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It is imperative that resources are channelled towards programs that are efficient and cost effective in combating the spread of COVID-19, the disease caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). This study proposed and analyzed control strategies for that purpose. We developed a mathematical disease model within an optimal control framework that allows us to investigate the best approach for curbing COVID-19 epidemic. We address the following research question: what is the role of community compliance as a measure for COVID-19 control? Analyzing the impact of community compliance of recommended guidelines by health authorities—examples, social distancing, face mask use, and sanitizing—coupled with efforts by health authorities in areas of vaccine provision and effective quarantine—showed that the best intervention in addition to implementing vaccination programs and effective quarantine measures, is the active incorporation of individuals' collective behaviours, and that resources should also be directed towards community campaigns on the importance of face mask use, social distancing, and frequent sanitizing, and any other collective activities. We also demonstrated that collective behavioral response of individuals influences the disease dynamics; implying that recommended health policy should be contextualized. [ABSTRACT FROM AUTHOR]

Sequential antimicrobial de-escalation aims to minimize resistance to high-value broad-spectrum empiric antimicrobials by switching to alternative drugs when testing confirms susceptibility. Though widely practiced, the effects de-escalation are not well understood. Definitions of interventions and outcomes differ among studies. We use mathematical models of the transmission and evolution of Pseudomonas aeruginosa in an intensive care unit to assess the effect of de-escalation on a broad range of outcomes, and clarify expectations. In these models, de-escalation reduces the use of high-value drugs and preserves the effectiveness of empiric therapy, while also selecting for multidrug-resistant strains and leaving patients vulnerable to colonization and superinfection. The net effect of de-escalation in our models is to increase infection prevalence while also increasing the probability of effective treatment. Changes in mortality are small, and can be either positive or negative. The clinical significance of small changes in outcomes such as infection prevalence and death may exceed more easily detectable changes in drug use and resistance. Integrating harms and benefits into ranked outcomes for each patient may provide a way forward in the analysis of these tradeoffs. Our models provide a conceptual framework for the collection and interpretation of evidence needed to inform antimicrobial stewardship. [ABSTRACT FROM AUTHOR]

In a model of tuberculosis with relapse, the basic reproduction numberR0includes new and relapse infections. Lyapunov functions help to prove that the global dynamic is completely determined byR0. Replicated Latin hypercube sampling shows that early diagnosis and treatment are more efficient when relapse cases are considered. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the local synchronization problem for delayed phase-coupled oscillators with plastic coupling (also referred as a generalized Kuramoto model). By linearizing the phase-coupled oscillators system at a special solution, an approximation phase-coupled system with delay effects is deduced. Moreover, we find the multiplicity of semisimple zero eigenvalue for coupling strength coefficients matrix and the rank of Vandermonde matrix associated initial values are two sensitive factors. The former is closely related to the maximum number of clusters phase of linear coupled system, and the latter determines clusters phase synchronization. As results, both frequency synchronization criteria and phase synchronization criteria are established in this literature. Also, the final synchronization frequency and phase are formulated in terms of coupling strength, initial values and time delay. [ABSTRACT FROM AUTHOR]

The main purpose is to develop novel analytical techniques and provide a comprehensive qualitative analysis of global dynamics for a state-dependent feedback control system arising from biological applications including integrated pest management. The model considered consists of a planar system of differential equations with state-dependent impulsive control. We characterize the impulsive and phase sets, using the phase portraits of the planar system and the Lambert W function to define the Poincaré map for impulsive point series defined in the phase set. The existence, local and global stability of an order-1 limit cycle and obtain sharp sufficient conditions for the global stability of the boundary order-1 limit cycle have been provided. We further examine the flip bifurcation related to the existence of an order-2 limit cycle. We show that the existence of an order-2 limit cycle implies the existence of an order-1 limit cycle. We derive sufficient conditions under which any trajectory initiating from a phase set will be free from impulsive effects after finite state-dependent feedback control actions, and we also prove that order- k ( $k\geq3$) limit cycles do not exist, providing a solution to an open problem in the integrated pest management community. We then investigate multiple attractors and their basins of attraction, as well as the interior structure of a horseshoe-like attractor. We also discuss implications of the global dynamics for integrated pest management strategy. The analytical techniques and qualitative methods developed in the present paper could be widely used in many fields concerning state-dependent feedback control. [ABSTRACT FROM AUTHOR]

From February to May, 2013, 132 human avian influenza H7N9 cases were identified in China resulting in 37 deaths. We developed a novel, simple and effective compartmental modeling framework for transmissions among (wild and domestic) birds as well as from birds to human, to infer important epidemiological quantifiers, such as basic reproduction number for bird epidemic, bird-to-human infection rate and turning points of the epidemics, for the epidemic via human H7N9 case onset data and to acquire useful information regarding the bird-to-human transmission dynamics. Estimated basic reproduction number for infections among birds is 4.10 and the mean daily number of human infections per infected bird is 3.16*10−5 [3.08*10−5, 3.23*10−5]. The turning point of 2013 H7N9 epidemic is pinpointed at April 16 for bird infections and at April 9 for bird-to-human transmissions. Our result reveals very low level of bird-to-human infections, thus indicating minimal risk of widespread bird-to-human infections of H7N9 virus during the outbreak. Moreover, the turning point of the human epidemic, pinpointed at shortly after the implementation of full-scale control and intervention measures initiated in early April, further highlights the impact of timely actions on ending the outbreak. This is the first study where both the bird and human components of an avian influenza epidemic can be quantified using only the human case data. [ABSTRACT FROM AUTHOR]

Abstract: The processing delay is incorporated into the influence function of the well-known Cucker–Smale model for self-organized systems with multiple agents. Both symmetric and non-symmetric pairwise influence functions are considered, and a Lyapunov functional approach is developed to establish the existence of flocking solutions for the proposed delayed Cucker–Smale model. An analytic formula is given to calculate the asymptotic flocking velocity in terms of model parameters and the variation of the position during the initial time interval. [Copyright &y& Elsevier]

The purposes of this paper are twofold: to develop a rigorous approach to analyze the threshold behaviors of nonlinear virus dynamics models with impulsive drug effects and to examine the feasibility of virus clearance following the Manuals of National AIDS Free Antiviral Treatment in China. An impulsive system of differential equations is developed to describe the within-host virus dynamics of both wild-type and drug-resistant strains when a combination of antiretroviral drugs is used to induce instantaneous drug effects at a sequence of dosing times equally spaced while drug concentrations decay exponentially after the dosing time. Threshold parameters are derived using the basic reproduction number of periodic epidemic models, and are used to depict virus clearance/persistence scenarios using the theory of asymptotic periodic systems and the persistence theory of discrete dynamical systems. Numerical simulations using model systems parametrized in terms of the antiretroviral therapy recommended in the aforementioned Manuals illustrate the theoretical threshold virus dynamics, and examine conditions under which the impulsive antiretroviral therapy leads to treatment success. In particular, our results show that only the drug-resistant strain can dominate (the first-line treatment program guided by the Manuals) or both strains may be rapidly eliminated (the second-line treatment program), thus the work indicates the importance of implementing the second-line treatment program as soon as possible. [ABSTRACT FROM AUTHOR]

A big problem in malaria control is the rapidity with which mosquitoes can develop resistance to insecticides. The possibility of creating evolution-proof insecticides is therefore of considerable interest. Biologists have suggested that effective malaria control, with only weak selection for insecticide resistance, could be achieved if insecticides target only old mosquitoes that have already laid most of their eggs. The strategy aims to exploit the fact that most malarial mosquitoes do not live long enough to transmit the disease. We derive, analyse and compare two mathematical models, one for an insecticide that kills on exposure, and the other for an insecticide that targets only older mosquitoes. Both models predict that insecticide-resistant mosquitoes will become dominant over time but, very importantly, this occurs on a very much slower time scale when the insecticide only affects older mosquitoes. We present analytical results on linear and global stability of the nontrivial equilibrium in which only the resistant mosquito strain is present, together with a theorem comparing the rates of convergence for the two models. Numerical simulations show that the effect of targeting only old mosquitoes on the evolution of resistance is dramatic. [ABSTRACT FROM AUTHOR]

Abstract: We consider SIR and SIS epidemic models with bilinear incidence and migration between two patches, where infected individuals cannot migrate from one patch to another due to medical screening. We find the thresholds classifying the global dynamics of the models in terms of the model parameters, and we obtain the global asymptotical stability of the disease free and the disease endemic (in one patch or in both patches) equilibria. This global asymptotic stability of endemic equilibria is established by using a novel Lyapunov function. [Copyright &y& Elsevier]

In this paper, we analyze a few opinion formation or election game dynamics models. For a simple model with two subpopulations with opposing opinions A and B , if the fraction of committed believers of opinion A (“ A zealots”) is less than a critical value, then the system has two bistable equilibrium points. When the fraction is equal to the critical value, the system undergoes a saddle-node bifurcation. When the fraction is larger than the critical value, a boundary equilibrium point is globally asymptotically stable, suggesting that the entire population reaches a consensus on A . We find a similar bistability property in the model in which both opinions have their own zealots. We also extend the model to include multiple competitors and show the dynamical behavior of multistability. The more competitors subpopulation A has, the fewer zealots opinion A needs to obtain consensus. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of the paper is to use numerical analysis and optimization tools to suggest improved therapies to try and cure HIV infection. A HIV model of an ordinary differential equation, which includes immune response, neutralizing antibodies and multi-drug effects, is improved. For a fixed time, two drugs treatment strategies are explored based on Pontryagin’s Maximum Principle. Four types of treatments are used, and existence and uniqueness results for the optimal control fair are established. The optimality system is derived and then solved numerically using Gradient Projection Method. On the basis of weight factors for controls, we find a well treatment strategy with steady lower dosage of RTIs and PIs during the main part of treatment, almost unchanged higher population of uninfected cells and few increase of active virus throughout the duration. [Copyright &y& Elsevier]

We develop a mathematical model to closely mimic the integrated program of impulsive vector control (every Friday afternoon since the initiation of the program) and continuous patient treatment and isolation implemented in the Guangdong Province of China during its 2014 dengue outbreak. We fitted the data of accumulated infections and used the parameterized model to carry out a retrospective analysis to estimate the basic reproduction number 1.7425 (95% CI 1.4443–2.0408), the control reproduction number 0.1709, and the mosquito-killing ratios 0.1978, 0.2987, 0.6158 and 0.5571 on October 3, 10, 17 and 24, respectively. This suggests that integrated intervention is highly effective in controlling the dengue outbreak. We also simulated outbreak outcomes under different variations of the implemented interventions. We showed that skipping one Friday for vector control would not result in raising the control reproduction number to the threshold value 1 but would lead to significant increase in the accumulated infections at the end of the outbreak. The findings indicate that quick and persistent impulsive implementation of vector control result in an effective reduction in the control reproduction number and hence lead to significant decline of new infections. [ABSTRACT FROM AUTHOR]

The interim guidance issued by the World Health Organization during the West Africa 2014 Ebola outbreak provides guidelines on the use of convalescent blood from Ebola survivors for transfusion therapy. Here we develop a novel mathematical model, based on the interim guidance, to examine the nonlinear transmission–treatment–donation–stockpile dynamics during an Ebola outbreak and with a large scale use of the transfusion therapy in the population. We estimate the reduction of case fatality ratio by introducing convalescent blood transfusion as a therapy, and inform optimal treatment–donation–stockpile strategies to balance the treatment need for case fatality ratio reduction and the strategic need of maintaining a minimal blood bank stockpile for other control priorities. [ABSTRACT FROM AUTHOR]

Abstract: We propose and analyze a mathematical model to mimic its transmission dynamics to assess the transmission potential of the novel avian influenza A(H7N9) virus. By fitting the model to data of the confirmed human cases we estimate the reproduction number for human-to-human transmission as 0.467 (95% CI 0.387–0.651). Simulation results indicate that approximate twofold of the current human-to-human transmission rate or periodic outbreaks of avian influenza in poultry may induce an outbreak in human. Through the recent limited transmission potential of the novel avian influenza A(H7N9) virus, a new outbreak may be possible due to virus mutation and adaption or periodic outbreaks in poultry, and hence careful surveillance and persistent intervention strategies in poultry have to be required. [Copyright &y& Elsevier]