A nonstandard finite difference scheme for the SVICDR model to predict COVID-19 dynamics.

In the context of 2019 coronavirus disease (COVID-19), considerable attention has been paid to mathematical models for predicting country- or region-specific future pandemic developments. In this work, we developed an SVICDR model that includes a susceptible, an all-or-nothing vaccinated, an infected, an intensive care, a deceased, and a recovered compartment. It is based on the susceptible-infectious-recovered (SIR) model of Kermack and McKendrick, which is based on ordinary differential equations (ODEs). The main objective is to show the impact of parameter boundary modifications on the predicted incidence rate, taking into account recent data on Germany in the pandemic, an exponential increasing vaccination rate in the considered time window and trigonometric contact and quarantine rate functions. For the numerical solution of the ODE systems a model-specific non-standard finite difference (NSFD) scheme is designed, that preserves the positivity of solutions and yields the correct asymptotic behaviour.

Compartment models for vaccine effectiveness and non-specific effects for Tuberculosis.

In this paper, we attempt to set a framework of conditions for model-specific predictions of newly arising TB epidemics by e.g. immigration of infected persons from high prevalence countries. In addition, we address the aspect of trained immunity in our model. Using a mathematical approach of a system of ordinary differential equations which can be developed over several time-points we obtained varying infection or attack rates that led to different effects of the vaccination, depending on the setting of certain parameters and starting values in the compartments of a SEIR-model. We finally obtained different graphs of disease progression and were able to outline which upgrades and expansions our system requires in order to be exact and well adapted for predicting the course of future TB outbreaks. The model might also be beneficial in predicting non-specific effects of vaccines.

Model for simulation of HIV/AIDS and cost-effectiveness of preventing non-tuberculous mycobacterial (MAC)-disease.

Because most HIV-infected patients die of diseases caused by opportunistic pathogens, the prevention of these infections is an important clinical issue. Cost-containment in the healthcare system is a subject of high priority in public debate. Methods to determine cost-effectiveness of different therapeutic strategies are therefore needed to obtain valid data as the basis for decisions on cost reduction without a decrease in the quality of care. A disease state transition model based on a Markov process was developed to simulate the natural history of HIV infection and the acquired immunodeficiency syndrome (AIDS). Using this model survival time and treatment costs for every patient can be estimated and the results of alternative medications compared. We determined the cost-effectiveness (per life-year saved, LYS) of different strategies for prevention of Mycobacterium avium complex infections in AIDS patients whose treatment regimens include protease inhibitors. The cost-effectiveness ratios for treatment strategies vary from 13,510 euro to 46,152 euro per LYS without protease inhibitors and from 22,309 euro to 51,336 euro with protease inhibitors. When azithromycin, clarithromycin, and rifabutin were compared, azithromycin was the most cost-effective medication for preventing M. avium complex. The results were stable against a wide range of parameter variations concerning costs and incidence rates.

Economic evaluations of granulocyte colony-stimulating factor: in the prevention and treatment of chemotherapy-induced neutropenia.

The prevailing uncertainty about the pharmacoeconomic positioning of granulocyte colony-stimulating factor (G-CSF) in the prevention and treatment of chemotherapy-induced febrile neutropenia has resulted in a number of pharmacoeconomic evaluations published in the past 10 years. These studies vary considerably regarding the approaches used and the results presented. In order to contribute to a clearer pharmacoeconomic positioning of G-CSF, a systematic review of economic evaluations was carried out. The focus of the review was prophylaxis and therapy of chemotherapy-induced neutropenia in patients with cancer. A computerised bibliography search of several databases was conducted yielding 33 studies. The findings demonstrated the cost-saving potential of G-CSF in standard-dose chemotherapy to be limited, with lower costs often seen in the control group. The results of these studies were too heterogeneous to extract a clear recommendation from a cost-saving point of view. The administration of G-CSF after high-dose chemotherapy with stem cell support resulted more often in cost savings in the G-CSF group as compared with standard-dose chemotherapy, illustrating a possible cost-saving potential of G-CSF. In the treatment of established chemotherapy-induced febrile neutropenia, cost savings were found in all studies. This result is surprising but hampered by the small number of studies (n = 5) and remains to be confirmed by more rigourously designed prospective economic analyses. Despite the substantial research on this topic, the economic evaluation of G-CSF is far from being settled and needs further investigation.