A robust phenomenological approach to investigate COVID-19 data for France

We provide a new method to analyze the COVID-19 cumulative reported cases data based on a two-step process: first we regularize the data by using a phenomenological model which takes into account the endemic or epidemic nature of the time period, then we use a mathematical model which reproduces the epidemic exactly. This allows us to derive new information on the epidemic parameters and to compute the effective basic reproductive ratio on a daily basis. Our method has the advantage of identifying robust trends in the number of new infectious cases and produces an extremely smooth reconstruction of the epidemic. The number of parameters required by the method is parsimonious: for the French epidemic between February 2020 and January 2021 we use only 11 parameters in total.

The COVID-19 basic reproductive ratio using SEIR model for the Middle East countries and some other countries for two stages of the disease

Background The new coronavirus disease appeared at the end of 2019, and it is now a global problem over the world. There are multiple epidemiologic indicators used for discussing the spread of pandemics, one of these indicators is the basic reproductive ratio which indicates whether the pandemic is going to spread more or relax, and the aim of this work is estimating this ratio for the Middle East countries for two stages of the pandemic. Main body of the abstract We employ Runge–Kutta method on SEIR model to simulate the basic reproductive ratio values of SARS-CoV-2 disease by using the recorded data of the disease for two stages, up to date May 29, 2020, in the first stage and up to date September 7, 2020, in the second stage. We estimate the coefficient of exposing rate, the coefficient of infection rate, the coefficient of recovery rate and the coefficient of mortality rate of the new coronavirus disease in addition to the basic reproductive ratio values of the disease in the Middle East countries, namely Bahrain, Cyprus, Egypt, Iran, Iraq, Jordan, Kuwait, Lebanon, Oman, Qatar, Saudi Arabia, the Syrian Arab Republic, the United Arab Emirates, Turkey and Yemen where we apply the SEIR epidemic model. Short conclusion We find that the values of the basic reproductive ratio of the new coronavirus disease based on the used model in the Middle East countries start from 1.5583 to 3.0395 in the first stage and from 1.0001 to 4.5757. Besides, we find that the problem of the new coronavirus disease in Lebanon and in the Syrian Arab Republic is not good at all in the recent stage based on the values of the basic reproductive ratio comparing with other Middle East countries. Also, we find that the value of the basic reproductive ratio for the second stage is near one; however, if we apply the method for the following stages, we find that the values return to be larger because lots of people in that stage and after did not follow the governmental procedures for stopping the spreading of the disease.

On the effect of postponing pregnancy in a Zika transmission model

We construct a Zika transmission model to investigate the effect of postponing pregnancy on the infection intensity. We perform analytical and numerical investigations for deterministic and stochastic analysis to obtain the basic reproductive ratio, endemic state, probability of disease extinction, and the probability of outbreak. The results indicate that by reducing the pregnancy rate the mosquito-to-human ratio increases, and, consequently, the basic reproductive ratio increases. Simultaneously, the probability of disease extinction decreases, and the probability of disease outbreak increases. On the other hand, the endemic state of infected infants initially increases with the decrease of the pregnancy recruitment rate, up to a certain level, and decreases as the recruitment rate of pregnancy tends to zero. This work highlights that postponing pregnancy that gives the individual temporary protection for unexpected infected newborns may increase the population infectivity.

A robust phenomenological approach to investigate COVID-19 data for France

We provide a new method to analyze the COVID-19 cumulative reported cases data based on a two-step process: first we regularize the data by using a phenomenological model which takes into account the endemic or epidemic nature of the time period, then we use a mathematical model which reproduces the epidemic exactly. This allows us to derive new information on the epidemic parameters and to compute the effective basic reproductive ratio on a daily basis. Our method has the advantage of identifying robust trends in the number of new infectious cases and produces an extremely smooth reconstruction of the epidemic. The number of parameters required by the method is parsimonious: for the French epidemic between February 2020 and January 2021 we use only 11 parameters in total.

On the global attractors in one mathematical model of antiviral immunity

We consider the mathematical model introduced by Batholdy et al. [1] describing the interaction between viral pathogens and immune system. We prove the global asymptotic stability of the infection steady-state if the basic reproductive ratio R0 is greater than unity. That solves the conjecture announced in [7].

Susceptible-Infected-Susceptible Epidemic Discrete Dynamic System Based on Tsallis Entropy

This investigation deals with a discrete dynamic system of susceptible-infected-susceptible epidemic (SISE) using the Tsallis entropy. We investigate the positive and maximal solutions of the system. Stability and equilibrium are studied. Moreover, based on the Tsallis entropy, we shall formulate a new design for the basic reproductive ratio. Finally, we apply the results on live data regarding COVID-19.

Estimation of country-level basic reproductive ratios for novel Coronavirus (COVID-19) using synthetic contact matrices

The outbreak of novel coronavirus (COVID-19) has the potential for global spread, infecting large numbers in all countries. In this case, estimating the country-specific basic reproductive ratio is a vital first step in public-health planning. The basic reproductive ratio (R0) is determined by both the nature of pathogen and the network of contacts through which the disease can spread - with this network determined by socio-demographics including age-structure and household composition. Here we focus on the age-structured transmission within the population, using data from China to inform age-dependent susceptibility and synthetic age-mixing matrices to inform the contact network. This allows us to determine the country-specific basic reproductive ratio as a multiplicative scaling of the value from China. We predict that R0 will be highest across Eastern Europe and Japan, and lowest across Africa, Central America and South-Western Asia. This pattern is largely driven by the ratio of children to older adults in each country and the observed propensity of clinical cases in the elderly.