Mario Villalobos-Arias
In this work, a proposal to forecast the populations using generalized logistics regression curve fitting is presented. This type of curve is used to study population growth, in this case population of people infected with the Covid-19 virus; and it can also be used to approximate the survival curve used in actuarial and similar studies.
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In this work, a proposal for the estimation of the populations using logistic curve fitting is presented. This type of curve is used to study population growth, in this case population of people infected with the Covid-19 virus; and it can also be used to approximate the survival curve used in actuarial and similar studies in Spanish: En este trabajos se presenta una propuesta para la estimación de la poblaciones usando ajuste de curvas del tipo logística. Este tipo de curvas se utilizan para el estudio de crecimiento de poblaciones, en este casos población de personas infectadas por el virus …
This work covers the analysis of the COVID 19 spread in different countries and dealing the main feature of COVID 19 growth, which is the spread due to the social-contact structure, which is governed by the parameter \b{eta}. The dependency of this parameter \b{eta} on the transmission level in society gives a sense of the effectiveness of the measures taken for social distancing. A separate algorithm is hardcoded in python using Scipy which learns the social-contact structure and gives a suitable value for \b{eta}, which has a major impact on the outcome of the result. Forecasting for the epi…
I estimate the Susceptible-Infected-Recovered (SIR) epidemic model for Coronavirus Disease 2019 (COVID-19). The transmission rate is heterogeneous across countries and far exceeds the recovery rate, which enables a fast spread. In the benchmark model, 28% of the population may be simultaneously infected at the peak, potentially overwhelming the healthcare system. The peak reduces to 6.2% under the optimal mitigation policy that controls the timing and intensity of social distancing. A stylized asset pricing model suggests that the stock price temporarily decreases by 50% in the benchmark case …
Due to modern transportation networks (airplanes, cruise ships, etc.) an epidemic in a given country or city may be triggered by the arrival of external infected agents. Posterior government quarantine policies are usually taken in order to control the epidemic growth. We formulate a minimal epidemic evolution model that takes into account these components. The previous and posterior evolutions to the quarantine policy are modeled in a separate way by considering different complexities parameters in each stage. Application of this model to COVID-19 data in different countries is implemented. E…
We report a statistical analysis of some highly infected countries by the novel coronavirus (COVID-19). The cumulative infected data were fitted with various growth models (e.g. Logistic equation, Weibull equation and Hill equation) and obtained the power index of top ten highly infected countries. The newly infected data were fitted with Gaussian distribution with the peak at ~40 days for the countries whose infection curves are seem to be saturated. The similarity in growth kinetics of infected people of different countries provides first-hand guidelines to take proper precautions to minimiz…
We study the increases of infections and deaths in Sweden caused by COVID-19 with several different models: Firstly an analytical susceptible-infected (SI) model and the standard susceptible-infected-recovered (SIR) model. Then within the SIR framework we study the susceptible-infected-deceased (SID) correlations. All models reproduce well the number of infected cases and give similar predictions. What causes us deep concern is the large number of deaths projected by the SI and SID models. Our analysis shows that, irrespective of the possible uncertainty of our model prediction, the next few d…
We have studied the dynamic evolution of the Covid-19 pandemic in Argentina. The marked heterogeneity in population density and the very extensive geography of the country becomes a challenge itself. Standard compartment models fail when they are implemented in the Argentina case. We extended a previous successful model to describe the geographical spread of the AH1N1 influenza epidemic of 2009 in two essential ways: we added a stochastic local mobility mechanism, and we introduced a new compartment in order to take into account the isolation of infected asymptomatic detected people. Two funda…
The SIQR model is reformulated where compartments for infected and quarantined are redefined so as to be appropriate to COVID-19, and exact properties of the model are presented. It is shown that the maximum number of infected at large depends strongly on the quarantine rate and that the quarantine measure is more effective than the lockdown measure in controlling the pandemic. The peak of the number of quarantined patients is shown to appear some time later than the time that the number of infected becomes maximum. On the basis of the expected utility theory, a theoretical framework to find o…
We apply optimal control theory to a generalized SEIR-type model. The proposed system has three controls, representing social distancing, preventive means, and treatment measures to combat the spread of the COVID-19 pandemic. We analyze such optimal control problem with respect to real data transmission in Italy. Our results show the appropriateness of the model, in particular with respect to the number of quarantined/hospitalized (confirmed and infected) and recovered individuals. Considering the Pontryagin controls, we show how in a perfect world one could have drastically diminish the numbe…
The COVID-19 pandemic has had worldwide devastating effects on human lives, highlighting the need for tools to predict its development. Dynamics of such public-health threats can often be efficiently analysed through simple models that help to make quantitative timely policy decisions. We benchmark a minimal version of a Susceptible-Infected-Removed model for infectious diseases (SIR) coupled with a simple least-squares Statistical Heuristic Regression (SHR) based on a lognormal distribution. We derived the three free parameters for both models in several cases and tested them against the amou…
Given the ongoing Covid-19 pandemic, it is of interest to understand how the infections spread as the combined result of measures taken by central planners (governments) and individual behavior. In this work, the spread of Covid-19 is modelled as a differentiable game between the planner and population with appropriate disease spread dynamical equations. We first characterise the equilibrium dynamics of only the population with modifed Susceptible-Infected-Recovered (SIR) equations to highlight the qualitative nature of the equilbrium. Using this result, we formulate the joint equilibrium expo…
At the time of writing, the ongoing COVID-19 pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), had already resulted in more than thirty-two million cases infected and more than one million deaths worldwide. Given the fact that the pandemic is still threatening health and safety, it is in the urgency to understand the COVID-19 contagion process and know how it might be controlled. With this motivation in mind, in this paper, we consider a version of a stochastic discrete-time Susceptible-Infected-Recovered-Death~(SIRD)-based epidemiological model with two uncerta…
On the base of logic discrete equations system mathematical modeling of COVID-19 epidemic spread was carried out in the world and in the countries with the largest number of infected people such as the USA, Brasil, Russia and India in the first half of 2020. It was shown that for the countries with strong restrictive measures the spread of COVID-19 fit on a single wave with small capacity as for a number of countries with violation of restrictive measures the spread of the epidemic fit on a waves superposition. For countries with large population mixing, the spread of the epidemic today also f…
We consider the pandemic spreading of COVID-19 for some selected countries after the outbreak of the coronavirus in Wuhan City, China. We estimated the infection rate and the initial infected individuals of COVID-19 by using the officially reported data at the early stage of the epidemic for the susceptible (S), infectable (I), quarantined (Q), and the cofirmed recovered (Rk) population model, so called SIQRk model. In the reported data we know the quarantined cases and the recovered cases. We can not know the recovered cases from the asymptomatic cases. In the SIQRk model we can estimated the…
I use a very simple deterministic model for the spread of Covid-19 in a large population. Using this to compare the relative decay of the number of deaths per day between different regions in Italy, Spain and England, each applying in principle the same social distancing procedures across the whole country, I obtain an estimate of the total fraction of the population which had already become infected by April 10th. In the most heavily affected regions, Lombardy, Madrid and London, this fraction is higher than expected, i.e. $\approx 0.3$. This result can then be converted to a determination of…
Since the first outbreak of the COVID-19 epidemic at the end of 2019, data has been made available on the number of infections, deaths and recoveries for all countries of the World, and that data can be used for statistical analysis. The primary interest of this paper is how well the logistic equation can predict the outcome of COVID-19 epidemic in any regions of the World assuming that the methodology of the testing process, namely the data collection method and social behavior is not changing over the course of time. Besides the social relevance, this study has two scientific purposes: we in…
In this paper we propose an epidemiological model for the spread of COVID-19. The dynamics of the spread is based on four fundamental categories of people in a population: Tested and infected, Non-Tested but infected, Tested but not infected, and non-Tested and not infected. The model is based on two levels of dynamics of spread in the population: at local level and at the global level. The local level growth is described with data and parameters which include testing statistics for COVID-19, preventive measures such as nationwide lockdown, and the migration of people across neighboring locati…
We present an early version of a Susceptible-Exposed-Infected-Recovered-Deceased (SEIRD) mathematical model based on partial differential equations coupled with a heterogeneous diffusion model. The model describes the spatio-temporal spread of the COVID-19 pandemic, and aims to capture dynamics also based on human habits and geographical features. To test the model, we compare the outputs generated by a finite-element solver with measured data over the Italian region of Lombardy, which has been heavily impacted by this crisis between February and April 2020. Our results show a strong qualitati…
This paper shows that the generalized logistic distribution model is derived from the well-known compartment model, consisting of susceptible, infected and recovered compartments, abbreviated as the SIR model, under certain conditions. In the SIR model, there are uncertainties in predicting the final values for the number of infected population and the infectious parameter. However, by utilizing the information obtained from the generalized logistic distribution model, we can perform the SIR numerical computation more stably and more accurately. Applications to severe acute respiratory syndrom…
We analyze the spread of COVID-19 by considering the transmission of the disease among individuals both within and between regions. A set of regions can be defined as any partition of a population such that travel/social contact within each region far exceeds that between them. COVID-19 can be eliminated if the region-to-region reproductive number---i.e. the average number of other regions to which a single infected region will transmit the virus---is reduced to less than one. We find that this region-to-region reproductive number is proportional to the travel rate between regions and exponent…
We shall apply a generalized SEIR model to study the outbreak of COVID-19 in Brazil. In particular, we would like to explain the projections of the increase in the level of infection over a long period of time, overlapping large local outbreaks in the most populous states in the country. A time-dependent dynamic SEIR model inspired in a model previously used during the outbreak in China was used to analyses the time trajectories of infected, recovered, and deaths. The model has parameters that vary with time and are fitted considering a nonlinear least-squares method. The simulations starting …
The COVID-19 pandemic has caused major disturbance to human life. An important reason behind the widespread social anxiety is the huge uncertainty about the pandemic. A fundamental uncertainty is how many or what percentage of people have been infected. There are published and frequently updated data on various statistics of the pandemic, at local, country or global level. However, due to various reasons, many cases were not included in those reported numbers. We propose a structured approach for the estimation of the number of unreported cases, where we distinguish cases that arrive late in t…
In India the COVID-19 infected population has not yet been accurately established. As always in the early stages of any epidemic, the need to test serious cases first has meant that the population with asymptomatic or mild sub-clinical symptoms has not yet been analyzed. Using counts of fatalities, and previously estimated parameters for the progress of the disease, we give statistical estimates of the infected population. The doubling time is a crucial unknown input parameter which affects these estimates, and may differ strongly from one geographical location to another. We suggest a method …
The presence of a large number of infected individuals with few or no symptoms is an important epidemiological difficulty and the main mathematical feature of COVID-19. The A-SIR model, i.e. a SIR (Susceptible-Infected-Removed) model with a compartment for infected individuals with no symptoms or few symptoms was proposed by Giuseppe Gaeta, arXiv:2003.08720 [q-bio.PE] (2020). In this paper we investigate a slightly generalized version of the same model and propose a scheme for fitting the parameters of the model to real data using the time series only of the deceased individuals. The scheme is…
The generalized logistic equation is used to interpret the COVID-19 epidemic data in several countries: Austria, Switzerland, the Netherlands, Italy, Turkey and South Korea. The model coefficients are calculated: the growth rate and the expected number of infected people, as well as the exponent indexes in the generalized logistic equation. It is shown that the dependence of the number of the infected people on time is well described on average by the logistic curve (within the framework of a simple or generalized logistic equation) with a determination coefficient exceeding 0.8. At the same t…
Objective: To evaluate the relationship between coronavirus disease 2019 (COVID-19) diagnosis with SARS-CoV-2 variant B.1.1.7 (also known as Variant of Concern 202012/01) and the risk of hospitalisation compared to diagnosis with wildtype SARS-CoV-2 variants. Design: Retrospective cohort, analysed using stratified Cox regression. Setting: Community-based SARS-CoV-2 testing in England, individually linked with hospitalisation data. Participants: 839,278 laboratory-confirmed COVID-19 patients, of whom 36,233 had been hospitalised within 14 days, tested between 23rd November 2020 and 31st January…
The Covid-19 pandemic is ongoing worldwide, and the damage it has caused is unprecedented. For prevention, South Korea has adopted a local quarantine strategy rather than a global lockdown. This approach not only minimizes economic damage, but it also efficiently prevents the spread of the disease. In this work, the spread of COVID-19 under local quarantine measures is modeled using the Susceptible-Exposed-Infected-Recovered model on complex networks. In this network approach, the links connected to isolated people are disconnected and then reinstated when they are released. This link dynamics…
Background: Recent work showed that the temporal growth of the novel coronavirus disease (COVID-19) follows a sub-exponential power-law scaling whenever effective control interventions are in place. Taking this into consideration, we present a new phenomenological logistic model that is well-suited for such power-law epidemic growth. Methods: We empirically develop the logistic growth model using simple scaling arguments, known boundary conditions and a comparison with available data from four countries, Belgium, China, Denmark and Germany, where (arguably) effective containment measures were …
Exploiting the SIQR model for COVID-19, I show that the wavy infection curve in Japan is the result of fluctuation of policy on isolation measure imposed by the government and obeyed by citizens. Assuming the infection coefficient be a two-valued function of the number of daily confirmed new cases, I show that when the removal rate of infected individuals is between these two values, the wavy infection curve is self-organized. On the basis of the infection curve, I classify the outbreak of COVID-19 into five types and show that these differences can be related to the relative magnitude of the …
In this paper, we conduct mathematical and numerical analyses to address the following crucial questions for COVID-19: (Q1) Is it possible to contain COVID-19? (Q2) When will be the peak and the end of the epidemic? (Q3) How do the asymptomatic infections affect the spread of disease? (Q4) What is the ratio of the population that needs to be infected to achieve herd immunity? (Q5) How effective are the social distancing approaches? (Q6) What is the ratio of the population infected in the long run? For (Q1) and (Q2), we propose a time-dependent susceptible-infected-recovered (SIR) model that tr…
The COVID-19 pandemic (SARS-CoV-2 virus) is the defying global health crisis of our time. The absence of mass testing and the relevant presence of asymptomatic individuals causes the available data of the COVID-19 pandemic in Brazil to be largely under-reported regarding the number of infected individuals and deaths. We propose an adapted Susceptible-Infected-Recovered (SIR) model which explicitly incorporates the under-reporting and the response of the population to public policies (such as confinement measures, widespread use of masks, etc) to cast short-term and long-term predictions. Large…
We study the SIR epidemiological model, with a variable contagion rate, applied to the evolution of COVID19 in Cuba. It is highlighted that an increase in the predictive character depends on understanding the dynamics for the temporal evolution of the rate of contagion $β^*$. A semi-empirical model for this dynamics is formulated, where reaching $β^*\approx0$ due to isolation is achieved after the mean duration of the disease $τ=1/γ$, in which the number of infected in the confined families has decreased. It is considered that $β^*(t)$ should have an abrupt decrease on the day of initiation of…
This paper develops an individual-based stochastic network SIR model for the empirical analysis of the Covid-19 pandemic. It derives moment conditions for the number of infected and active cases for single as well as multigroup epidemic models. These moment conditions are used to investigate the identification and estimation of the transmission rates. The paper then proposes a method that jointly estimates the transmission rate and the magnitude of under-reporting of infected cases. Empirical evidence on six European countries matches the simulated outcomes once the under-reporting of infected…
Ever since the outbreak of the COVID-19 epidemic, various public health control strategies have been proposed and tested against the coronavirus SARS-CoV-2. We study three specific COVID-19 epidemic control models: the susceptible, exposed, infectious, recovered (SEIR) model with vaccination control; the SEIR model with shield immunity control; and the susceptible, un-quarantined infected, quarantined infected, confirmed infected (SUQC) model with quarantine control. We express the control requirement in metric temporal logic (MTL) formulas (a type of formal specification languages) which can …
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-…
For the last few years there has been a resurgence in the use of phenomenological growth models for predicting the early dynamics of infectious diseases. These models assume that time is a continuous variable whereas in the present contribution, the discrete versions of Gompertz and Generalized Logistic models are used for early monitoring and short-term forecasting of the spread of an epidemic in a region. The time-continuous models are represented mathematically by first-order differential equations while their discrete versions are represented by first-order difference equations that involv…
The paper deals with a modeling of the ongoing epidemic caused by Coronavirus disease 2019 (COVID-19) on the closed territory of the Republic of Croatia. Using the official public information on the number of confirmed infected, recovered and deceased individuals, the modified SEIR compartmental model is developed to describe the underlying dynamics of the epidemic. Fitted modified SEIR model provides the prediction of the disease progression in the near future, considering strict control interventions by means of social distancing and quarantine for infected and at-risk individuals introduced…
The cumulative number of confirmed infected individuals by the new coronavirus outbreak until April 30th, 2020, is presented for the countries: Belgium, Brazil, United Kingdom (UK), and United States of America (USA). After an initial period with a low incidence of newly infected people, a power-law growth of the number of confirmed cases is observed. For each country, a distinct growth exponent is obtained. For Belgium, UK, and USA, countries with a large number of infected people, after the power-law growth a distinct behavior is obtained when approaching saturation. Brazil is still in the p…
We give some numerical observations on the total number of infected by the SARS-CoV-2 in Italy. The analysis is based on a tanh formula involving two parameters. A polynomial correlation between the parameters gives an upper bound for the time of the peak of new infected. A numerical indicator of the temporal variability of the upper bound is introduced. The result and the possibility to extend the analysis to other countries are discussed in the conclusions.
In this paper, we develop a probabilistic mathematical model for the spread of coronavirus disease (COVID-19). It takes into account the known special characteristics of this disease such as the existence of infectious undetected cases and the different social and infectiousness conditions of infected people. In particular, it considers the social structure and governmental measures in a country, the fraction of detected cases over the real total infected cases, and the influx of undetected infected people from outside the borders. Although the model is simple and allows a reasonable identific…
We propose a mathematical model to analyze the time evolution of the total number of infected population with Covid-19 disease at a region in the ongoing pandemic. Using the available data of Covid-19 infected population on various countries we formulate a model which can successfully track the time evolution from early days to the saturation period in a given wave of this infectious disease. It involves a set of effective parameters which can be extracted from the available data. Using those parameters the future trajectories of the disease spread can also be projected. A set of differential …
In this note we analyze the temporal dynamics of the coronavirus disease 2019 outbreak in China, Italy and France in the time window $22/01-09/03/2020$. A first analysis of simple day-lag maps points to some universality in the epidemic spreading, suggesting that simple mean-field models can be meaningfully used to gather a quantitative picture of the epidemic spreading, and notably the height and time of the peak of confirmed infected individuals. The analysis of the same data within a simple susceptible-(confirmed) infected-recovered-deaths model indicates that the kinetic parameter that des…
We revisit well-established concepts of epidemiology, the Ising-model, and percolation theory. Also, we employ a spin $S$ = 1/2 Ising-like model and a (logistic) Fermi-Dirac-like function to describe the spread of Covid-19. Our analysis reinforces well-established literature results, namely: \emph{i}) that the epidemic curves can be described by a Gaussian-type function; \emph{ii}) that the temporal evolution of the accumulative number of infections and fatalities follow a logistic function, which has some resemblance with a distorted Fermi-Dirac-like function; \emph{iii}) the key role played …
In this paper, we firstly propose SQIARD and SIARD models to investigate the transmission of COVID-19 with quarantine, infected and asymptomatic infected, and discuss the relation between the respective basic reproduction number $R_0, R_Q$ and the stability of the equilibrium points of model. Secondly, after training the related data parameters, in our numerical simulations, we respectively conduct the forecast of the data of US, South Korea, Brazil, India, Russia and Italy, and the effect of prediction of the epidemic situation in each country. Furthermore, we apply US data to compare SQIARD …
The study carries out predictive modeling based on publicly available COVID-19 data for the duration 01 April to 20 June 2020 pertaining to India and five of its most infected states: Maharashtra, Tamil Nadu, Delhi, Gujarat, and Rajasthan using susceptible, infected, recovered, and dead (SIRD) model. The basic reproduction number R0 is derived by exponential growth method using RStudio package R0. The differential equations reflecting SIRD model have been solved using Python 3.7.4 on Jupyter Notebook platform. For visualization, Python Matplotlib 3.2.1 package is used. The study offers insight…
We present an empirical algorithm to forecast the evolution of the number of COVID-19 symptomatic patients in the early stages of the pandemic spread and after strict social distancing interventions. The algorithm is based on a low dimensional model for the variation of the exponential growth rate that decreases after the implementation of strict social distancing measures. From the observable data given by the number of tested positive, our model estimates the number of infected hindcast introducing in the model formulation the incubation time. We also use the model to follow the number of in…
We consider the pandemic spreading of COVID-19 in India after the outbreak of the coronavirus in Wuhan city, China. We estimate the transmission rate of the initial infecting individuals of COVID-19 in India by using the officially reported data at the early stage of the epidemic with the help of Susceptible (S), Exposed (E), Infected (I), and Removed (R) population model, the so-called SEIR dynamical model. Numerical analysis and model verification are performed to calibrate the system parameters with official public information about the number of people infected, and then to evaluate severa…
This article describes a simple Susceptible Infected Recovered (SIR) model fitting with COVID-19 data for the month of march 2020 in New York (NY) state. The model is a classical SIR, but is non-autonomous; the rate of susceptible people becoming infected is adjusted over time in order to fit the available data. The death rate is also secondarily adjusted. Our fitting is made under the assumption that due to limiting number of tests, a large part of the infected population has not been tested positive. In the last part, we extend the model to take into account the daily fluxes between New Jers…
Intent of this research is to explore how mathematical models, specifically Susceptible-Infected-Removed (SIR) model, can be utilized to forecast peak outbreak timeline of COVID-19 epidemic amongst a population of interest starting from the date of first reported case. Till the time of this research, there was no effective and universally accepted vaccine to control transmission and spread of this infection. COVID-19 primarily spreads in population through respiratory droplets from an infected person cough and sneeze which infects people who are in proximity. COVID-19 is spreading contagiously…
In this paper we analyze the effects of commuting and social inequalities for the epidemic development of the novel coronavirus (COVID-19). With this aim we consider a SEIRD (susceptible, exposed, infected, recovered and dead by disease) model without vital dynamics in a population divided into patches that have different economic resources and in which the individuals can commute from one patch to another (bilaterally). In the modeling we choose the social and commuting parameters arbitrarily. We calculate the basic reproductive number $R_0$ with the next generation approach and analyze the s…
In a previous note we made an analysis of the spreading of the COVID disease in Italy. We used a model based on the logistic and Hubbert functions, the analysis we exploited has shown limited usefulness in terms of predictions and failed in fixing fundamental indications like the point of inflection of the disease growth. In this note we elaborate on the previous model, using multi-logistic models and attempt a more realistic analysis.
To model the spread of COVID-19 coronavirus in Russian regions and in Moscow, a discrete logistic equation describing the increase in the number of cases is used. To check the adequacy of the mathematical model, the simulation results were compared with the spread of coronavirus in China, in a number of European and Asian countries, and the United States. The parameters of the logistics equation for Russia, Moscow and other large regions were determined in the interval (01.03 - 08.04). A comparative analysis of growth rates of COVID-19 infected population for different countries and regions is…
In this letter we study the temporal evolution of the Sars-Cov-2 in Italy. The time window of the real data is between February 24 and March 25. After we upgrade the data until April 1.We perform the analysis with 4 different model and we think that the best candidate to describe correctly the italian situation is a generalized Logistic equation. We use two coupled differential equations that describe the evolution of the severe infected and the deaths. We have done this choice, because in Italy the pharyngeal swabs are made only to severe infected and so we have no information about asymptoma…
Optimal screening strategies in the control of an infectious disease: a case of the COVID-19 in a population with age structure
本研究针对COVID-19防控，基于年龄结构模型，运用Pontryagin最大值原理求解兼顾感染人数与经济成本最小化的最优检疫控制策略，给出隔离放宽日程并分析延迟启动检疫的影响。
We develop and analyze in this work an epidemiological model for COVID-19 using Tunisian data. Our aims are first to evaluate Tunisian control policies for COVID-19 and secondly to understand the effect of different screening, quarantine and containment strategies and the rule of the asymptomatic patients on the spread of the virus in the Tunisian population. With this work, we show that Tunisian control policies are efficient in screening infected and asymptomatic individuals and that if containment and curfew are maintained the epidemic will be quickly contained.
The current outbreak is known as Coronavirus Disease or COVID-19 caused by the virus SAR-COV-2 which continues to wreak havoc across the globe. The World Health Organization (WHO) has declared the outbreak a Public Health Emergency of International Concern. In Pakistan, the spread of the virus is on the rise with the number of infected people and causalities rapidly increasing. In the absence of proper vaccination and treatment, to reduce the number of infections and casualties, the only option so far is to educate people regarding preventive measures and to enforce countrywide lock-down. Any …
The World Health Organization (WHO) made the assessment that COVID-19 can be characterized as a pandemic on March 11, 2020. To the COVID-19 outbreak, there is no vaccination and no treatment. The only way to control the COVID-19 outbreak is sustained physical distancing. In this work, a simple control law was proposed to keep the infected individuals during the COVID-19 outbreak below the desired number. The proposed control law keeps the value of infected individuals controlled only adjusting the social distancing level. The stability analysis of the proposed control law is done and the uncer…
Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible $S$, infected $I$, removed $R$ and dead people $D$. In order to have a cross validation, a deterministic version of such a model is also devised which is represented by a system of ordinary differential equations with delays. In the second stochastic model two further compartments are added: the class $A$ of asymptomatic individuals and the class $L$ of isolated infected people. Effects such as social distancing measures are…
Currently the COVID-19 epidemic is developing in the City of Culiacń Sinaloa, Mexico, where up to April 20 of this year there have been 35 deaths associated with this epidemic. The reproduction number $(R_0)$ of an epidemic represents the average number of people infected by an infected person during their period of infection. In this work we use the data published by the Secretary of Health of the State of Sinaloa on the number of new infected cases confirmed per day and we estimate that the value of $R_0$ is 1.562 with a 95% confidence interval given by (1.401,1.742). We also estimate the mo…
In a previous article [1] we have described the temporal evolution of the Sars- Cov-2 in Italy in the time window February 24-April 1. As we can see in [1] a generalized logistic equation captures both the peaks of the total infected and the deaths. In this article our goal is to study the missing peak, i.e. the currently infected one (or total currently positive). After the April 7 the large increase in the number of swabs meant that the logistical behavior of the infected curve no longer worked. So we decided to generalize the model, introducing new parameters. Moreover, we adopt a similar a…
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