Dynamics of Feline Coronavirus and FIP: A Compartmental Modeling Approach.

The investigation of infectious agents invading human and nonhuman populations represents a rich research domain within the framework of mathematical biology, captivating the interest of scientists across various disciplines. In this work, we examine the endemic equilibrium of feline coronavirus and feline infectious peritonitis by using a modified susceptible-infected-susceptible epidemiological model. We incorporate the concept of mutations from FCoV to FIP to enrich our analysis. We establish that the model, when subjected to reasonable parameter ranges, supports an endemic equilibrium wherein the FCoV group dominates. To demonstrate the stability of the equilibria under typical parameters and initial conditions, we employ the model SCF presented by Dobie in 2022 (Dobie, 2022). We ascertain that the equilibrium values reside within the interior domains of stability. Additionally, we displayed perturbed solutions to enhance our understanding. Remarkably, our findings align qualitatively with existing literature, which reports the prevalence of seropositivity to FCoV among stray cats (Tekelioglu et al. 2015, Oguzoglu et al. 2010, Pratelli 2008, Arshad et al. 2004).

What Can We Estimate From Fatality and Infectious Case Data Using the Susceptible-Infected-Removed (SIR) Model? A Case Study of Covid-19 Pandemic.

The rapidly spreading Covid-19 that affected almost all countries, was first reported at the end of 2019. As a consequence of its highly infectious nature, countries all over the world have imposed extremely strict measures to control its spread. Since the earliest stages of this major pandemic, academics have done a huge amount of research in order to understand the disease, develop medication, vaccines and tests, and model its spread. Among these studies, a great deal of effort has been invested in the estimation of epidemic parameters in the early stage, for the countries affected by Covid-19, hence to predict the course of the epidemic but the variability of the controls over the course of the epidemic complicated the modeling processes. In this article, the determination of the basic reproduction number, the mean duration of the infectious period, the estimation of the timing of the peak of the epidemic wave is discussed using early phase data. Daily case reports and daily fatalities for China, South Korea, France, Germany, Italy, Spain, Iran, Turkey, the United Kingdom and the United States over the period January 22, 2020-April 18, 2020 are evaluated using the Susceptible-Infected-Removed (SIR) model. For each country, the SIR models fitting cumulative infective case data within 5% error are analyzed. It is observed that the basic reproduction number and the mean duration of the infectious period can be estimated only in cases where the spread of the epidemic is over (for China and South Korea in the present case). Nevertheless, it is shown that the timing of the maximum and timings of the inflection points of the proportion of infected individuals can be robustly estimated from the normalized data. The validation of the estimates by comparing the predictions with actual data has shown that the predictions were realized for all countries except USA, as long as lock-down measures were retained.

An Overview of the 2009 A(H1N1) Pandemic in Europe: Efficiency of the Vaccination and Healthcare Strategies.

2009 A(H1N1) data for 13 European countries obtained from the weekly influenza surveillance overview (WISO) reports of European Centre for Disease Prevention and Control (ECDC) in the form of weekly cumulative fatalities are analyzed. The variability of relative fatalities is explained by the health index of analyzed countries. Vaccination and healthcare practices as reported in the literature are used to explain the departures from this model. The timing of the vaccination with respect to the peak of the epidemic and its role in the efficiency of the vaccination is discussed. Simulations are used to show that on-time vaccination reduces considerably the final value of R( t), R f , but it has little effect on the shape of normalized curve R( t)/ R f .

On the uniqueness of epidemic models fitting a normalized curve of removed individuals.

The susceptible-infected-removed (SIR) and the susceptible-exposed-infected-removed (SEIR) epidemic models with constant parameters are adequate for describing the time evolution of seasonal diseases for which available data usually consist of fatality reports. The problems associated with the determination of system parameters starts with the inference of the number of removed individuals from fatality data, because the infection to death period may depend on health care factors. Then, one encounters numerical sensitivity problems for the determination of the system parameters from a correct but noisy representative of the number of removed individuals. Finally as the available data is necessarily a normalized one, the models fitting this data may not be unique. We prove that the parameters of the (SEIR) model cannot be determined from the knowledge of a normalized curve of "Removed" individuals and we show that the proportion of removed individuals, [Formula: see text], is invariant under the interchange of the incubation and infection periods and corresponding scalings of the contact rate. On the other hand we prove that the SIR model fitting a normalized curve of removed individuals is unique and we give an implicit relation for the system parameters in terms of the values of [Formula: see text] and [Formula: see text], where [Formula: see text] is the steady state value of [Formula: see text] and [Formula: see text] and [Formula: see text] are the values of [Formula: see text] and its derivative at the inflection point [Formula: see text] of [Formula: see text]. We use these implicit relations to provide a robust method for the estimation of the system parameters and we apply this procedure to the fatality data for the H1N1 epidemic in the Czech Republic during 2009. We finally discuss the inference of the number of removed individuals from observational data, using a clinical survey conducted at major hospitals in Istanbul, Turkey, during 2009 H1N1 epidemic.