Mathematical modeling of the epidemic propagation with limited time spent in compartments taking and vaccination

Abstract

The paper proposes discrete and continuous mathematical models of epidemic development. A division of the population into nine compartments is suggested: susceptible, exposed, vaccinated, contact vaccinated, undetected patients, isolated patients, hospitalized patients, recovered and deceased. At the same time, the time spent in exposed and infected compartments is considered limited. According to the assumptions made in the models, a susceptible person can encounter the patient and go into the exposed compartment, and be vaccinated, and then also encounter the infection and go into the contact vaccinated compartment. Exposed people may become ill to any degree of severity or not, returning to the susceptible group. A contact vaccinated either does not become ill or becomes undetected or isolated patient. Every patient can recover. An undiagnosed patient may develop symptoms of the disease, because of which he moves into the isolated compartment. An isolated patient may be hospitalized, and a hospitalized patient may die. In the discrete model, discrete quantitative data for each day of the epidemic are considered, in the continuous one, these indicators are considered continuous functions. The article provides a qualitative and quantitative analysis of the proposed models. The influence of all parameters on the process under study is investigated.

Keywords

• mathematical model
• epidemic
• vaccination