Computer simulation of the dynamics of a spatial susceptible-infected-recovered epidemic model with time delays in transmission and treatment

Dynamics of a diffusive model for cancer stem cells with time delay in microRNA-differentiated cancer cell interactions and radiotherapy effects

Understand the dynamics of cancer stem cells (CSCs), prevent the non-recurrence of cancers and develop therapeutic strategies to destroy both cancer cells and CSCs remain a challenge topic. In this paper, we study both analytically and numerically the dynamics of CSCs under radiotherapy effects. The dynamical model takes into account the diffusion of cells, the de-differentiation (or plasticity) mechanism of differentiated cancer cells (DCs) and the time delay on the interaction between microRNAs molecules (microRNAs) with DCs. The stability of the model system is studied by using a Hopf bifurcation analysis. We mainly investigate on the critical time delay τ c , that represents the time for DCs to transform into CSCs after the interaction of microRNAs with DCs. Using the system parameters, we calculate the value of τ c for prostate, lung and breast cancers. To confirm the analytical predictions, the numerical simulations are performed and show the formation of spatiotemporal circular patterns. Such patterns have been found as promising diagnostic and therapeutic value in management of cancer and various diseases. The radiotherapy is applied in the particular case of prostate model. We calculate the optimum dose of radiation and determine the probability of avoiding local cancer recurrence after radiotherapy treatment. We find numerically a complete eradication of patterns when the radiotherapy is applied before a time t < τ c . This scenario induces microRNAs to act as suppressors as experimentally observed in prostate cancer. The results obtained in this paper will provide a better concept for the clinicians and oncologists to understand the complex dynamics of CSCs and to design more efficacious therapeutic strategies to prevent the non-recurrence of cancers.

Dynamics of a cross-superdiffusive SIRS model with delay effects in transmission and treatment

We investigate the dynamics of a SIRS epidemiological model taking into account cross-superdiffusion and delays in transmission, Beddington-DeAngelis incidence rate and Holling type II treatment. The superdiffusion is induced by inter-country and inter-urban exchange. The linear stability analysis for the steady-state solutions is performed, and the basic reproductive number is calculated. The sensitivity analysis of the basic reproductive number is presented, and we show that some parameters strongly influence the dynamics of the system. A bifurcation analysis to determine the direction and stability of the model is carried out using the normal form and center manifold theorem. The results reveal a proportionality between the transmission delay and the diffusion rate. The numerical results show the formation of patterns in the model, and their epidemiological implications are discussed.

Theoretically quantifying the direct and indirect benefits of vaccination against SARS-CoV-2 in terms of avoided deaths

The Coronavirus Disease 2019 (COVID)-19 pandemic has placed unprecedented pressures on societies around the world. Successful vaccines, developed against the spike protein of the Severe Acute Respiratory Syndrome Virus 2 (SARS-CoV-2) virus, offer hope that new hospitalisations and new deaths will subside. However, vaccination takes place in a dynamic environment. For example, new variants of the disease may occur where the effectiveness of a vaccine lies below that of the original target of the vaccine, while changes in the behaviour of a population are accompanied by a changed basic reproduction number. Here, we aim to understand how changes in values of basic parameters affect the benefits of vaccination at the direct level, of the individuals vaccinated, and at the indirect level, of the wider, unvaccinated community. We work within the framework of a Susceptible-Infected-Recovered model, and produce a metric for the benefits of vaccination, at both direct and indirect levels, in terms of the number of avoided deaths. Taking into account the initial prevalence of a SARS-CoV-2 infection, the mortality rate of the disease, the basic reproduction number, the vaccination rate, and the effectiveness of a vaccine, we explore how these basic parameters affect the benefits of vaccination. We find a range of situations where indirect benefits of vaccination outweigh direct benefits. This especially occurs at lower rates of vaccination (20% – \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$40\%$$\end{document}40%) and intermediate values of the basic reproduction number (1–1.5). The indirect benefits can be substantial, in some cases being more than 400% of the direct benefits. For an initial prevalence of SARS-CoV-2 infection of 2%, a basic reproduction number of 1.2, a mortality rate of 2%, and a vaccine effectiveness of 95%, our findings show, for a population of 500,000 people, where 100,000 susceptible individuals are vaccinated, that approximately 2200 deaths are avoided. However, approximately 600 of these deaths are avoided amongst vaccinated individuals, while approximately 1600 deaths are avoided in the wider, unvaccinated community.