Modelling the preventive treatment under media impact on tuberculosis: A comparison in four regions of China.

Preventive treatment for people with latent Tuberculosis infection (LTBI) has aroused our great interest. In this paper, we propose and analyze a novel mathematical model of TB considering preventive treatment with media impact. The basic reproduction number R0 is defined by the next generation matrix method. In the case without media impact, we prove that the disease-free equilibrium is globally asymptotically stable (unstable) if R0<1(R0>1). Furthermore, we obtain that a unique endemic equilibrium exists when R0>1, which is globally asymptotically stable in the case of permanent immunity and no media impact. We fit the model to the newly reported TB cases data from 2009 to 2019 of four regions in China and estimate the parameters. And we estimated R0=0.5013<1 in Hubei indicating that TB in Hubei will be eliminated in the future. However, the estimated R0=1.015>1 in Henan, R0=1.282>1 in Jiangxi and R0=1.930>1 in Xinjiang imply that TB will continue to persist in these three regions without further prevention and control measures. Besides, sensitivity analysis is carried out to illustrate the role of model parameters for TB control. Our finding reveals that appropriately improving the rate of timely treatment for actively infected people and increasing the rate of individuals with LTBI seeking preventive treatment could achieve the goal of TB elimination. In addition, another interesting finding shows that media impact can only reduce the number of active infections to a limited extent, but cannot change the prevalence of TB.

Drug-Primed Self-Assembly of Platinum-Single-Atom Nanozyme to Regulate Cellular Redox Homeostasis Against Cancer.

Single-atom nanozymes (SAzymes) with high catalytic activity exhibit the potential to disequilibrate the reactive oxygen metabolic balance in the tumor microenvironment (TME), which contains several endogenous reductive substances such as glutathione (GSH). Herein, a novel nano-assembly (CDs@Pt SAs/NCs@DOX) is first constructed using drug-primed platinum (Pt) single-atom or nanocluster nanozymes with a Pt loading of 34.8%, which exhibits prominent dual enzymatic activities to mimic peroxidase (POD) and glutathione oxidase (GSHOx). The unique GSHOx-like activity can efficiently scavenge GSH with a relatively low Km (1.04 mm) and high Vmax (7.46 × 10-6  m s-1 ), thus avoiding single oxygen (1 O2 ) depletion. CDs@Pt SAs/NCs@DOX simultaneously demonstrates low-temperature photothermal therapy and TME- or laser-controlled disassembly and drug release, which can effectively regulate cellular redox homeostasis and achieve high tumor growth inhibition. These outcomes may provide promising strategies for the preparation of Pt SAzymes with multiple activities and variable-sized nano-assemblies, allowing for broader applications of SAzymes and nano-assemblies in the biomedical field.

Stability and Hopf bifurcation of an HIV infection model with two time delays.

This work focuses on an HIV infection model with intracellular delay and immune response delay, in which the former delay refers to the time it takes for healthy cells to become infectious after infection, and the latter delay refers to the time when immune cells are activated and induced by infected cells. By investigating the properties of the associated characteristic equation, we derive sufficient criteria for the asymptotic stability of the equilibria and the existence of Hopf bifurcation to the delayed model. Based on normal form theory and center manifold theorem, the stability and the direction of the Hopf bifurcating periodic solutions are studied. The results reveal that the intracellular delay cannot affect the stability of the immunity-present equilibrium, but the immune response delay can destabilize the stable immunity-present equilibrium through the Hopf bifurcation. Numerical simulations are provided to support the theoretical results.

Coexistence under Hierarchical Resource Exploitation: The Role of the R*-Preemption Trade-Off.

AbstractResource competition theory predicts coexistence and exclusion patterns based on species' R*s, the minimum resource values required for a species to persist. A central assumption of the theory is that all species have equal access to resources. However, many systems are characterized by preemption exploitation, where some species deplete resources before their competitors can access them (e.g., asymmetric light competition, contest competition among animals). We hypothesized that coexistence under preemption requires an R*-preemption trade-off-that is, the species with the priority access should have a higher R* (lower "efficiency"). Thus, we developed an extension of resource competition theory to investigate partial and total preemption (in the latter, the preemptor is unaffected by species with lower preemption rank). We found that an R*-preemption trade-off is a necessary condition for coexistence in all models. Moreover, under total preemption, the trade-off alone is sufficient for coexistence. In contrast, under partial preemption, more conditions are needed, which restricts the parameter space of coexistence. Finally, we discuss the implications of our finding for seemingly distinct trade-offs, which we view as special cases of the R*-preemption trade-off. These trade-offs include the digger-grazer trade-off, the competition-colonization trade-off, and trade-offs related to light competition between trees and understories.

Dynamical analysis on a predator-prey model with stage structure and mutual interference.

In this paper, we formulate a stage-structured predator-prey model with mutual interference, in which includes two discrete delays. By theoretical analysis, we establish the stability of the unique positive equilibrium and the existence of Hopf bifurcation when the maturation delay for predators is used as the bifurcation parameter. Our results exhibit that the maturation delay for preys does not affect the stability of the positive equilibrium. However, the maturation delay for predator is able to destabilize the positive equilibrium and causes periodic solutions. Numerical simulations are carried out to illustrate the theoretical results and display the differential impacts of two type delays and mutual interference.

Mathematical modeling on T-cell mediated adaptive immunity in primary dengue infections.

At present, dengue is the most common mosquito-borne viral disease in the world, and the global dengue incidence is increasing day by day due to climate changing. Here, we present a mathematical model of dengue viruses (DENVs) dynamics in micro-environment (cellular level) consisting of healthy cells, infected cells, virus particles and T-cell mediated adaptive immunity. We have considered the explicit role of cytokines and antibody in our model. We find that the virus load goes down to zero within 6 days as it is common for DENV infection. From our analysis, we have identified the important model parameters and done the numerical simulation with respect to such important parameters. We have shown that the cytokine mediated virus clearance plays a very important role in dengue dynamics. It can change the dynamical behavior of the system and causes essential extinction of the virus. Finally, we have incorporated the antiviral treatment for dengue in our model and shown that the basic reproduction number is directly proportional to the antiviral treatment effects.

Dual role of delay effects in a tumour-immune system.

In this paper, a previous tumour-immune interaction model is simplified by neglecting a relatively weak direct immune activation by the tumour cells, which can still keep the essential dynamics properties of the original model. As the immune activation process is not instantaneous, we now incorporate one delay for the activation of the effector cells (ECs) by helper T cells (HTCs) into the model. Furthermore, we investigate the stability and instability regions of the tumour-presence equilibrium state of the delay-induced system with respect to two parameters, the activation rate of ECs by HTCs and the HTCs stimulation rate by the presence of identified tumour antigens. We show the dual role of this delay that can induce stability switches exhibiting destabilization as well as stabilization of the tumour-presence equilibrium. Besides, our results reveal that an appropriate immune activation time delay plays a significant role in control of tumour growth.

Identifying determinants of heterogeneous transmission dynamics of the Middle East respiratory syndrome (MERS) outbreak in the Republic of Korea, 2015: a retrospective epidemiological analysis.

OBJECTIVES: To investigate the heterogeneous transmission patterns of Middle East respiratory syndrome (MERS) in the Republic of Korea, with a particular focus on epidemiological characteristics of superspreaders. DESIGN: Retrospective epidemiological analysis. SETTING: Multiple healthcare facilities of secondary and tertiary care centres in an urban setting. PARTICIPANTS: A total of 185 laboratory-confirmed cases with partially known dates of illness onset and most likely sources of infection. PRIMARY AND SECONDARY OUTCOME MEASURES: Superspreaders were identified using the transmission tree. The reproduction number, that is, the average number of secondary cases produced by a single primary case, was estimated as a function of time and according to different types of hosts. RESULTS: A total of five superspreaders were identified. The reproduction number throughout the course of the outbreak was estimated at 1.0 due to reconstruction of the transmission tree, while the variance of secondary cases generated by a primary case was 52.1. All of the superspreaders involved in this outbreak appeared to have generated a substantial number of contacts in multiple healthcare facilities (association: p<0.01), generating on average 4.0 (0.0-8.6) and 28.6 (0.0-63.9) secondary cases among patients who visited multiple healthcare facilities and others. The time-dependent reproduction numbers declined substantially below the value of 1 on and after 13 June 2015. CONCLUSIONS: Superspreaders who visited multiple facilities drove the epidemic by generating a disproportionate number of secondary cases. Our findings underscore the need to limit the contacts in healthcare settings. Contact tracing efforts could assist early laboratory testing and diagnosis of suspected cases.

Apoptosis in virus infection dynamics models.

In this paper, on the basis of the simplified two-dimensional virus infection dynamics model, we propose two extended models that aim at incorporating the influence of activation-induced apoptosis which directly affects the population of uninfected cells. The theoretical analysis shows that increasing apoptosis plays a positive role in control of virus infection. However, after being included the third population of cytotoxic T lymphocytes immune response in HIV-infected patients, it shows that depending on intensity of the apoptosis of healthy cells, the apoptosis can either promote or comfort the long-term evolution of HIV infection. Further, the discrete-time delay of apoptosis is incorporated into the pervious model. Stability switching occurs as the time delay in apoptosis increases. Numerical simulations are performed to illustrate the theoretical results and display the different impacts of a delay in apoptosis.