Random modelling of contagious diseases

Age Dependent Epidemic Modeling of COVID-19 Outbreak in Kuwait, France, and Cameroon

Revisiting the classical model by Ross and Kermack-McKendrick, the Susceptible−Infectious−Recovered (SIR) model used to formalize the COVID-19 epidemic, requires improvements which will be the subject of this article. The heterogeneity in the age of the populations concerned leads to considering models in age groups with specific susceptibilities, which makes the prediction problem more difficult. Basically, there are three age groups of interest which are, respectively, 0−19 years, 20−64 years, and >64 years, but in this article, we only consider two (20−64 years and >64 years) age groups because the group 0−19 years is widely seen as being less infected by the virus since this age group had a low infection rate throughout the pandemic era of this study, especially the countries under consideration. In this article, we proposed a new mathematical age-dependent (Susceptible−Infectious−Goneanewsusceptible−Recovered (SIGR)) model for the COVID-19 outbreak and performed some mathematical analyses by showing the positivity, boundedness, stability, existence, and uniqueness of the solution. We performed numerical simulations of the model with parameters from Kuwait, France, and Cameroon. We discuss the role of these different parameters used in the model; namely, vaccination on the epidemic dynamics. We open a new perspective of improving an age-dependent model and its application to observed data and parameters.

Estimation of Daily Reproduction Numbers during the COVID-19 Outbreak

(1) Background: The estimation of daily reproduction numbers throughout the contagiousness period is rarely considered, and only their sum R0 is calculated to quantify the contagiousness level of an infectious disease. (2) Methods: We provide the equation of the discrete dynamics of the epidemic’s growth and obtain an estimation of the daily reproduction numbers by using a deconvolution technique on a series of new COVID-19 cases. (3) Results: We provide both simulation results and estimations for several countries and waves of the COVID-19 outbreak. (4) Discussion: We discuss the role of noise on the stability of the epidemic’s dynamics. (5) Conclusions: We consider the possibility of improving the estimation of the distribution of daily reproduction numbers during the contagiousness period by taking into account the heterogeneity due to several host age classes.

Application of Optimal Control of Infectious Diseases in a Model-Free Scenario

Optimal control for infectious diseases has received increasing attention over the past few decades. In general, a combination of cost state variables and control effort have been applied as cost indices. Many important results have been reported. Nevertheless, it seems that the interpretation of the optimal control law for an epidemic system has received less attention. In this paper, we have applied Pontryagin's maximum principle to develop an optimal control law to minimize the number of infected individuals and the vaccination rate. We have adopted the compartmental model SIR to test our technique. We have shown that the proposed control law can give some insights to develop a control strategy in a model-free scenario. Numerical examples show a reduction of 50% in the number of infected individuals when compared with constant vaccination. There is not always a prior knowledge of the number of susceptible, infected, and recovered individuals required to formulate and solve the optimal control problem. In a model-free scenario, a strategy based on the analytic function is proposed, where prior knowledge of the scenario is not necessary. This insight can also be useful after the development of a vaccine to COVID-19, since it shows that a fast and general cover of vaccine worldwide can minimize the number of infected, and consequently the number of deaths. The considered approach is capable of eradicating the disease faster than a constant vaccination control method.

Temperature Decreases Spread Parameters of the New Covid-19 Case Dynamics

(1) Background: The virulence of coronavirus diseases due to viruses like SARS-CoV or MERS-CoV decreases in humid and hot weather. The putative temperature dependence of infectivity by the new coronavirus SARS-CoV-2 or covid-19 has a high predictive medical interest. (2) Methods: External temperature and new covid-19 cases in 21 countries and in the French administrative regions were collected from public data. Associations between epidemiological parameters of the new case dynamics and temperature were examined using an ARIMA model. (3) Results: We show that, in the first stages of the epidemic, the velocity of contagion decreases with country- or region-wise temperature. (4) Conclusions: Results indicate that high temperatures diminish initial contagion rates, but seasonal temperature effects at later stages of the epidemy remain questionable. Confinement policies and other eviction rules should account for climatological heterogeneities, in order to adapt the public health decisions to possible geographic or seasonal gradients.

Discrete dynamics of contagious social diseases: Example of obesity

Modeling contagious diseases needs to incorporate information about social networks through which the disease spreads as well as data about demographic and genetic changes in the susceptible population. In this paper, we propose a theoretical framework (conceptualization and formalization) which seeks to model obesity as a process of transformation of one's own body determined by individual (physical and psychological), inter-individual (relational, i.e., relative to the relationship between the individual and others) and socio-cultural (environmental, i.e., relative to the relationship between the individual and his milieu) factors. Individual and inter-individual factors are tied to each other in a socio-cultural context whose impact is notably related to the visibility of anybody being exposed on the public stage in a non-contingent way. The question we are dealing with in this article is whether such kind of social diseases, i.e., depending upon socio-environmental exposure, can be considered as "contagious". In other words, can obesity be propagated from individual to individual or from environmental sources throughout an entire population?