPC) is proposed, resulting in Filippov system. Considering the limitation of environmental resources, Filippov system with the weighted sum as the index is put forward in the prey–predator model with Ivlev’s function response. Firstly, the existences of sliding segments in four cases have been discussed completely. Further, the sliding mode dynamics, the existences of different types of equilibria and tangent point, regular/virtual equilibrium and sliding mode bifurcations have been addressed. Moreover, the results obtained in present work indicate that the local sliding bifurcations such as boundary focus, boundary node and tangent bifurcations occur sequentially with the threshold value varying. Finally, some global sliding bifurcations including touching and buckling bifurcations are investigated by employing numerical techniques. [Copyright &y& Elsevier]

Abstract: A non-smooth Gause predator–prey model with a constant refuge is proposed and analyzed. Firstly, the existence and stability of regular, virtual, pseudo-equilibria and tangent points are addressed. Then the relations between the existence of a regular equilibrium and a pseudo-equilibrium are studied, and the results indicate that the two types of equilibria cannot coexist. The sufficient and necessary conditions for the global stability of limit cycle, sliding touching cycle, canard cycle, focus point and pseudo-equilibrium are provided by using qualitative analysis techniques of non-smooth Filippov dynamic systems. Furthermore, sliding bifurcations related to boundary node (focus) and touching bifurcations were investigated by employing theoretical and numerical techniques. Finally, we compare our results with previous studies on a non-smooth Gause predator–prey model without involving a carrying capacity for the prey population, and some biological implications are discussed. [Copyright &y& Elsevier]

Abstract: The present paper aims to provide a detailed qualitative analysis of a non-smooth Gause predator–prey model. In this model, the saturating functional response function with a discontinuity at a critical prey density was employed to show the effects of a prey refuge on the population dynamic behavior. Analysis of this model revealed rich dynamics including locally (or globally) stable canard cycles, a locally (globally) stable pseudo-equilibrium, unbounded trajectories in which both populations go to infinity or the prey goes to infinity and the predator dies out eventually. The main purpose of the present work is to carry out a completely qualitative analysis for this model. In particular, two sets of sufficient conditions drive both populations to approach infinity and the sufficient and necessary conditions for all of the other main results are presented. [Copyright &y& Elsevier]

Abstract: Pulse-like pest management actions such as spraying pesticides and killing a pest instantly and the release of natural enemies at critical times can be modelled with impulsive differential equations. In practice, many pesticides have long-term residual effects and, also, both pest and natural enemy populations may have delayed responses to pesticide applications. In order to evaluate the effects of the duration of the residual effectiveness of pesticides and of delayed responses to pesticides on a pest management strategy, we developed novel mathematical models. These combine piecewise-continuous periodic functions for chemical control with pulse actions for releasing natural enemies in terms of fixed pulse-type actions and unfixed pulse-type actions. For the fixed pulse-type model, the stability threshold conditions for the pest eradication periodic solution and permanence of the model are derived, and the effects of key parameters including killing efficiency rate, decay rate, delayed response rate, number of pesticide applications and number of natural enemy releases on the threshold values are discussed in detail. The results indicate that there exists an optimal releasing period or an optimal number of pesticide applications which maximizes the threshold value. For unfixed pulse-type models, the effects of the killing efficiency rate, decay rate and delayed response rate on the pest outbreak period, and the frequency of control actions are also investigated numerically. [Copyright &y& Elsevier]

Abstract: Assuming that a fish population follows the continuous logistic growth or the discrete Beverton–Holt model, several optimal impulsive harvesting policies for the maximum stock level of the fish at the end of a fishing season are investigated under the condition of fixed intensity and frequency of impulsive harvesting. The optimal impulsive harvesting moments for all cases considered are given analytically and the related numerical simulations are also provided. Furthermore, the methods employed can also be used to investigate the optimal timing of chemical control in pest management. Our results confirm that the optimal timing of pesticide applications such that the density of the pest population is minimal at any time during a planting season or the average of density of the pest population over the planting season is minimal is the beginning of the planting season. In practice, the results can be used to guide the fisherman to manage fisheries and guide farmers to control pests. [Copyright &y& Elsevier]

Abstract: In the present paper the different releasing methods including constant releasing and proportional to the predator population are considered and analyzed. The effects of these releasing methods of natural enemies on dynamical behavior are investigated. We firstly take into account the model with an impulsive effect at fixed moments, and the results imply that under some conditions the pest may serve to extinction. Several types of attractors can coexist, with switch-like transitions among their attractors showing that varying dosages and frequencies of insecticide applications and the numbers of natural enemies released are crucial. Secondly, the model with unfixed moments is further investigated. Different periodic solutions also exist and the maximum amplitude of the host is always less than the economic threshold. Comparing the results obtained for the two models concludes that the proportional releasing predator has strong effects on the dynamical behavior. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the population dynamics described by the theta logistic model with periodic impulsive harvesting and by-catch mortality. We examine the existence and stability of two positive periodic solutions by using qualitative methods and cobwebs. Then the sufficient conditions under which the unique positive periodic solution exists and is semi-stable are established, and qualifications for the solutions approach zero are also obtained. Further, choosing the maximum sustainable yield as the management objective, we investigate the optimal harvesting policy for the theta logistic model with periodic impulsive harvesting. Moreover the corresponding theta logistic difference equation is considered subject to the impulsive perturbation, and the dynamics which is parallel to that for the differential equation is examined. The main results extend and generalize the classical results for populations described by the autonomous logistic equation in renewable resources management. [Copyright &y& Elsevier]

Abstract: We develop and analyze a simple SIV epidemic model including susceptible, infected and imperfectly vaccinated classes, with a nonlinear incidence rate. We investigate the interaction of the nonlinear incidence and partial immunity. Our main results show that nonlinear incidence rate could induce the forward bifurcation with hysteresis except for the backward bifurcation. The plausible effects of vaccination program have been demonstrated by two models with nonlinear incidence rate. Vaccination program may contribute to disease spread, depending on which transmission term involves nonlinear incidence rate. [ABSTRACT FROM AUTHOR]

Abstract: Optimal timing (or Economic Threshold) and dosage of pesticide applications which maximize the profit function depend on many factors including pest population demography, crop susceptibility to damage and the rate at which a pesticide loses its toxicity. To analyze the effects of these factors on pest management, several pest control models with single and multiple treatments are presented by using impulsive differential equations. That is, pest control models with a single treatment and with multiple treatments of pesticides sprayed at fixed moments and unfixed moments (i.e. the model with an Economic Threshold) were investigated. In particular, choosing the maximum profits as the management objective, we investigated profit function directed at the problems of optimal timing of pesticide applications, Economic Threshold and optimal dosage of pesticides. Several sufficient conditions which guarantee the existences of optimum timing, dosage and Economic Threshold are provided. This approach can be used with more general models involving age structure of pest populations and the effects of stochastic factors. [Copyright &y& Elsevier]

Abstract: In this paper, we firstly consider a Lotka–Volterra predator–prey model with impulsive constant releasing for natural enemies and a proportion of killing or catching pests at fixed moments, and we have proved that there exists a pest-eradication periodic solution which is globally asymptotically stable. Further, we extend the model for the population to move in a two-patch environment. The effects of population dispersal and impulsive control tactics are investigated, i.e. we chiefly address the question of whether population dispersal is beneficial or detrimental for pest persistence. To do this, some special cases are theoretically investigated and numerical investigations are done for general case. The results indicate that for some ranges of dispersal rates, population dispersal is beneficial to pest control, but for other ranges, it is harmful. These clarify that we can get some new effective pest control strategies by controlling the dispersal rates of pests and natural enemies. [Copyright &y& Elsevier]

Non-smooth Filippov systems may be used to provide natural description and characterize ecosystems with threshold control strategies. One common control strategy is the economic threshold (E T) often seen in integrated pest management. Recently switching systems consisting of free and controlled subsystems and guided by the threshold E T were developed and investigated. The key hypothesis in these systems is to consider only the pest density against a certain threshold value to construct the switching condition. This means that the rapid or saturated growth of pest population was not taken into account. Practical pest control strategies depend not only on the number of pests, but also on the growth rate of pests. This paper examines a new switching system guided by weighting the pest number and its growth rate as the threshold level. Theoretical analyses reveal that the proposed threshold strategy results in nonlinear sliding curve with complex sliding mode dynamics including multiple sliding segments and pseudo-equilibrium, confirmed by the sliding segment bifurcations. Moreover, the local and global sliding bifurcations clarify the fact that variations of E T and the new threshold control strategy not only lead to rich sliding dynamics such as various sliding periodic solutions, but also have important consequences on pest control. • Switching system guided by weighting the pest number and its growth rate is developed. • Multiple sliding segments as well as rich sliding bifurcations are investigated. • Conditions for the occurrence of pseudo-equilibrium are provided. • Global bifurcations including touching, buckling, crossing bifurcations are discussed. • New modelling method for multiple sliding segments has been developed. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we use Markov chain Monte Carlo (MCMC) techniques to carry out Bayesian inference for piecewise stochastic logistic growth models using discretely observed data sets, which allows us to fit models for time series data, including data on fish productions and yields, with structural changes. The estimation framework involves the introduction of latent data points between each pair of observations, and the use of MCMC techniques, based on the Gibbs sampling algorithm, in conjunction with the Euler–Maruyama discretization scheme. These methods are used to sample from the posterior distribution using exact bridges, allowing estimation of the model parameters including switching point(s). We apply our methods to examples involving both simulated data and real data for fisheries resources management. [Copyright &y& Elsevier]

Abstract: Many recent advances in the theory of the optimal economic exploitation of renewable fish resources have been gained by applying optimal control theory. However, despite these successes, much less is known about how seasonal environments affect the maximum sustainable yield (MSY) (or population persistence) and any effects of relations between intensity and frequency of harvesting. Assuming that fish populations follow Beverton–Holt equations we investigated impulsive harvesting in seasonal environments, focusing on both economic aspects and resource sustainability. We first investigated the existence and stability of a periodic solution and its analytic formula, and then showed that the population persistence depends on the intensity and frequency of harvesting. With the MSY as a management objective, we investigated optimal impulsive harvesting policies. The optimal harvesting effort that maximizes the sustainable yield, the corresponding optimal population level, and the MSY are obtained by using discrete Euler–Lagrange equations and product formulae, and their explicit expressions were obtained in terms of the intrinsic growth rate, the carrying capacity, and the impulsive moments. These results imply that harvest timing is of crucial importance to the MSY. Since impulsive differential equations incorporate elements of continuous and discrete systems, we can apply all results obtained for Beverton–Holt equations with impulsive effects to periodic logistic equations with impulsive harvesting. [Copyright &y& Elsevier]

Abstract: Two new models for controlling diseases, incorporating the best features of different control measures, are proposed and analyzed. These models would draw from poultry, livestock and government expertise to quickly, cooperatively and cost-effectively stop disease outbreaks. The combination strategy of pulse vaccination and treatment (or isolation) is implemented in both models if the number of infectives reaches the risk level (RL). Firstly, for one time impulsive effect we compare three different control strategies for both models in terms of cost. The theoretical and numerical results show that there is an optimal vaccination and treatment proportion such that integrated pulse vaccination and treatment (or isolation) reaches its minimum in terms of cost. Moreover, this minimum cost of integrated strategy is less than any cost of single pulse vaccination or single treatment. Secondly, a more realistic case for the second model is investigated based on periodic impulsive control strategies. The existence and stability of periodic solution with the maximum value of the infectives no larger than RL is obtained. Further, the period T of the periodic solution is calculated, which can be used to estimate how long the infectious population will take to return back to its pre-control level (RL) once integrated control tactics cease. This implies that we can control the disease if we implement the integrated disease control tactics every period T. For periodic control strategy, if we aim to control the disease such that the maximum number of infectives is relatively small, our results show that the periodic pulse vaccination is optimal in terms of cost. [Copyright &y& Elsevier]

• Since January 23 2020, stringent measures for controlling novel coronavirus epidemics have been enforced and strengthened in mainland China. • Most infected cases have been quarantined or put in suspected class, which had been ignored in existing models. • Results of our model show that the trend of the epidemics mainly depends on quarantined and suspected cases. • It is important to continue enhancing the quarantine and isolation strategy and improving the detection rate in mainland China. Since January 23, 2020, stringent measures for controlling the novel coronavirus epidemic have been gradually enforced and strengthened in mainland China. The detection and diagnosis have been improved, as well. However, the daily reported cases remaining at a high level make the epidemic trend prediction difficult. Since the traditional SEIR model does not evaluate the effectiveness of control strategies, a novel model in line with the current epidemic's process and control measures was proposed, utilizing multisource datasets including the cumulative number of reported, deceased, quarantined and suspected cases. Results show that the trend of the epidemic mainly depends on quarantined and suspected cases. The predicted cumulative numbers of quarantined and suspected cases nearly reached static states, and their inflection points have already been achieved, with the epidemic's peak coming soon. The estimated effective reproduction numbers using model-free and model-based methods are decreasing, as well as new infections, while newly reported cases are increasing. Most infected cases have been quarantined or put in the suspected class, which has been ignored in existing models. The uncertainty analyses reveal that the epidemic is still uncertain, and it is important to continue enhancing the quarantine and isolation strategy and improving the detection rate in mainland China. [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]

Abstract: In this paper we consider a delayed population model with delay-dependent parameters. Its dynamics are studied in terms of stability and Hopf bifurcations. We prove analytically that the positive equilibrium switches from being stable to unstable and then back to stable as the delay increases, and Hopf bifurcations occur finite times between the two critical values of stability changes. Moreover, the critical values for stability switches and Hopf bifurcations can be analytically determined. Using the perturbation approach and Floquet technique, we also obtain an approximation to the bifurcating periodic solution and derive the formulas for determining the direction and stability of the Hopf bifurcations. Finally, we illustrate our results with some numerical examples. [Copyright &y& Elsevier]

Abstract: The main aim of this paper is to study the existence and global exponential stability of periodic solution for high-order bidirectional associative memory (BAM) neural networks with and without impulses. Easily verifiable sufficient conditions are established. The method is based on coincidence degree theory as well as a priori estimates and Lyapunov functional. It is shown that the convergence characteristics of periodic solution for the impulsive system are preserved by the corresponding nonimpulsive system with some restriction imposed on the impulse effect. Numerical simulation results are given to support the theoretical predictions. [Copyright &y& Elsevier]

We use a two-patch model to address the spread of antibiotic-resistant bacteria (ARB) within and between hospitals. Specifically, we consider patients being referred and transferred from a small community hospital with inappropriate antibiotic use to a large teaching hospital with good antibiotic treatment. Our analyses show that screening and decolonizing patients transferred between hospitals and avoiding misuse of antibiotics are both crucial factors to contain nosocomial infections. [ABSTRACT FROM AUTHOR]

• Effective reproductive numbers (R t) for COVID-19 are linked to dates of interventions. • From 3.98 before lockdown, R t declined to below 1 by the second week of February 2020. • Declines follow "early detection, early report, early quarantine and early treatment". • Evaluations of interventions provide lessons for others. Effective reproductive numbers (R t) were calculated from data on the COVID-19 outbreak in China and linked to dates in 2020 when different interventions were enacted. From a maximum of 3.98 before the lockdown in Wuhan City, the values of R t declined to below 1 by the second week of February, after the construction of hospitals dedicated to COVID-19 patients. The R t continued to decline following additional measures in line with the policy of "early detection, early report, early quarantine, and early treatment." The results provide quantitative evaluations of how intervention measures and their timings succeeded, from which lessons can be learned by other countries dealing with future outbreaks. [ABSTRACT FROM AUTHOR]

Integrodifference equations have been widely used to describe the spatiotemporal dynamics of a population. Here, we first extended the discrete Beverton–Holt model, to model the effects of an instantaneous control measure within each generation on a population’s growth. Then we investigated the effects of instantaneous killing rate and timing of pesticide application on a pest’s dynamics, together with the effects of a spatial factor on the existence of a travelling wave solution, its spreading speed and asymptotic stability, and the occurrence of paradoxical effects. The main results indicate that the instantaneous killing rate significantly influences the existence of a travelling wave and its speed of spread, while the timing of pesticide applications does not. In order to address how such dynamic complexities affect the above results, we included an interruption constant into the model which can generate chaotic dynamics. The results indicate that the pesticide efficacy not only affects the existence of a travelling wave and its speed of spread, but it can also produce paradoxical effects, i.e. low pesticide efficacy can result in an increase, not a decrease, of the stable population size, while high pesticide efficacy could inhibit the pests growth. Furthermore, different patterns of stable population sizes between odd and even generations can be produced. The results reveal that the pest control tactics should be designed according to the spatial characteristics and the pest generation. [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]

Understanding mechanisms of cross-contamination during poultry processing is vital for effective pathogen control. As an initial step toward this goal, we develop a mathematical model of the chilling process in a typical high speed Canadian processing plant. An important attribute of our model is that it provides quantifiable links between processing control parameters and microbial levels, simplifying the complexity of these relationships for implementation into risk assessment models. We apply our model to generic, non-pathogenic Escherichia coli contamination on broiler carcasses, connecting microbial control with chlorine sanitization, organic load in the water, and pre-chiller E. coli levels on broiler carcasses. In particular, our results suggest that while chlorine control is important for reducing E. coli levels during chilling, it plays a less significant role in the management of cross-contamination issues. [ABSTRACT FROM AUTHOR]