The main purpose of the article is to develop an optimisation pattern for the process of a preventive evacuation of people from flood-risk areas (at the first sign of a flood), aimed at mitigating the negative effects of the flood performed through the application of modern computer tools. It has been assumed that the use of both GIS tools and apps for vehicle traffic modelling (the research includes the use of a method developed by the authors) in emergency procedures implemented in response to a flood may increase the efficiency of the anti-flood campaign (here: the evacuation of residents from flooded areas), and thus, it may also minimise the negative effects of the flooding itself. The article distinguishes 14 stages of research, which were chiefly completed by means of the following methods: distance-based accessibility, cumulative accessibility, the Enhanced Two-Step Floating Catchment Area Method (E2SFCA) and the Two-Step Floating Catchment Area Method (2SFCA), the vehicle routing method, algorithms by Dinitz, Edmonds-Karp, and Ford-Fulkerson, and a comparative method applied to draw a comparison between the actual state of affairs and the optimum condition determined by the aforementioned methods.

We obtain characterizations of non-negative functions on $$[0,+\infty )$$[ 0 , + ∞ ) which preserve some classes of semimetrics. In particular, one of our main results says that for a non-decreasing function $$f:[0,+\infty )\rightarrow [0,+\infty )$$f : [ 0 , + ∞ ) → [ 0 , + ∞ ) the following statements are equivalent: (i) for any semimetric space (X, d), if d satisfies the relaxed polygonal inequality, then so does $$f\circ d$$f ∘ d ; (ii) there exist a constant $$c\geqslant 1$$c ⩾ 1 and a subadditive function $$g:[0,+\infty ) \rightarrow [0,+\infty )$$g : [ 0 , + ∞ ) → [ 0 , + ∞ ) such that $$g^{-1}\left( \{ 0 \} \right) = \{ 0 \}$$g - 1 { 0 } = { 0 } and $$g\leqslant f \leqslant cg$$g ⩽ f ⩽ c g . We also obtain a complete characterization of functions preserving regularity of a semimetric space in the sense of Bessenyei and Páles. Finally, we give another proof of the theorem of Pongsriiam and Termwuttipong on functions transforming metrics into ultrametrics.

The article presents a study into the impact that the COVID-19 pandemic had on the daily mobility of those over 60 residing in small towns in the Lodz Province. The study determines the impact on the trip destination, trip frequency, preferred means of transport, distance and duration of trips, and length of the target activity. To achieve these objectives, a survey was conducted using the CATI technique (Computer Assisted Telephone Interviewing), which comprised 500 residents of small towns in the Lodz Province aged 60+, who were divided into three classes of small towns (by population size). In order to determine the impact of the COVID-19 pandemic on the daily mobility of those over 60, the tools the authors decided to use descriptive statistics and hypothesis testing. Overall, the pandemic was found to have had only a minor impact on the changes in transport behavior of those over 60 in small towns. Only 9% of respondents declared any effect on their daily mobility. The impact mainly involved a reduction in travel time and frequency, primarily among the oldest residents. Since a low level of daily mobility leads to low social activity, especially for the elderly—with a consequent sense of loneliness or even depression-towns should take measures to improve the already poor situation, one that has been further exacerbated by the pandemic.