a b s t r a c tIn this paper, we show that under suitable simple assumptions the classical two populations system may exhibit unexpected behaviors. Considering a more elaborated social model, in which the individuals of one population gather together in herds, while the other one shows a more individualistic behavior, we model the fact that interactions among the two occur mainly through the perimeter of the herd. We account for all types of populations' interactions, symbiosis, competition and the predator-prey interactions. There is a situation in which competitive exclusion does not hold: the socialized herd behavior prevents the competing individualistic population from becoming extinct. For the predator-prey case, sustained limit cycles are possible, the existence of Hopf bifurcations representing a distinctive feature of this model compared with other classical predator-prey models. The system's behavior is fully captured by just one suitably introduced new threshold parameter, defined in terms of the original model parameters.

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The dynamics of interacting ecological populations results from the interplay between various deterministic and stochastic factors and this is particularly the case for the phenomenon of biological invasion. Whereas the spread of invasive species via propagation of a population front was shown to appear as a result of deterministic processes, the spread via formation, interaction and movement of separate patches has been recently attributed to the influence of environmental stochasticity. An appropriate understanding of the comparative importance of deterministic and stochastic mechanisms is still lacking, however. In this paper, we show that the patchy invasion appears to be possible also in a fully deterministic predator-prey model as a result of the Allee effect.

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Objectives We performed data collection concerning the coronavirus disease 2019 (COVID-19) pandemic-related delay in the diagnosis of cancers to individuate proper corrective procedures. Methods A comparison was made among the number of first pathologic diagnoses of malignancy made from weeks 11 to 20 of 2018, 2019, and 2020 at seven anatomic pathology units serving secondary care hospitals in northern-central Italy. Results Cancer diagnoses fell in 2020 by 44.9% compared with the average number recorded in 2018 and 2019. Melanoma and nonmelanoma skin cancer represented 56.7% of all missing diagnoses. The diagnostic decrease in colorectal (–46.6%), prostate (–45%), and bladder (–43.6%) cancer was the most relevant among internal malignancies; for prostate, however, high-grade tumors were only moderately affected (–21.7%). Conclusions Diagnosis of cutaneous malignancies was mostly affected by the lockdown; among internal malignancies, corrective actions were mostly needed for colorectal cancer and invasive bladder cancer.

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In this paper, we propose a mathematical model to assess the impact of social media advertisements in combating the coronavirus pandemic in India. We assume that dissemination of awareness among susceptible individuals modifies public attitudes and behaviours towards this contagious disease which results in reducing the chance of contact with the coronavirus and hence decreasing the disease transmission. Moreover, the individual’s behavioral response in the presence of global information campaigns accelerate the rate of hospitalization of symptomatic individuals and also encourage the asymptomatic individuals for conducting health protocols, such as self-isolation, social distancing, etc. We calibrate the proposed model with the cumulative confirmed COVID-19 cases for the Republic of India. We estimate eight epidemiologically important parameters, and also the size of basic reproduction number for India. We find that the basic reproduction number for India is greater than unity, which represents the substantial outbreak of COVID-19 in the country. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected population. Our results reveal that to reduce disease burden in India, non-pharmaceutical interventions strategies should be implemented effectively to decrease basic reproduction number below unity. Continuous propagation of awareness through the internet and social media platforms should be regularly circulated by the health authorities/government officials for hospitalization of symptomatic individuals and quarantine of asymptomatic individuals to control the prevalence of disease in India.