We developed a particle agglutination test (KPA) with poly(gamma-methyl L-glutamate) as the solid particle for measurement of pertussis toxin (PT) antibody. In this study, KPA was assessed as a means of serodiagnosing pertussis, and the results were compared with those of indirect enzyme-linked immunosorbent assay (indirect ELISA) and the microagglutination test. First, four serum samples were collected from each of 21 healthy children: before and 4 weeks after receiving three primary doses of acellular pertussis vaccines and before and 4 weeks after receiving a booster dose. In all 21 vaccinees, a significant rise in PT antibody titers was observed by KPA after each vaccination, and among all 84 serum samples collected, an excellent correlation was demonstrated between the values obtained by indirect ELISA and those obtained by KPA (r = 0.92). Second, paired serum samples were collected at intervals of approximately 2 weeks from 51 patients with culture-confirmed pertussis. A significant increase in titer (fourfold or more) was observed in 39 (76%) patients by KPA, 34 (67%) patients by indirect ELISA, and 23 (45%) patients by the microagglutination test. In acute- and convalescent-phase sera collected from 20 nonpertussis patients, there were no changes in titers by KPA. The KPA procedure was as simple as that of the microagglutination test, and the reaction time was only 2 h (or overnight). In this study, KPA was demonstrated to be a simple, speedy, sensitive, and specific serodiagnostic method for pertussis.

Tumor–immune system interactions are very complicated, being highly nonlinear and not well understood. A large number of tumors can potentially weaken the immune system through various mechanisms such as secreting cytokines that suppress the immune response. In this paper, we propose a tumor–immune system interaction model with a nonmonotonic immune response function and adoptive cellular immunotherapy (ACI). The model has a tumor-free equilibrium and at most three tumor-presence equilibria (low, moderate and high ones). The stability of all equilibria is studied by analyzing their characteristic equations. The consideration of nonmonotonic immune response results in a series of bifurcations such as the saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation. In addition, numerical simulation results show the coexistence of periodic orbits and homoclinic orbits. Interestingly, along with various bifurcations, we also found two bistable scenarios: the coexistence of a stable tumor-free as well as a high-tumor-presence equilibrium and the coexistence of a stable-low as well as a high-tumor-presence equilibrium, which can show symmetric and antisymmetric properties in a range of model parameters and initial cell concentrations. The new findings indicate that under ACI, patients can possibly reach either a stable tumor-free state or a low-tumor-presence state in the presence of nonmonotonic immune response once the immune system is activated.

The improper medication behavior among drug-sensitive tuberculosis (TB) patients increases the risk of developing drug resistance, a risk that can be mitigated through effective media campaigns and warnings. In this paper, we propose and analyze a novel two-strain (drug-sensitive versus drug-resistant) TB model that focuses on the media impact on the medication behavior of drug-sensitive patients. We first investigate the existence and stability of the model’s possible equilibria. Additionally, we explore the presence of forward and backward bifurcations near the disease-free equilibrium and the drug-resistance-dominated equilibrium, respectively, revealing rich and intriguing dynamics. Our analysis identifies two types of bistability, along with their corresponding regions in the two-parameter bifurcation diagram. To showcase the application of our model, we fit it to data on monthly new drug-sensitive and drug-resistant TB cases in Hubei province, China, from January to December 2019, estimating the basic reproduction number [Formula: see text]. Our results reveal that reducing the conversion rate from drug-sensitive to drug-resistant cases increased the instantaneous number of infections, but decreased the total number of all new cases in 2019. And the instantaneous economic cost of treating current patients and the total cost of treating all new cases in 2019 both decreasd as the conversion rate declined. Furthermore, our findings indicate that enhancing media impact achieves similar effects to reducing the conversion rate, highlighting the potential role of medication awareness among drug-sensitive patients in TB control strategies.