On stiff, fuzzy IRD-14 day average transmission model of COVID-19 pandemic disease

Abstract

COVID-19, a new pandemic disease is becoming one of the major threats for surviving. Many new models are arrived to study the disease mathematically. Here we are introducing a new model in which instead of studying a day by day changes we are studying the average of 14 day transmission because its life or the patients incubation period is about an average of 14 days. Also, since this is pandemic, and being not aware of susceptible population among the world’s population, we considered the model without S-susceptible population. i.e., IRD- Infectious, Recovered, Death- model. In this new model, we are also introducing a new method of calculating new number called N 0 -average transmission number. This is used to study the average spread of infection instead of basic reproduction number R 0 . The motto of this paper is not to predict the daily cases but to control the current spread of disease and deaths by identifying the threshold number, exceeding which will increase the spread of infection and number of deaths due to this pandemic. Also if the 14 day average IRD-populations are maintained under this threshold number, will definitely control this pandemic disease globally. Stability analysis and test for stiff system of differential equations are studied. Our main aim is to present the medical world, a threshold population of infected, recovered and death cases for every average of 14 days to quickly overcome this pandemic disease COVID-19.

Keywords

• covid-19
• equilibrium points
• stability analysis
• basic reproduction number
• average transmission number
• ird-model
• fuzzy differential equations
• stiff differential equations
• threshold population