On 11 March 2020, coronavirus disease 2019 (COVID-19) was declared a pandemic by the World Health Organization (WHO). As of 12.44 GMT on 15 January 2021, it has produced 93,640,296 cases and 2,004,984 deaths. The use of mathematical modelling was applied in Italy, Spain, and UK to help in the prediction of this pandemic. We used equations from general and reduced logistic models to describe the epidemic development phenomenon and the trend over time. We extracted this information from the Italian Ministry of Health, the Spanish Ministry of Health, Consumer Affairs, and Social Welfare, and the UK Statistics Authority from 3 February to 30 April 2020. We estimated that, from the seriousness of the phenomenon, the consequent pathology, and the lethal outcomes, the COVID-19 trend relate to the same classic laws that govern epidemics and their evolution. The curve d(t) helps to obtain information on the duration of the epidemic phenomenon, as its evolution is related to the efficiency and timeliness of the system, control, diagnosis, and treatment. In fact, the analysis of this curve, after acquiring the data of the first three weeks, also favors the advantage to formulate forecast hypotheses on the progress of the epidemic.

When an epidemic breaks out, many health, economic, social, and political problems arise that require a prompt and effective solution. It would be useful to obtain all information about the virus, including epidemiological ones, as soon as possible. In a previous study of our group, the analysis of the positive-alive was proposed to estimate the epidemic duration. It was stated that every epidemic ends when the number of positive-alive (=infected-healed-dead) glides toward zero. In fact, if with the contagion everyone can enter the epidemic phenomenon, only by healing or dying can they get out of it. In this work, a different biomathematical model is proposed. A necessary condition for the epidemic to be resolved is that the mortality reaches the asymptotic value, from there, remains stable. At that time, the number of positive-alive must also be close to zero. This model seems to allow us to interpret the entire development of the epidemic and highlight its phases. It is also more appropriate than the previous one, especially when the spread of the infection is so rapid that the increase in live positives is staggering.

Nowadays, obesity is a pandemic, and some people seek slimming diets to guarantee their health and quality of life. However, the cult of the healthy body has been an ongoing concern since the beginning of time. Irrespective of the century to which they belong, these cults reflect no empirical knowledge about physiology, nutrients or kilocalories, with some of them being quantitative diets in contrast to qualitative diets, or even simple food recommendations. On the other hand, some of these treatments might have led to the death of a patient, meaning that it is important for people seeking to lose weight to be followed by a nutrition professional until the individual reaches a desirable body weight. In this article, we highlight that each century and each decade have devised different treatments with the aim of improving health, but it will be science and history that will judge whether the results of these treatments have been adequate.

Nowadays, slimming diet methodology works within a reduction of body mass using a decrease of dietary energy intake. However, there is no suitable method for understanding the dynamic process of body mass metabolic transformation over time. In the present paper, we have developed a biomathematic model to explain the temporal trend of body mass and its variations of people who have undergone a change in their diet using the solving equation of the model. Data relating to sex, age, body mass, and BMI were collected, and the compartmental model used to interpret the body mass trends was constructed by assuming that the mass results from the sum of the metabolic processes: catabolic, anabolic, distributive. The validation of the model was carried out by variance analysis both on the total and individual data sets. The results confirm that the trend of body mass and its variations over time depends on metabolic rates. These are specific to each individual and characterize the distribution of nutritional molecules in the various body districts and the processes catabolic, anabolic, distributive. Body mass and its variations are justified by the metabolic transformations of the nutritional quantities. This would explain why energetically equal diets can correspond to people of different body mass and that energy-different diets can correspond to people of body mass at all similar.

Lately, we've witnessed the emergence of obesity as a prominent concern for public health and the economy. This issue commands serious attention, impacting millions worldwide, particularly in the most developed nations. Practical approaches to tackling obesity involve tailored physical activity and dietary interventions overseen by qualified healthcare professionals. Nonetheless, some individuals opt for quicker routes, embracing dietary regimens that promise rapid and effortless weight reduction yet lack substantiated scientific backing. Given the potential hazards these approaches pose to well-being, this calls for immediate address, occasionally leading to unexpected and severe consequences. In this review, we aim to analyze the curiosities of popular diets embraced by adults from the 1960s to the present day, including the scientific justification that supports or contradicts their effectiveness.