Few techniques of stability analysis for infectious disease employ the compartmental model

The cycle of life includes everything from joy to sorrow to good health to sickness. Most people have had a viral infection at some point in their lives, whether it was a small infections or the flu. It is amazing that a microscopic particle that cannot even be seen under a microscope and cannot even replicate on its own can enter any living creature and use the resources of that life form to create thousands of copies of the virus, some of which can even be fatal to the living species. Understanding the origin, means of prevention, means of control, and attempts at preventative measures are essential in the fight against these illnesses. It is immoral to experiment on infectious diseases, unlike other types of research. On the other hand, mathematical models can reasonably explain how the disease is spreading. This article focuses on few compartmental models and a technique to analyze the infectious disease. The control analysis technique which employ to comprehend how diseases move among the populations and where the controls are required. In this article Routh-Hurwitz criterion is employed to analyze the system of equations

The approximately universal shapes of epidemic curves in the Susceptible-Exposed-Infectious-Recovered (SEIR) model.

Compartmental transmission models have become an invaluable tool to study the dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR) model is known to have an exact semi-analytical solution. In the current study, the approach of Harko et al. (Appl. Math. Comput. 236:184-194, 2014) is generalised to obtain an approximate semi-analytical solution of the Susceptible-Exposed-Infectious-Recovered (SEIR) model. The SEIR model curves have nearly the same shapes as the SIR ones, but with a stretch factor applied to them across time that is related to the ratio of the incubation to infectious periods. This finding implies an approximate characteristic timescale, scaled by this stretch factor, that is universal to all SEIR models, which only depends on the basic reproduction number and initial fraction of the population that is infectious

Flattening the Curve

We quantify flattening the curve under the assumption of a soft quarantine in the spread of a contagious viral disease in a society. In particular, the maximum daily infection rate is expected to drop by twice the percentage drop in the virus reproduction number. The same percentage drop is expected for the maximum daily hospitalization or fatality rate. A formula for the expected maximum daily fatality rate is given

COVID-19 Predictions Using Regression Growth Model in Ireland and Israel

The World Health Organization (WHO) asserted the recently discovered severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), also known as COVID-19, a pandemic on March 11, 2020. Since the genesis and growth mechanisms of this virus are unclear and impossible to detect, there are still many uncertainties concerning it and no vaccination or effective treatment. The main goal is to halt its global spread. This paper employed a regression growth model with an extended Weibull function on the dynamics of COVID-19 to make predictions about its spread. Our findings demonstrate the viability of using this model to forecast the spread of the virus. Using a logistic growth regression model, the note tabulates the COVID-19-related final epidemic sizes for a few sites, including Ireland and Israel

Spread of infection on homogeneous tree

This paper concerns a probabilistic model of spread of infection on a homogeneous tree. The model is related to stochastic SIR model on graphs. We derive an integral equation for the distribution of the waiting time for an individual to get infected. In a special case the integral equation is equivalent to the Bernoulli differential equation and implies the classic SIR model under an appropriate scaling

How to reduce epidemic peaks keeping under control the time-span of the epidemic

One of the main challenges of the measures against the COVID-19 epidemic is to reduce the amplitude of the epidemic peak without increasing without control its timescale. We investigate this problem using the SIR model for the epidemic dynamics, for which reduction of the epidemic peak $I_P$ can be achieved only at the price of increasing the time $t_P$ of its occurrence and its entire time-span $t_E$. By means of a time reparametrization we linearize the equations for the SIR dynamics. This allows us to solve exactly the dynamics in the time domain and to derive the scaling behaviour of the size, the timescale and the speed of the epidemics, by reducing the infection rate $\alpha$ and by increasing the removal rate $\beta$ by a factor of $\lambda$. We show that for a given value of the size ($I_P$, the total, $I_E$ and average $\hat I_P$ number of infected), its occurrence time $t_P$ and entire time-span $t_E$ can be reduced by a factor $1/\lambda$ if the reduction of $I$ is achieved by increasing the removal rate instead of reducing the infection rate. Thus, epidemic containment measures based on tracing, early detection followed by prompt isolation of infected individuals are more efficient than those based on social distancing. We apply our results to the COVID-19 epidemic in Northern Italy. We show that the peak time $t_P$ and the entire time span $t_E$ could have been reduced by a factor $0.9 \le 1/\lambda\le 0.34$ with containment measures focused on increasing $\beta$ instead of reducing $\alpha$.Comment: 9 pages, no figure