epidemiology

Viable control of COVID-19 spread with vaccination

The rapid and widespread transmission of COVID-19 has necessitated the development and implementation of effective control measures.  Vaccination has emerged as a key tool in combating the pandemic.  This article introduces a novel approach to modeling the dynamics of COVID-19 transmission by integrating vaccination strategies into the susceptible-infected-recovered (SIR) framework using viability theory.  We have defined a set of constraints including a guaranteed level of vaccination, we analyze the impact of different vaccination rates on curbing the spread of the vi

Modeling of the COVID-19 pandemic in the limit of no acquired immunity

We propose the SEIRS compartmental epidemiology model aimed at modeling the COVID-19 pandemy dynamics.  The limit case of no acquired immunity (neither natural nor via vaccination) is considered mimicking the situation (i) when no effective vaccine being developed or available yet, and (ii) the virus strongly mutates causing massive reinfections.  Therefore, the only means of suppressing the virus spread are via quarantine measures and effective identification and isolation of infected individuals.  We found both the disease-free and the endemic fixed points and examined their stab

Simple epidemiology model for a non-immune disease with ordinary and resistant carriers

We consider the compartmental model for the non-immune disease with both ordinary and resistant carriers. The same infecting rate $\beta$ is assumed for both types of carriers, whereas the curing rates $\gamma$ and  $\gamma'$ for the ordinary and resistant carriers, respectively, are different. The conversion from an ordinary into resistant carrier takes place with the rate $\delta$. The stationary states for the model are evaluated and rewritten in a compact form using two reduced parameters that are combinations of initial four rates.

Computer simulations of a stochastic model for the non-immune disease spread

We present a model of the non-immune disease spread, as well as an algorithmic approach and the corresponding results of its study by computer simulations. The model is a generalization of the SIS model with the uniform two-dimensional spatial distribution of individuals undergoing a Markov-type evolution with discrete time.