Global dynamics of a time-delayed nonlocal reaction-diffusion model of within-host viral infections.

In this paper, we study a time-delayed nonlocal reaction-diffusion model of within-host viral infections. We introduce the basic reproduction number R 0 and show that the infection-free steady state is globally asymptotically stable when R 0 ≤ 1 , while the disease is uniformly persistent when R 0 > 1 . In the case where all coefficients and reaction terms are spatially homogeneous, we obtain an explicit formula of R 0 and the global attractivity of the positive constant steady state. Numerically, we illustrate the analytical results, conduct sensitivity analysis, and investigate the impact of drugs on curtailing the spread of the viruses.

Activation of TRPV1 receptor facilitates myelin repair following demyelination via the regulation of microglial function.

The transient receptor potential vanilloid 1 (TRPV1) is a non-selective cation channel that is activated by capsaicin (CAP), the main component of chili pepper. Despite studies in several neurological diseases, the role of TRPV1 in demyelinating diseases remains unknown. Herein, we reported that TRPV1 expression was increased within the corpus callosum during demyelination in a cuprizone (CPZ)-induced demyelination mouse model. TRPV1 deficiency exacerbated motor coordinative dysfunction and demyelination in CPZ-treated mice, whereas the TRPV1 agonist CAP improved the behavioral performance and facilitated remyelination. TRPV1 was predominantly expressed in Iba1+ microglia/macrophages in human brain sections of multiple sclerosis patients and mouse corpus callosum under demyelinating conditions. TRPV1 deficiency decreased microglial recruitment to the corpus callosum, with an associated increase in the accumulation of myelin debris. Conversely, the activation of TRPV1 by CAP enhanced the recruitment of microglia to the corpus callosum and potentiated myelin debris clearance. Using real-time live imaging we confirmed an increased phagocytic function of microglia following CAP treatment. In addition, the expression of the scavenger receptor CD36 was increased, and that of the glycolysis regulators Hif1a and Hk2 was decreased. We conclude that TRPV1 is an important regulator of microglial function in the context of demyelination and may serve as a promising therapeutic target for demyelinating diseases such as multiple sclerosis.

Threshold dynamics of an almost periodic vector-borne disease model.

Many infectious diseases cannot be transmitted from human to human directly, and the transmission needs to be done via a vector. It is well known that vectors' life cycles are highly dependent on their living environment. In order to investigate dynamics of vector-borne diseases under environment influence, we propose a vector-borne disease model with almost periodic coefficients. We derive the basic reproductive number [Formula: see text] for this model and establish a threshold type result on its global dynamics in terms of [Formula: see text]. As an illustrative example, we consider an almost periodic model of malaria transmission. Our numerical simulation results show that the basic reproductive number may be underestimated if almost periodic coefficients are replaced by their average values . Finally, we use our model to study the dengue fever transmission in Guangdong, China. The parameters are chosen to fit the reported data available for Guangdong. Numerical simulations indicate that the annual dengue fever case in Guangdong will increase steadily in the near future unless more effective control measures are implemented. Sensitivity analysis implies that the parameters with strong impact on the outcome are recovery rate, mosquito recruitment rate, mosquito mortality rate, baseline transmission rates between mosquito and human. This suggests that the effective control strategies may include intensive treatment, mosquito control, decreasing human contact number with mosquitoes (e.g., using bed nets and preventing mosquito bites), and environmental modification.

A reaction-advection-diffusion model of cholera epidemics with seasonality and human behavior change.

Cholera is a water- and food-borne infectious disease caused by V. cholerae. To investigate multiple effects of human behavior change, seasonality and spatial heterogeneity on cholera spread, we propose a reaction-advection-diffusion model that incorporates human hosts and aquatic reservoir of V. cholerae. We derive the basic reproduction number [Formula: see text] for this system and then establish a threshold type result on its global dynamics in terms of [Formula: see text]. Further, we show that the bacterial loss at the downstream end of the river due to water flux can reduce the disease risk, and describe the asymptotic behavior of [Formula: see text] for small and large diffusion in a special case (where the diffusion rates of infected human and the pathogen are constant). We also study the transmission dynamics at the early stage of cholera outbreak numerically, and find that human behavior change may lower the infection level and delay the disease peak. Moreover, the relative rate of bacterial loss, together with convection rate, plays an important role in identifying the severely infected areas. Meanwhile spatial heterogeneity may dilute or amplify cholera infection, which in turn would increase the complexity of disease spread.

Global Dynamics of a Reaction-Diffusion Model of Zika Virus Transmission with Seasonality.

In this paper, we propose a periodic reaction-diffusion model of Zika virus with seasonal and spatial heterogeneous structure in host and vector population. We introduce the basic reproduction ratio [Formula: see text] for this model and show that the disease-free periodic solution is globally asymptotically stable if [Formula: see text], while the system admits a globally asymptotically stable positive periodic solution if [Formula: see text]. Numerically, we study the Zika transmission in Rio de Janeiro Municipality, Brazil, and investigate the effects of some model parameters on [Formula: see text]. We find that the neglect of seasonality underestimates the value of [Formula: see text] and the maximum carrying capacity affects the spread of Zika virus.

Target reproduction numbers for reaction-diffusion population models.

A very important population threshold quantity is the target reproduction number, which is a measure of control effort required for a target prevention, intervention or control. This concept, as a generalization of type reproduction number, was first introduced in Shuai et al. (J Math Biol 67:1067-1082, 2013) for nonnegative matrices with immediate applications to compartmental population models of ordinary differential equations. The current paper is devoted to the study of all target reproduction numbers for reaction-diffusion population models with compartmental structure. It turns out that the target reproduction number can be regarded as the basic reproduction number of a modified system, where the state of newborn individuals is limited to the target control set and the offspring from the non-target set is regarded as a part of the transition. In other words, the target reproduction number can be interpreted as the expected number of offspring in a specific target set that a primary newborn individual of the same set would produce during its lifetime. We also characterize the target reproduction number so that it can be easily computed numerically for reaction-diffusion models. At the end, we demonstrate our theoretical observations using two examples.

Basic reproduction ratios for periodic and time-delayed compartmental models with impulses.

Much work has focused on the basic reproduction ratio [Formula: see text] for a variety of compartmental population models, but the theory of [Formula: see text] remains unsolved for periodic and time-delayed impulsive models. In this paper, we develop the theory of [Formula: see text] for a class of such impulsive models. We first introduce [Formula: see text] and show that it is a threshold parameter for the stability of the zero solution of an associated linear system. Then we apply this theory to a time-delayed computer virus model with impulse treatment and obtain a threshold result on its global dynamics in terms of [Formula: see text]. Numerically, it is found that the basic reproduction ratio of the time-averaged delayed impulsive system may overestimate the spread risk of the virus.

Regional climate affects salmon lice dynamics, stage structure and management.

Regional variation in climate can generate differences in population dynamics and stage structure. Where regional differences exist, the best approach to pest management may be region-specific. Salmon lice are a stage-structured marine copepod that parasitizes salmonids at aquaculture sites worldwide, and have fecundity, development and mortality rates that depend on temperature and salinity. We show that in Atlantic Canada and Norway, where the oceans are relatively cold, salmon lice abundance decreases during the winter months, but ultimately increases from year to year, while in Ireland and Chile, where the oceans are warmer, the population size grows monotonically without any seasonal declines. In colder regions, during the winter the stage structure is dominated by the adult stage, which is in contrast to warmer regions where all stages are abundant year round. These differences translate into region-specific recommendations for management: regions with slower population growth have lower critical stocking densities, and regions with cold winters have a seasonal dependence in the timing of follow-up chemotherapeutic treatments. Predictions of our salmon lice model agree with empirical data, and our approach provides a method to understand the effects of regional differences in climate on salmon lice dynamics and management.

A periodic SEIRS epidemic model with a time-dependent latent period.

Many infectious diseases have seasonal trends and exhibit variable periods of peak seasonality. Understanding the population dynamics due to seasonal changes becomes very important for predicting and controlling disease transmission risks. In order to investigate the impact of time-dependent delays on disease control, we propose an SEIRS epidemic model with a periodic latent period. We introduce the basic reproduction ratio [Formula: see text] for this model and establish a threshold type result on its global dynamics in terms of [Formula: see text]. More precisely, we show that the disease-free periodic solution is globally attractive if [Formula: see text]; while the system admits a positive periodic solution and the disease is uniformly persistent if [Formula: see text]. Numerical simulations are also carried out to illustrate the analytic results. In addition, we find that the use of the temporal average of the periodic delay may underestimate or overestimate the real value of [Formula: see text].

A climate-based malaria model with the use of bed nets.

Insecticide-treated bed nets (ITNs) are among the most important and effective intervention measures against malaria. In order to investigate the impact of bed net use on disease control, we formulate a periodic vector-bias malaria model incorporating the juvenile stage of mosquitoes and the use of ITNs. We derive the vector reproduction ratio [Formula: see text] and the basic reproduction ratio [Formula: see text]. We show that the global dynamics of the model is completely determined by these two reproduction ratios. More precisely, the mosquito-free periodic solution is globally attractive if [Formula: see text]; the unique disease-free periodic solution is globally attractive if [Formula: see text] and [Formula: see text]; and the model admits a unique positive periodic solution and it is globally attractive if [Formula: see text] and [Formula: see text]. Numerically, we study the malaria transmission case in Port Harcourt, Nigeria. Our findings show that the use of ITNs has a positive effect on reducing [Formula: see text], and that malaria may be eliminated from this area if over 75% of the human population were to use ITNs. The simulation about the long term behavior of solutions has good agreement with the obtained analytic result. Moreover, we find that the ignorance of the vector-bias effect may result in underestimation of the basic reproduction ratio [Formula: see text]. Another notable result is that the infection risk would be underestimated if the basic reproduction ratio [Formula: see text] of the time-averaged autonomous system were used.

A reaction-diffusion malaria model with seasonality and incubation period.

In this paper, we propose a time-periodic reaction-diffusion model which incorporates seasonality, spatial heterogeneity and the extrinsic incubation period (EIP) of the parasite. The basic reproduction number [Formula: see text] is derived, and it is shown that the disease-free periodic solution is globally attractive if [Formula: see text], while there is an endemic periodic solution and the disease is uniformly persistent if [Formula: see text]. Numerical simulations indicate that prolonging the EIP may be helpful in the disease control, while spatial heterogeneity of the disease transmission coefficient may increase the disease burden.

Synthesis and Evolution of Berberine Derivatives as a New Class of Antiviral Agents against Enterovirus 71 through the MEK/ERK Pathway and Autophagy.

Taking berberine (BBR) as the lead, 23 new BBR derivatives were synthesized and examined for their antiviral activities against four different genotype enterovirus 71 (EV71) strains with a cytopathic effect (CPE) assay. Structure-activity relationship (SAR) studies indicated that introduction of a suitable substituent at the 9-position might be beneficial for potency. Among them, compound 2d exhibited most potent activities with IC50 values of 7.12⁻14.8 µM, similar to that of BBR. The effect of 2d was further confirmed in a dose-dependent manner both in RNA and protein level. The mechanism revealed that 2d could inhibit the activation of MEK/ERK signaling pathway. Meanwhile, it could suppress the EV71-induced autophagy by activating AKT and inhibiting the phosphorylation of JNK and PI3KIII proteins. We consider BBR derivatives to be a new family of anti-EV71 agents through targeting host components, with an advantage of broad-spectrum anti-EV71 potency.

A Malaria Transmission Model with Temperature-Dependent Incubation Period.

Malaria is an infectious disease caused by Plasmodium parasites and is transmitted among humans by female Anopheles mosquitoes. Climate factors have significant impact on both mosquito life cycle and parasite development. To consider the temperature sensitivity of the extrinsic incubation period (EIP) of malaria parasites, we formulate a delay differential equations model with a periodic time delay. We derive the basic reproduction ratio [Formula: see text] and establish a threshold type result on the global dynamics in terms of [Formula: see text], that is, the unique disease-free periodic solution is globally asymptotically stable if [Formula: see text]; and the model system admits a unique positive periodic solution which is globally asymptotically stable if [Formula: see text]. Numerically, we parameterize the model with data from Maputo Province, Mozambique, and simulate the long-term behavior of solutions. The simulation result is consistent with the obtained analytic result. In addition, we find that using the time-averaged EIP may underestimate the basic reproduction ratio.

DPYD gene polymorphisms are associated with risk and chemotherapy prognosis in pediatric patients with acute lymphoblastic leukemia.

We aimed to investigate the association between dihydropyrimidine dehydrogenase (DPYD) gene polymorphisms and the risk of pediatric acute lymphoblastic leukemia (ALL) and its prognosis after chemotherapy. A total of 147 pediatric ALL patients diagnosed by our hospital between January 2011 and December 2014 were included in the case group, and 102 healthy people who received a physical examination during the same time frame in our hospital were included in the control group. DNA sequencing was applied for site determination and genotyping of the DPYD 85T > C, 2194G > A, 1156G > T, and IVS14 + 1G > A polymorphisms. The genotype and allele frequencies of the two groups were compared. A significant difference was found in the comparison of the mutant gene and allele frequencies of the 85T > C polymorphism between the case and control groups (P < 0.05). The CT and CC genotypes in the 85T > C polymorphism were associated with the risk of the disease (OR = 1.592, 95 % CI = 1.010-2.509), suggesting that the recessive gene (85C) was more likely to lead to the occurrence of ALL compared with the dominant gene (85T) (P < 0.05). Patients carrying the C allele of the 85T > C polymorphism presented higher damage of their liver functions and higher infection rates compared with patients carrying the non-C allele (P < 0.05). A higher proportion of liver function damage and a higher infection rate were found in patients with the GA genotype in the IVS14 + 1G > A polymorphism compared with the GG genotype (P < 0.05). The complete remission (CR) rate in patients with the GG genotype in the IVS14 + 1G > A polymorphism was higher than in patients with the GA genotype (P = 0.020). After 5-fluorouracil/calcium folinate (5-FU/CF)-based chemotherapy, the event-free survival (EFS) rate of patients with the TT genotype was higher than patients with the CT and CC genotypes (P < 0.05). Our results revealed that the C allele of the 85T > C polymorphism might be associated with susceptibility to pediatric ALL. Patients carrying the C allele may have an increased risk of ALL. Thus, the 85T > C polymorphism may be a predictor of CR for pediatric ALL patients.

A nonlocal and periodic reaction-diffusion-advection model of a single phytoplankton species.

In this article, we are concerned with a nonlocal reaction-diffusion-advection model which describes the evolution of a single phytoplankton species in a eutrophic vertical water column where the species relies solely on light for its metabolism. The new feature of our modeling equation lies in that the incident light intensity and the death rate are assumed to be time periodic with a common period. We first establish a threshold type result on the global dynamics of this model in terms of the basic reproduction number R0. Then we derive various characterizations of R0 with respect to the vertical turbulent diffusion rate, the sinking or buoyant rate and the water column depth, respectively, which in turn give rather precise conditions to determine whether the phytoplankton persist or become extinct. Our theoretical results not only extend the existing ones for the time-independent case, but also reveal new interesting effects of the modeling parameters and the time-periodic heterogeneous environment on persistence and extinction of the phytoplankton species, and thereby suggest important implications for phytoplankton growth control.

Sanguinarine modulates microglial function via PPARγ activation and protects against CNS demyelination.

Microglia aggregate in regions of active inflammation and demyelination in the CNS of multiple sclerosis (MS) patients and are considered pivotal in the disease process. Targeting microglia is a promising therapeutic approach for myelin repair. Previously, we identified two candidates for microglial modulation and remyelination using a Connectivity Map (CMAP)-based screening strategy. Interestingly, with results that overlapped, sanguinarine (SAN) emerged as a potential drug candidate to modulate microglial polarization and promote remyelination. In the current study, we demonstrate the efficacy of SAN in mitigating the MS-like experimental autoimmune encephalomyelitis (EAE) in a dose-dependent manner. Meanwhile, prophylactic administration of a medium dose (2.5 mg/kg) significantly reduces disease incidence and ameliorates clinical signs in EAE mice. At the cellular level, SAN reduces the accumulation of microglia in the spinal cord. Morphological analyses and immunophenotyping reveal a less activated state of microglia following SAN administration, supported by decreased inflammatory cytokine production in the spinal cord. Mechanistically, SAN skews primary microglia towards an immunoregulatory state and mitigates proinflammatory response through PPARγ activation. This creates a favorable milieu for the differentiation of oligodendrocyte progenitor cells (OPCs) when OPCs are incubated with conditioned medium from SAN-treated microglia. We further extend our investigation into the cuprizone-induced demyelinating model, confirming that SAN treatment upregulates oligodendrocyte lineage genes and increases myelin content, further suggesting its pro-myelination effect. In conclusion, our data propose SAN as a promising candidate adding to the preclinical therapeutic arsenal for regulating microglial function and promoting myelin repair in CNS demyelinating diseases such as MS.

A within-host virus model with periodic multidrug therapy.

This paper is devoted to the investigation of the effects of periodic drug treatment on a standard within-host virus model. We first introduce the basic reproduction ratio for the model, and then show that the infection free equilibrium is globally asymptotically stable, and the disease eventually disappears if R0<1, while there exists at least one positive periodic state and the disease persists when R0>1. We also consider an optimization problem by shifting the phase of these drug efficacy functions. It turns out that shifting the phase can certainly affect the stability of the infection free steady state. A numerical study is performed to illustrate our analytic results.

Global dynamics of a reaction and diffusion model for Lyme disease.

This paper is devoted to the mathematical analysis of a reaction and diffusion model for Lyme disease. In the case of a bounded spatial habitat, we obtain the global stability of either disease-free or endemic steady state in terms of the basic reproduction number R0. In the case of an unbounded spatial habitat, we establish the existence of the spreading speed of the disease and its coincidence with the minimal wave speed for traveling fronts. Our analytic results show that R0 is a threshold value for the global dynamics and that the spreading speed is linearly determinate.

A Lotka-Volterra competition model with seasonal succession.

A complete classification for the global dynamics of a Lotka-Volterra two species competition model with seasonal succession is obtained via the stability analysis of equilibria and the theory of monotone dynamical systems. The effects of two death rates in the bad season and the proportion of the good season on the competition outcomes are also discussed.

Modelling malaria control by introduction of larvivorous fish.

Malaria creates serious health and economic problems which call for integrated management strategies to disrupt interactions among mosquitoes, the parasite and humans. In order to reduce the intensity of malaria transmission, malaria vector control may be implemented to protect individuals against infective mosquito bites. As a sustainable larval control method, the use of larvivorous fish is promoted in some circumstances. To evaluate the potential impacts of this biological control measure on malaria transmission, we propose and investigate a mathematical model describing the linked dynamics between the host-vector interaction and the predator-prey interaction. The model, which consists of five ordinary differential equations, is rigorously analysed via theories and methods of dynamical systems. We derive four biologically plausible and insightful quantities (reproduction numbers) that completely determine the community composition. Our results suggest that the introduction of larvivorous fish can, in principle, have important consequences for malaria dynamics, but also indicate that this would require strong predators on larval mosquitoes. Integrated strategies of malaria control are analysed to demonstrate the biological application of our developed theory.