Infectious Disease Modelling

In this work, we proposed a variant of the SIR model, taking as based on models used to describe the epidemic outbreak in South Korea and Portugal, to study the SARS-CoV-2 epidemic curve in Brazil. The model presented here describes with reasonable agreement the number of COVID-19 cases registered in Brazil between February 26 and April 25, 2020 based on the hypothesis that there a large number no notified cases (11 to 1) and variation in contagion rate according to social isolation measures and...

A SIRU-type epidemic model is employed for the prediction of the COVID-19 epidemy evolution in Brazil, and analyse the influence of public health measures on simulating the control of this infectious disease. Since the reported cases are typically only a fraction of the total number of the symptomatic infectious individuals, the model accounts for both reported and unreported cases. Also, the model allows for a time variable functional form of both the transmission rate and the fraction of asymp...

The novel of COVID-19 disease started in late 2019 making the worldwide governments came across a high number of critical and death cases, beyond constant fear of the collapse in their health systems. Since the beginning of the pandemic, researchers and authorities are mainly concerned with carrying out quantitative studies (modeling and predictions) overcoming the scarcity of tests that lead us to under-reporting cases. To address these issues, we introduce a Bayesian approach to the SIR model ...

Lassa fever (Lf) is a viral haemorrhagic disease endemic to West Africa and is caused by the Lassa mammarenavirus. The rodent Mastomys natalensis serves as the primary reservoir and its ecology and behaviour have been linked to the distinct spatial and temporal patterns in the incidence of Lf. Nigeria has experienced an unprecedented epidemic that lasted from January until April of 2018, which has been followed by subsequent epidemics of Lf in the same period every year since. While previous res...

This study aims to understand the features of the COVID-19 spread in the South Region of Brazil by estimating the Effective Reproduction Number (ERN)[R] e for the states of Parana (PR), Rio Grande do Sul (RS), and Santa Catarina (SC). We used the SIRD (Susceptibles-Infectious-Recovered-Dead) model to describe the past data and to simulate strategies for the gradual mitigation of the epidemic curve by applying non-pharmacological measures. Besides the SIRD model does not include some aspects of C...

The first case of COVID-19 was reported in Kenya in March 2020 and soon after non-pharmaceutical interventions (NPIs) were established to control the spread of the disease. The NPIs consisted, and continue to consist, of mitigation measures followed by a period of relaxation of some of the measures. In this paper, we use a deterministic mathematical model to analyze the dynamics of the disease, during the first wave, and relate it to the intervention measures. In the process, we develop a new me...

We formulated a mathematical model considering young (below 60 years old) and elder (above 60 years) subpopulations to describe the introduction and dissemination of new coronavirus epidemics in the Sao Paulo State, Brazil. From the data collected in Sao Paulo State, we estimated the model parameters and calculated the basic reproduction number as R0 = 6.828. Considering isolation as a control mechanism, we varied the releasing proportions of young and elder persons to assess their epidemiologic...

To flatten the curve of the natural epidemic of covid-19, many countries adopted lockdown or isolation resulting in the containment of the SARS-CoV-2 transmission. However, an important question arises about the strategies of release of isolated persons to avoid overloaded hospitals and increased deaths. Sao Paulo State (Brazil) implemented the isolation of the population in non-essential activities on March 24, and the progressive flexibilization considering the characteristics of each location...

Sao Paulo State registered the first case of CoViD-19 on 26 February, the first death due to CoViD-19 on 16 March, and implemented the isolation of the population in non-essential activities on 24 March, which is programmed to end on 1 June. A mathematical model considering young (below 60 years old) and elder (above 60 years) subpopulations was formulated based on the natural history of CoViD-19 to study the transmission of the new coronavirus in Sao Paulo State, Brazil. This deterministic mode...

A simple and well known epidemiological deterministic model was selected to estimate the main results for the basic dynamics of the Covid-19 epidemic breakout in the city of Sao Paulo - Brazil. The methodology employed the SEIR Model to characterize the epidemics outbreak and future outcomes. A time-dependent incidence weight on the SEIR reproductive basic number accounts for local Mitigation Policies (MP). The insights gained from analysis of these successful interventions were used to quantify...

COVID-19 global dynamics is modeled by an adaptation of the deterministic SEIR Model, which takes into account two dominant lineages of the SARS-CoV-2, and a time-varying reproduction number to estimate the disease transmission behavior. Such a methodology can be applied worldwide to predict forecasts of the outbreak in any infected country. The pandemic in Brazil was selected as a first study case. Brazilian official published data from February 25th to August 30th, 2020 was used to adjust a fe...

Mathematical models are useful in epidemiology to understand the COVID-19 contagion dynamics. Our aim is to demonstrate the effectiveness of parameter regression methods to calibrate an established epidemiological model describing COVID-19 infection rates subject to active and varying non-pharmaceutical interventions (NPIs). To do this, we assess the potential of some established chemical engineering modelling principles and practice for application to modelling of epidemiological systems. This ...

We investigate time scale separation in the vector borne disease model SIRUV, as previously described in the literature [1], and recently reanalyzed with the singular perturbation technique [2]. We focus on the analysis with a single small parameter, the birth and death rate {micro}, whereas all other model parameters are much larger and describe fast transitions. The scaling of the endemic stationary state, the Jacobian matrix around it and its eigenvalues with this small parameter {micro} is c...

In this work, the modified SEIR model was proposed to account separately for the tested and isolated cases, with severe and critical symptoms, from those not tested, with mild and moderate symptoms. Two parameters were estimated and evaluated for the cases registered in Rondonia, Brazil, between March 20 and April 22. The basic reproduction rate did not remain constant during the period, showing eventual variations due to social behavior. The results show that an increase in the proportion of te...

An agent-based model is proposed to access the impact of vaccination strategies to halt the COVID-19 spread. The model is parameterized using data from Sao Paulo State, Brazil. It was considered the two vaccines that are already approved for emergency use in Brazil, the CoronaVac vaccine developed by the Chinese bio-pharmaceutical company Sinovac and the Oxford-AstraZeneca vaccine (ChadOx1) developed by Oxford University and the British laboratory AstraZeneca. Both of them are two-dose schemes, ...

Coronavirus disease 2019 (covid-19), with the fatality rate in elder (60 years old or more) being much higher than young (60 years old or less) patients, was declared a pandemic by the World Health Organization on March 11, 2020. Taking into account this age-dependent fatality rate, a mathematical model considering young and elder subpopulations was formulated based on the natural history of covid-19 to study the transmission of the SARS-CoV-2. This model can be applied to study the epidemiologi...

Rate parameters are critical in estimating the covid burden using mathematical models. In the Covid-19 mathematical models, these parameters are assumed to be constant. However, uncertainties in these rate parameters are almost inevitable. In this paper, we study a stochastic epidemic model of the SARS-CoV-2 virus infection in the presence of vaccination in which some parameters fluctuate around its average value. Our analysis shows that if the stochastic basic reproduction number (SBRN) of the ...

Malaria is still a life threatening parasitic disease due to the change in environmental and socio-economic conditions. This paper introduces a novel mathematical model to study the impact of drug-resistant strain, recovered-carrier, and relapse on malaria dynamics by implementing Caputo-Fabrizio fractional order derivative (CFFOD). We begin by presenting theoretical results that are derived for our model. We also derive the expression for the control reproduction number and investigate the equi...

The coronavirus disease (COVID-19) outbreak is the biggest public health challenge in the last 100 years. No successful pharmaceutical treatment is yet available, thus effective public health interventions to contain COVID-19 include social distancing, isolation and quarantine measures, however the efficiency of these containment measures varied among countries and even within states in the same country. Despite Brazil being deeply affected by coronavirus, the federal government never proposed a...

The existence of a universal law which maps the bell curve of daily cases to a sigmoid curve for cumulative ones is used for making robust estimations about the final outcome of a disease. Computations of real time effective reproduction rate are presented and its limited usefulness is derived. After using methods ESE & EDE we are able to find the inflection point of the cumulative curve under consideration and study its time evolution. Since mortality processes tend to follow a Gompertz distrib...