ABSTRACT
In this paper, a SEIR model proposed in the article "Dynamic analysis of mathematical model with health care capacity for COVID-19 pandemic” by S. Çakan (2020) is analysed. The model describes COVID-19 pandemic spread affected by healthcare capacity and is expressed by a system of delay differential equations. To prove the local stability of stationary states, S. Çakan uses linearization technique, though she does this as if the equations did not depend on the delay. Additionally, it is shown that the crucial argument used by S. Çakan to prove boundedness of the solutions is not correct, which implies that the proofs of global stability in the original article are not correct either. In this paper, improved proofs of local and global stability of the stationary states are provided. For local stability of the stationary states a standard linearization technique is used. Global stability of the stationary states is proved based on Lyapunov's functionals. Although the functionals are the same as those proposed by S. Çakan, additional properties of the solutions (in the case of disease-free stationary state) and the functional (in the case of the endemic stationary state) are proved. © 2022 Polish Mathematical Society. All rights reserved.
ABSTRACT
The anti-CD38 monoclonal antibody Daratumumab has shown impressive activity in combination with other agents for the treatment of multiple myeloma (MM), improving progression free survival and overall survival in several phase 3 studies. We conducted a phase 1b study of intravenous Daratumumab (16 mg/kg) with weekly subcutaneous bortezomib (1.3-1.5 mg/m 2 ), cyclophosphamide (150-300 mg/m 2), and dexamethasone (40 mg) (CyBorD-DARA) as induction before autologous stem cell transplantation (ASCT), followed by CyBorD-DARA consolidation (2 cycles) and monthly DARA +/- bortezomib (in high-risk disease) maintenance for 24 months. We hypothesized that the addition of cyclophosphamide could lead to enhanced antibody dependent cellular phagocytosis (ADCP). This trial was registered at www.clinicaltrials.gov as NCT02955810. We previously reported the initial results of this study. 1. In addition to a favourable safety profile we observed promising anti-MM activity with 10 of 13 patients (77%) in whom assessment was possible achieving measurable residual disease (MRD) negativity at a sensitivity of 10 -5 by next generation sequencing (NGS) after ASCT. We now report the results at EOT, with a focus on MRD. Eligible patients were ≤70 years of age with untreated transplant-eligible MM. 18 patients were enrolled. Median age was 56.5 years (range, 32-66 years), 61% were male and 94% of patients had Eastern Cooperative Oncology Group performance status ≤1. The International Staging System stages were I, II, and III in 78%, 17%, and 6% of patients, respectively. 29% of patients had high-risk genetic features by fluorescent in situ hybridisation (FISH) or gene expression profiling, including 17p deletion in 12% and t(4;14) and t(14;16) in 6% each. On an ITT basis, the rates of very good partial remission or better (≥VGPR) after ASCT, consolidation and at end of treatment (EOT) (after completion of 24 months of DARA) were 94%, 94% and 81% respectively, and rates of complete response or better (≥CR) were 50%, 63% and 63% respectively. Measurable residual disease (MRD) assessment was possible in 13 patients after induction, ASCT and consolidation, and 10 at EOT. Sustained MRD negativity (ie. MRD negativity after ASCT, consolidation and at EOT) to a level of 10 -5 by NGS was achieved in 33% (ITT). Of 13 patients who remained on study at EOT in VGPR or better, 54% were MRD negative (MRD was unavailable in 23%). 7 patients were MRD negative after both ASCT and consolidation. Of these patients, all evaluable at EOT(6/7) remained MRD negative, with 1 patient unable to undergo MRD assessment due to the COVID-19 pandemic, but remaining in CR. Nausea and diarrhoea occurred in 89% of patients, but were mostly grade 1-2 (Grade ≥3 nausea 17%;diarrhoea 6%). Neutropenia occurred in 44% (Grade ≥3 17%), anaemia in 39% (Grade ≥3 22%), and thrombocytopenia in 33% (Grade ≥3 22%). The rate of neutropenic sepsis was 11%. Infusion-related reactions occurred in 50% (Grade ≥3 6%) and peripheral neuropathy occurred in 33% (Grade ≥3 0%) The most commonly reported serious adverse event (SAE) was sepsis in 22%. One patient developed abnormal liver function tests leading to discontinuation from the trial. CyBorD-DARA induction, consolidation and DARA-maintenance is an effective and well-tolerated IMiD free regimen in transplant-eligible patients with MM. MRD negativity at a level of > 10 -5 after ASCT and consolidation may be predictive of sustained MRD negativity at EOT. References: 1. Naicker SD, et al. Cyclophosphamide alters the tumor cell secretome to potentiate the anti-myeloma activity of daratumumab through augmentation of macrophage-mediated antibody dependent cellular phagocytosis. Oncoimmunology. 2021 Jan 25;10(1):1859263. doi: 10.1080/2162402X.2020.1859263. PMID: 33552684;PMCID: PMC7849715. 2. O'Dwyer M, et al. CyBorD-DARA is potent initial induction for MM and enhances ADCP: initial results of the 16-BCNI-001/CTRIAL-IE 16-02 study. Blood Adv. 2019 Jun 25;3(12):1815-1825. doi: 10.1182/bloodadvances.2019000010. PMID: 31201169;PMCI : PMC6595251. Disclosures: O'Dwyer: ONK Therapeutics: Current Employment, Current equity holder in publicly-traded company, Membership on an entity's Board of Directors or advisory committees;Janssen: Consultancy;Bristol Myers Squibb: Research Funding. Quinn: Takeda: Honoraria. Szegezdi: ONK Therapeutics: Research Funding.