Oscillations in a tumor-immune system interaction model with immune response delay.

In this paper we consider a tumor-immune system interaction model with immune response delay, in which a nonmonotonic function is used to describe immune response to the tumor burden and a time delay is used to represent the time for the immune system to respond and take effect. It is shown that the model may have one, two or three tumor equilibria, respectively, under different conditions. Time delay can only affect the stability of the low tumor equilibrium and local Hopf bifurcation occurs when the time delay passes through a critical value. The direction and stability of the bifurcating periodic solutions are also determined. Moreover, the global existence of periodic solutions is established by using a global Hopf bifurcation theorem. We also observe the existence of relaxation oscillations and complex oscillating patterns driven by the time delay. Numerical simulations are presented to illustrate the theoretical results.

Cyclicity of slow-fast cycles with two canard mechanisms.

In this paper, we study the cyclicity of some degenerate slow-fast cycles with two canard mechanisms in planar slow-fast systems. One canard mechanism originates from a slow-fast Hopf point and the other from a point of self-intersection where the so-called entry-exit relation can be used. By studying the difference map, we show that the cyclicity of such slow-fast cycles is at most two (the associated slow divergence integral is nonzero or vanishes). As an example, we apply this result to the modified Holling-Tanner model.

Effects of whaling and krill fishing on the whale-krill predation dynamics: bifurcations in a harvested predator-prey model with Holling type I functional response.

In the Antarctic, the whale population had been reduced dramatically due to the unregulated whaling. It was expected that Antarctic krill, the main prey of whales, would grow significantly as a consequence and exploratory krill fishing was practiced in some areas. However, it was found that there has been a substantial decline in abundance of krill since the end of whaling, which is the phenomenon of krill paradox. In this paper, to study the krill-whale interaction we revisit a harvested predator-prey model with Holling I functional response. We find that the model admits at most two positive equilibria. When the two positive equilibria are located in the region { ( N , P ) | 0 ≤ N < 2 N c , P ≥ 0 } , the model exhibits degenerate Bogdanov-Takens bifurcation with codimension up to 3 and Hopf bifurcation with codimension up to 2 by rigorous bifurcation analysis. When the two positive equilibria are located in the region { ( N , P ) | N > 2 N c , P ≥ 0 } , the model has no complex bifurcation phenomenon. When there is one positive equilibrium on each side of N = 2 N c , the model undergoes Hopf bifurcation with codimension up to 2. Moreover, numerical simulation reveals that the model not only can exhibit the krill paradox phenomenon but also has three limit cycles, with the outmost one crosses the line N = 2 N c under some specific parameter conditions.

Bifurcations driven by generalist and specialist predation: mathematical interpretation of Fennoscandia phenomenon.

In this paper, we revisit a predator-prey model with specialist and generalist predators proposed by Hanski et al. (J Anim Ecol 60:353-367, 1991) , where the density of generalist predators is assumed to be a constant. It is shown that the model admits a nilpotent cusp of codimension 4 or a nilpotent focus of codimension 3 for different parameter values. As the parameters vary, the model can undergo cusp type (or focus type) degenerate Bogdanov-Takens bifurcations of codimension 4 (or 3). Our results indicate that generalist predation can induce more complex dynamical behaviors and bifurcation phenomena, such as three small-amplitude limit cycles enclosing one equilibrium, one or two large-amplitude limit cycles enclosing one or three equilibria, three limit cycles appearing in a Hopf bifurcation of codimension 3 and dying in a homoclinic bifurcation of codimension 3. In addition, we show that generalist predation stabilizes the limit cycle driven by specialist predators to a stable equilibrium, which clearly explains the famous Fennoscandia phenomenon.

Relative prevalence-based dispersal in an epidemic patch model.

In this paper, we propose a two-patch SIRS model with a nonlinear incidence rate: [Formula: see text] and nonconstant dispersal rates, where the dispersal rates of susceptible and recovered individuals depend on the relative disease prevalence in two patches. In an isolated environment, the model admits Bogdanov-Takens bifurcation of codimension 3 (cusp case) and Hopf bifurcation of codimension up to 2 as the parameters vary, and exhibits rich dynamics such as multiple coexistent steady states and periodic orbits, homoclinic orbits and multitype bistability. The long-term dynamics can be classified in terms of the infection rates [Formula: see text] (due to single contact) and [Formula: see text] (due to double exposures). In a connected environment, we establish a threshold [Formula: see text] between disease extinction and uniform persistence under certain conditions. We numerically explore the effect of population dispersal on disease spread when [Formula: see text] and patch 1 has a lower infection rate, our results indicate: (i) [Formula: see text] can be nonmonotonic in dispersal rates and [Formula: see text] ([Formula: see text] is the basic reproduction number of patch i) may fail; (ii) the constant dispersal of susceptible individuals (or infective individuals) between two patches (or from patch 2 to patch 1) will increase (or reduce) the overall disease prevalence; (iii) the relative prevalence-based dispersal may reduce the overall disease prevalence. When [Formula: see text] and the disease outbreaks periodically in each isolated patch, we find that: (a) small unidirectional and constant dispersal can lead to complex periodic patterns like relaxation oscillations or mixed-mode oscillations, whereas large ones can make the disease go extinct in one patch and persist in the form of a positive steady state or a periodic solution in the other patch; (b) relative prevalence-based and unidirectional dispersal can make periodic outbreak earlier.

Uneven phosphoric acid interfaces with enhanced electrochemical performance for high-temperature polymer electrolyte fuel cells.

Ultrahigh mass transport resistance and excessive coverage of the active sites introduced by phosphoric acid (PA) are among the major obstacles that limit the performance of high-temperature polymer fuel cells, especially compared to their low-temperature counterparts. Here, an alternative strategy of electrode design with fibrous networks is developed to optimize the redistribution of acid within the electrode. Via structural tailoring with varied electrospinning parameters, uneven migration of PA with dispersed droplets is observed, subverting the immersion model of conventional porous electrode. Combining with experimental and calculation results, the microscaled uneven PA interfaces could not only provide extra diffusion pathways for oxygen but also minimize the thickness of PA layers. This electrode architecture demonstrates enhanced electrochemical performance of oxygen reduction within the PA phase, resulting in a 28% enhancement of the maximum power density for the optimally designed electrode as cathode compared to that of a conventional one.

An SIRS model with nonmonotone incidence and saturated treatment in a changing environment.

Nonmonotone incidence and saturated treatment are incorporated into an SIRS model under constant and changing environments. The nonmonotone incidence rate describes the psychological or inhibitory effect: when the number of the infected individuals exceeds a certain level, the infection function decreases. The saturated treatment function describes the effect of infected individuals being delayed for treatment due to the limitation of medical resources. In a constant environment, the model undergoes a sequence of bifurcations including backward bifurcation, degenerate Bogdanov-Takens bifurcation of codimension 3, degenerate Hopf bifurcation as the parameters vary, and the model exhibits rich dynamics such as bistability, tristability, multiple periodic orbits, and homoclinic orbits. Moreover, we provide some sufficient conditions to guarantee the global asymptotical stability of the disease-free equilibrium or the unique positive equilibrium. Our results indicate that there exist three critical values [Formula: see text] and [Formula: see text] for the treatment rate r: (i) when [Formula: see text], the disease will disappear; (ii) when [Formula: see text], the disease will persist. In a changing environment, the infective population starts along the stable disease-free state (or an endemic state) and surprisingly continues tracking the unstable disease-free state (or a limit cycle) when the system crosses a bifurcation point, and eventually tends to the stable endemic state (or the stable disease-free state). This transient tracking of the unstable disease-free state when [Formula: see text] predicts regime shifts that cause the delayed disease outbreak in a changing environment. Furthermore, the disease can disappear in advance (or belatedly) if the rate of environmental change is negative and large (or small). The transient dynamics of an infectious disease heavily depend on the initial infection number and rate or the speed of environmental change.

NKTR-255, a novel polymer-conjugated rhIL-15 with potent antitumor efficacy.

BACKGROUND: NKTR-255 is a novel polyethylene glycol-conjugate of recombinant human interleukin-15 (rhIL-15), which was designed to retain all known receptor binding interactions of the IL-15 molecule. We explored the biologic and pharmacologic differences between endogenous IL-15 receptor α (IL-15Rα)-dependent (NKTR-255 and rhIL-15) and IL-15Rα-independent (precomplexed rhIL-15/IL-15Rα) cytokines. METHODS: In vitro pharmacological properties of rhIL-15, NKTR-255 and precomplex cytokines (rhIL-15/IL-15Rα and rhIL-15 N72D/IL-15Rα Fc) were investigated in receptor binding, signaling and cell function. In vivo pharmacokinetic (PK) and pharmacodynamic profile of the cytokines were evaluated in normal mice. Finally, immunomodulatory effect and antitumor activity were assessed in a Daudi lymphoma model. RESULTS: NKTR-255 and rhIL-15 exhibited similar in vitro properties in receptor affinity, signaling and leukocyte degranulation, which collectively differed from precomplexed cytokines. Notably, NKTR-255 and rhIL-15 stimulated greater granzyme B secretion in human peripheral blood mononuclear cells versus precomplexed cytokines. In vivo, NKTR-255 exhibited a PK profile with reduced clearance and a longer half-life relative to rhIL-15 and demonstrated prolonged IL-15R engagement in lymphocytes compared with only transient engagement observed for rhIL-15 and precomplexed rhIL-15 N72D/IL-15Rα Fc. As a consequent, NKTR-255 provided a durable and sustained proliferation and activation of natural killer (NK) and CD8+ T cells. Importantly, NKTR-255 is more effective than the precomplexed cytokine at inducing functionally competent, cytotoxic NK cells in the tumor microenvironment and the properties of NKTR-255 translated into superior antitumor activity in a B-cell lymphoma model versus the precomplexed cytokine. CONCLUSIONS: Our results show that the novel immunotherapeutic, NKTR-255, retains the full spectrum of IL-15 biology, but with improved PK properties, over rhIL-15. These findings support the ongoing phase 1 first-in-human trial (NCT04136756) of NKTR-255 in participants with relapsed or refractory hematologic malignancies, potentially advancing rhIL-15-based immunotherapies for the treatment of cancer.

Modelling homosexual and heterosexual transmissions of hepatitis B virus in China.

Studies have shown that sexual transmission, both heterosexually and homosexually, is one of the main ways of HBV infection. Based on this fact, we propose a mathematical model to study the sexual transmission of HBV among adults by classifying adults into men and women and considering both same-sex and opposite-sex transmissions of HBV in adults. Firstly, we calculate the basic reproduction number R0 and the disease-free equilibrium point E0. Secondly, by analysing the sensitivity of R0 in terms of model parameters, we find that the infection rate among people who have same-sex partners, the frequency of homosexual contact and the immunity rate of adults play important roles in the transmission of HBV. Moreover, we use our model to fit the reported data in China and forecast the trend of hepatitis B. Our results demonstrate that popularizing the basic knowledge of HBV among residents, advocating healthy and reasonable sexual life style, reducing the number of adult carriers, and increasing the immunization rate of adults are effective measures to prevent and control hepatitis B.

Global Dynamics of a Susceptible-Infectious-Recovered Epidemic Model with a Generalized Nonmonotone Incidence Rate.

A susceptible-infectious-recovered (SIRS) epidemic model with a generalized nonmonotone incidence rate kIS 1 + ß I + α I 2 ( ß > - 2 α such that 1 + ß I + α I 2 > 0 for all I ≥ 0 ) is considered in this paper. It is shown that the basic reproduction number R 0 does not act as a threshold value for the disease spread anymore, and there exists a sub-threshold value R ∗ ( < 1 ) such that: (i) if R 0 < R ∗ , then the disease-free equilibrium is globally asymptotically stable; (ii) if R 0 = R ∗ , then there is a unique endemic equilibrium which is a nilpotent cusp of codimension at most three; (iii) if R ∗ < R 0 < 1 , then there are two endemic equilibria, one is a weak focus of multiplicity at least three, the other is a saddle; (iv) if R 0 ≥ 1 , then there is again a unique endemic equilibrium which is a weak focus of multiplicity at least three. As parameters vary, the model undergoes saddle-node bifurcation, backward bifurcation, Bogdanov-Takens bifurcation of codimension three, Hopf bifurcation, and degenerate Hopf bifurcation of codimension three. Moreover, it is shown that there exists a critical value α 0 for the psychological effect α , a critical value k 0 for the infection rate k, and two critical values ß 0 , ß 1 ( ß 1 < ß 0 ) for ß that will determine whether the disease dies out or persists in the form of positive periodic coexistent oscillations or coexistent steady states under different initial populations. Numerical simulations are given to demonstrate the existence of one, two or three limit cycles.

Mathematical modeling the dynamics of Clonorchiasis in Guangzhou City of China.

In this paper, we have set up a mathematical model on the basic life cycle of clonorchiasis to fit the data of human clonorchiasis infection ratios of Guangzhou City of Guangdong Province in China from 2006-2012. By this model, we have proved that the condition of the basic reproductive number R0>1 or R0<1 corresponds the globally asymptotically stable of the endemic equilibrium or the disease-free equilibrium, respectively. The basic reproductive number is estimated as 1.41 with those optimal parameters. Some efficient strategies to control clonorchiasis are provided by numerical analysis of the mathematical model.

Bifurcation analysis of an SIRS epidemic model with a generalized nonmonotone and saturated incidence rate.

In this paper, we study a susceptible-infectious-recovered (SIRS) epidemic model with a generalized nonmonotone and saturated incidence rate k I 2 S 1 + ß I + α I 2 , in which the infection function first increases to a maximum when a new infectious disease emerges, then decreases due to psychological effect, and eventually tends to a saturation level due to crowding effect. It is shown that there are a weak focus of multiplicity at most two and a cusp of codimension at most two for various parameter values, and the model undergoes saddle-node bifurcation, Bogdanov-Takens bifurcation of codimension two, Hopf bifurcation, and degenerate Hopf bifurcation of codimension two as the parameters vary. It is shown that there exists a critical value α = α 0 for the psychological effect, and two critical values k = k 0 , k 1 ( k 0 < k 1 ) for the infection rate such that: (i) when α > α 0 , or α ≤ α 0 and k ≤ k 0 , the disease will die out for all positive initial populations; (ii) when α = α 0 and k 0 < k ≤ k 1 , the disease will die out for almost all positive initial populations; (iii) when α = α 0 and k > k 1 , the disease will persist in the form of a positive coexistent steady state for some positive initial populations; and (iv) when α < α 0 and k > k 0 , the disease will persist in the form of multiple positive periodic coexistent oscillations and coexistent steady states for some positive initial populations. Numerical simulations, including the existence of one or two limit cycles and data-fitting of the influenza data in Mainland China, are presented to illustrate the theoretical results.

Modeling the Transmission Dynamics of Rabies for Dog, Chinese Ferret Badger and Human Interactions in Zhejiang Province, China.

Human rabies is one of the major public health problems in China with an average of 1977 cases per year. It is estimated that 95% of these human rabies cases are due to dog bites. In recent years, the number of wildlife-associated human rabies cases has increased, particularly in the southeast and northeast regions of mainland China. Chinese ferret badgers (CFBs) are one of the most popular wildlife animals which are distributed mostly in the southeast region of China. Human cases caused by rabid CFB were first recorded in Huzhou, Zhejiang Province, in 1994. From 1996 to 2004, more than 30 human cases were caused by CFB bites in Zhejiang Province. In this paper, based on the reported data of the human rabies caused by both dogs and CFB in Zhejiang Province, we propose a multi-host zoonotic model for the dog-CFB-human transmission of rabies. We first evaluate the basic reproduction number [Formula: see text] discuss the stability of the disease-free equilibrium, and study persistence of the disease. Then we use our model to fit the reported data in Zhejiang Province from 2004 to 2017 and forecast the trend of human or livestock rabies. Finally by carrying out sensitivity analysis of the basic reproduction number in terms of parameters, we find that the transmission between dogs and CFB, the quantity of dogs, and the vaccination rate of dogs play important roles in the transmission of rabies. Our study suggests that rabies control and prevention strategies should include enhancing public education and awareness about rabies, increasing dog vaccination rate, reducing the dog and CFB interactions, and avoiding CFB bites or contact.

Modeling the Transmission Dynamics of Clonorchiasis in Foshan, China.

Clonorchiasis, known as the Chinese liver fluke disease, is caused by Clonorchis sinensis infection with food-borne liver fluke, which is transmitted via snails to freshwater fish and then to human beings or other piscivorous mammals. Clonorchis sinensis infection is mainly related to liver and biliary disorders, especially cholangiocarcinoma, and has an increased human-health impact due to the greater consumption of raw freshwater fish. In this article, we propose a deterministic model to describe the spread of clonorchiasis among human-snail-fish populations and use the model to simulate the data on the numbers of inspected and infected individuals of Foshan City, located in Guangdong Province in the southeast of P.R China, from 1980-2010. Mathematical and numerical analyses of the model are carried out to understand the transmission dynamics of clonorchiasis and explore effective control measures for the local outbreaks of the disease. We find that (i) the transmission of clonorchiasis from cercariae to fish plays a more important role than that from eggs to snails and from fish to humans; (ii) As the cycle of infection-treatment-reinfection continues, it is unlikely that treatment with drugs alone can control and eventually eradicate clonorchiasis. These strongly suggest that a more comprehensive approach needs to include environmental modification in order to break the cercariae-fish transmission cycle, to enhance awareness about the disease, and to improve prevention measures.

Seasonal transmission dynamics of measles in China.

Measles, a highly contagious infection caused by the measles virus, is a major public health problem in China. The reported measles cases decreased dramatically from 2004 to 2012 due to the mandatory measles vaccine program started in 2005 and the goal of eliminating measles by 2012. However, after reaching its lowest level in 2012, measles has resurged again since 2013. Since the monthly data of measles cases exhibit a seasonally fluctuating pattern, based on the measles model in Earn et al. (Science 287:667-670, 2000), we propose a susceptible, exposed, infectious, and recovered model with periodic transmission rate to investigate the seasonal measles epidemics and the effect of vaccination. We calculate the basic reproduction number [Formula: see text], analyze the dynamical behavior of the model, and use the model to simulate the monthly data of measles cases reported in China. We also carry out some sensitivity analysis of [Formula: see text] in the terms of various model parameters which shows that measles can be controlled and eventually eradicated by increasing the immunization rate, improving the effective vaccine management, and enhancing the awareness of people about measles.

NKTR-214, an Engineered Cytokine with Biased IL2 Receptor Binding, Increased Tumor Exposure, and Marked Efficacy in Mouse Tumor Models.

PURPOSE: Aldesleukin, recombinant human IL2, is an effective immunotherapy for metastatic melanoma and renal cancer, with durable responses in approximately 10% of patients; however, severe side effects limit maximal dosing and thus the number of patients able to receive treatment and potential cure. NKTR-214 is a prodrug of conjugated IL2, retaining the same amino acid sequence as aldesleukin. The IL2 core is conjugated to 6 releasable polyethylene glycol (PEG) chains. In vivo, the PEG chains slowly release to generate active IL2 conjugates. EXPERIMENTAL DESIGN: We evaluated the bioactivity and receptor binding of NKTR-214 and its active IL2 conjugates in vitro; the tumor immunology, tumor pharmacokinetics, and efficacy of NKTR-214 as a single agent and in combination with anti-CTLA-4 antibody in murine tumor models. Tolerability was evaluated in non-human primates. RESULTS: In a murine melanoma tumor model, the ratio of tumor-killing CD8(+) T cells to Foxp3(+) regulatory T cells was greater than 400 for NKTR-214 compared with 18 for aldesleukin, supporting preferential activation of the IL2 receptor beta over IL2 receptor alpha, due to the location of PEG molecules. NKTR-214 provides a 500-fold greater exposure of the tumor to conjugated IL2 compared with aldesleukin. NKTR-214 showed efficacy as a single agent and provided durable immunity that was resistant to tumor rechallenge in combination with anti-CTLA-4 antibody. NKTR-214 was well tolerated in non-human primates. CONCLUSIONS: These data support further evaluation of NKTR-214 in humans for a variety of tumor types, adding to the repertoire of potent and potentially curative cancer immunotherapies.

Purification of a recombinant heavy chain fragment C vaccine candidate against botulinum serotype C neurotoxin [rBoNTC(H(c))] expressed in Pichia pastoris.

A purification process for the manufacture of a recombinant C-terminus heavy chain fragment from botulinum neurotoxin serotype C [rBoNTC(H(c))], a potential vaccine candidate, has been defined and successfully scaled-up. The rBoNTC(H(c)) was produced intracellularly in Pichia pastoris X-33 using a three step fermentation process, i.e., glycerol batch phase, a glycerol fed-batch phase to achieve high cell densities, followed by a methanol induction phase. The rBoNTC(H(c)) was captured from the soluble protein fraction of cell lysate using hydrophobic charge induction chromatography (HCIC; MEP HyperCel™), and then further purified using a CM 650M ion exchange chromatography step followed by a polishing step using HCIC once again. Method development at the bench scale was achieved using 5-100mL columns and the process was performed at the pilot scale using 0.6-1.6L columns in preparation for technology transfer to cGMP manufacturing. The process yielded approximately 2.5 g of rBoNTC(H(c))/kg wet cell weight (WCW) at the bench scale and 1.6 g rBoNTC(H(c))/kg WCW at the pilot scale. The purified rBoNTC(H(c)) was stable for at least 3 months at 5 and -80°C as determined by reverse phase-HPLC and SDS-PAGE and was stable for 24 months at -80 °C based on mouse potency bioassay. N-Terminal amino acid sequencing confirmed that the N-terminus of the purified rBoNTC(H(c)) was intact.

Purification of the N- and C-terminal subdomains of recombinant heavy chain fragment C of botulinum neurotoxin serotype C.

The N-terminal and C-terminal portions of the heavy chain fragment C from botulinum neurotoxin serotype C [rBoNT(HC)] were expressed in Pichia pastoris and purified by ion-exchange chromotography (IEC). The N-terminal fragment, rBoNTC(Hc)-N, was purified in three IEC steps: a Q Sepharose Fast Flow (FF) capture step followed by a negative SP Sepharose FF step, and finally, Q Sepharose FF as a polishing step. The purification process resulted in greater than 90% pure rBoNTC(Hc)-N based on SDS-PAGE, and yielded up to 1.02 g of rBoNTC(Hc)-N/kg of cells. Alternately, the C-terminal fragment, rBoNTC(Hc)-C, was purified by using a SP Sepharose FF capture step followed by a second SP Sepharose FF step, and finally a Q Sepharose FF as a polishing step. This purification process resulted in greater than 95% pure rBoNTC(Hc)-C based on SDS-PAGE, and yielded up to 0.2 g of rBoNTC(Hc)-C/kg cells. The final protein yield is a function of protein expression level during fermentation and the purification methods, and usually final protein yield between 0.1 and 2 mg/g cells is acceptable. Another concern is protein degradation. Especially with Pichia, protease activity during cell lysis and purification is always an issue. The importance of N-terminal degradation depends on product and its function. N-terminal sequencing revealed that the purified rBoNTC(Hc)-N is missing the first eight amino acids of the N-terminus of the protein, whereas the purified rBoNTC(Hc)-C protein is intact. After a mouse bioassay test, both the intact rBoNTC(Hc)-C and the rBoNTC(Hc)-N missing the first eight amino acids of the N-terminus have vaccine potency; consequently, partial degradation did not have an impact on these protein's utility.

Crystallization and preliminary X-ray analysis of Na-ASP-1, a multi-domain pathogenesis-related-1 protein from the human hookworm parasite Necator americanus.

Human hookworm infection is a major cause of anemia and malnutrition in the developing world. In an effort to control hookworm infection, the Human Hookworm Vaccine Initiative has identified candidate vaccine antigens from the infective larval stage (L3) of the parasite, including a family of pathogenesis-related-1 (PR-1) proteins known as the ancylostoma-secreted proteins (ASPs). The functions of the ASPs are unknown. In addition, it is unclear why some ASPs have one while others have multiple PR-1 domains. There are no known structures of a multi-domain ASP and in an effort to remedy this situation, recombinant Na-ASP-1 has been expressed, purified and crystallized. Na-ASP-1 is a 406-amino-acid multi-domain ASP from the prevalent human hookworm parasite Necator americanus. Useful X-ray data to 2.2 A have been collected from a crystal that belongs to the monoclinic space group P2(1) with unit-cell parameters a = 67.7, b = 74.27, c = 84.60 A, beta = 112.12 degrees. An initial molecular-replacement solution has been obtained with one monomer in the asymmetric unit.