Mathematical model for acquiring immunity to malaria: a PDE approach

We develop a new model of integro-differential equations coupled with a partial differential equation that focuses on the study of the? naturally acquiring immunity to malaria induced by exposure to infection. We analyze a continuous acquisition of immunity after infected individuals are treated. It exhibits complex and realistic mechanisms precised mathematically in both disease free or endemic context and in several numerical simulations showing the interplay between infection through the bite of mosquitoes. The model confirms the (partial) premunition of the human population in the regions where malaria is endemic. As common in literature, we indicate an equivalence of the basic reproduction rate as the spectral radius of a next generation operator.

An Integrated Neural Network and SEIR Model to Predict COVID-19

A novel coronavirus (COVID-19), which has become a great concern for the world, was identified first in Wuhan city in China. The rapid spread throughout the world was accompanied by an alarming number of infected patients and increasing number of deaths gradually. If the number of infected cases can be predicted in advance, it would have a large contribution to controlling this pandemic in any area. Therefore, this study introduces an integrated model for predicting the number of confirmed cases from the perspective of Bangladesh. Moreover, the number of quarantined patients and the change in basic reproduction rate (the R0-value) can also be evaluated using this model. This integrated model combines the SEIR (Susceptible, Exposed, Infected, Removed) epidemiological model and neural networks. The model was trained using available data from 250 days. The accuracy of the prediction of confirmed cases is almost between 90% and 99%. The performance of this integrated model was evaluated by showing the difference in accuracy between the integrated model and the general SEIR model. The result shows that the integrated model is more accurate than the general SEIR model while predicting the number of confirmed cases in Bangladesh.

Social heterogeneity and the COVID-19 lockdown in a multi-group SEIR model

The goal of the lockdown is to mitigate and if possible prevent the spread of an epidemic. It consists in reducing social interactions. This is taken into account by the introduction of a factor of reduction of social interactions q, and by decreasing the transmission coefficient of the disease accordingly. Evaluating q is a difficult question and one can ask if it makes sense to compute an average coefficient q for a given population, in order to make predictions on the basic reproduction rate ℛ0, the dynamics of the epidemic or the fraction of the population that will have been infected by the end of the epidemic. On a very simple example, we show that the computation of ℛ0 in a heterogeneous population is not reduced to the computation of an average q but rather to the direct computation of an average coefficient ℛ0. Even more interesting is the fact that, in a range of data compatible with the Covid-19 outbreak, the size of the epidemic is deeply modified by social heterogeneity, as is the height of the epidemic peak, while the date at which it is reached mainly depends on the average ℛ0 coefficient. This paper illustrates more technical results that can be found in [4], with new numerical computations. It is intended to draw the attention on the role of heterogeneities in a population in a very simple case, which might be difficult to apprehend in more realistic but also more complex models.

Prediction of the peak Covid-19 pandemic in Indonesia using SIR model

This research implements the Susceptible, Infected, and Removed (SIR) model to predict the Covid-19 outbreak in Indonesia. The government official data, consisting of infected, dead, and recovered, are used as actual data to interpolate the model through matching data with minimum mean squared error (MSE). The study uses one of the Quasi-Newton search methods, the Broyden, Fletcher, Goldfarb, and Shanno (BFGS) algorithm, to determine the interaction coefficient's optimal value in the model with the minimum MSE value. Based on data as of July 18, 2020, it predicts that the peak of the infected number will be in October 2020 with around 14 % of the total population infected, and the MSE of 18.42 is relative to the period of the actual data. Meanwhile, the basic reproduction rate is calculated to be 2.035 from the model, where it is underestimated about 29 % compared to the relative basic reproduction rate from the provided actual data.

INDEPENDENT ASSOCIATION OF METEOROLOGICAL CHARACTERISTICS WITH INITIAL SPREAD OF COVID-19 IN INDIA

Whether weather plays a part in the transmissibility of the novel COronaVIrus Disease-19 (COVID-19) is still not established. We tested the hypothesis that meteorological factors (air temperature, relative humidity, air pressure, wind speed and rainfall) are independently associated with transmissibility of COVID-19 quantified using the basic reproduction rate (R0). We used publicly available datasets on daily COVID-19 case counts (total n = 108,308), three-hourly meteorological data and community mobility data over a three-month period. Estimated R0 varied between 1.15-1.28. Mean daily air temperature (inversely) and wind speed (positively) were significantly associated with time dependent R0, but the contribution of countrywide lockdown to variability in R0 was over three times stronger as compared to that of temperature and wind speed combined. Thus, abating temperatures and easing lockdown may concur with increased transmissibility of COVID-19.

Comparative Analysis of SARS-CoV2 with Special Emphasis on Genome Sequences

Coronavirus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus – 2 (SARS-CoV-2), was declared a global pandemic on 11th March, 2020 by World Health Organization. As of now,27th May,2020, there are about 54,88,825 infected cases and 3,49,095 deaths globally. Coronavirus samples collected from all the countries have been sequenced for advanced studies in a bid to understand the structure and functioning of the virus. In our study, we have tried working on every available sequence to setup both comparisons and co-relations. There is no such available study as of now for reference and hence it can become a pioneer stone in this direction. The mortality rate calculated turns out to be 9.19%,34.37% and 6.29% for SARS-2003, MERS-2012 and COVID-19 respectively. The basic reproduction rate R0 was 2-5 for SARS-2003, 0.3-0.8 for MERS-2012 and 1.4-5.7 for COVID-19. We found out the relation between number of mutations and mortality as well as phylogenetic relations. High number of mutations corresponded to higher mortality rate as in countries like Italy and Spain. Alpha and Beta-coronaviruses show a common ancestor from which they descended. Brazil and Iran have shown similar phylogenetic descent explaining their mortality rate. India, however, showed a distant relation from the common ancestor of other genome sequences. This study highlights the mutations of the SARS-CoV2 virus as well as sets up a comparison with the previous outbreaks. Similar type of studies should be conducted when more genome samples are present. These results can also contribute towards making an effective anti-viral therapy and vaccines.

Social heterogeneity and the COVID-19 lockdown in a multi-group SEIR model

The goal of the lockdown is to mitigate and if possible prevent the spread of an epidemic. It consists in reducing social interactions. This is taken into account by the introduction of a factor of reduction of social interactions q, and by decreasing the transmission coefficient of the disease accordingly. Evaluating q is a difficult question and one can ask if it makes sense to compute an average coefficient q for a given population, in order to make predictions on the basic reproduction rate R0, the dynamics of the epidemic or the fraction of the population that will have been infected by the end of the epidemic. On a very simple example, we show that the computation of R0 in a heterogeneous population is not reduced to the computation of an average q but rather to the direct computation of an average coefficient R0. Even more interesting is the fact that, in a range of data compatible with the Covid-19 outbreak, the size of the epidemic is deeply modified by social heterogeneity, as is the height of the epidemic peak, while the date at which it is reached mainly depends on the average R0 coefficient.

Basic Reproduction Rate and Case Fatality Rate of COVID-19: Application of Meta-analysis

Background: The outbreak of novel coronavirus disease of 2019 (COVID-19) has a wider geographical spread than other previous viruses such as Ebola and H1N1. The onset of disease and its transmission and severity has become a global concern. The policymakers have a serious concern for containing the spread and minimising the risk of death. Aim: This study aims to provide the estimates of basic reproduction rate (R0) and case fatality rate (CFR) which applies to a generalised population. Methods: A systematic review was carried out to retrieve the published estimates of reproduction rate and case fatality rate in peer-reviewed articles from PubMed MEDLINE database with defined inclusion and exclusion criteria in the period 15 December 2019 to 3 May 2020. The systematic review led to the selection of 24 articles for R0 and 17 articles for CFR. These studies used data from China and its provinces, other Asian countries such as Japan, Korea, the Philippines, and countries from other parts of the world such as Nigeria, Iran, Italy, Europe as a whole, France, Latin America, Turkey, the United Kingdom (UK), and the United States of America (USA). These selected articles gave an output of 30 counts of R0 and 29 counts of CFR which were used in a meta-analysis. A meta-analysis, with the inverse variance method, fixed- and random-effects model and the Forest plot, was performed to estimate the mean effect size or mean value of basic reproduction rate and case fatality rate. The Funnel plot is used to comprehend the publication bias. Results: We estimated the robust estimate of R0 at 3.11 (2.49-3.71) persons and the robust estimate of CFR at 2.56 (2.06-3.05) per cent after accounting for heterogeneity among studies, using the random-effects model. The regional subgroup analysis in a meta-analysis was significant for R0 but was not significant for CFR. The R0 values varied from 1.90 (1.06-2.74) persons to 3.83 (2.44-5.22) persons across the regions. The Funnel plot confirms that the selected studies are significant at one per cent level of significance. Conclusion: We found that one person is likely to infect two to three persons in the absence of any control measures, and around three per cent of the population are at the risk of death within one-and-a-half months from the onset of disease COVID-19 in a generalised population. The emergence of SARS-CoV-2 varies across regions, but the risk of death remains the same. Contribution: The estimates of R0 and CFR are independent of data from a particular region or time or a homogeneous population. These estimates are applicable to a generalised population. Therefore, the estimates of R0 and CFR are unequivocally applicable to developing country like India and its states or districts, in ambivalence. The assessments of R0 and CFR values across the developed nations make all of us aware of consequences of COVID-19, and hence these estimates are of crucial importance for government authorities for the practical implementation of strategies and control measures to contain the disease. Keywords: Covid-19, SARS-CoV-2, Reproduction Rate, Case Fatality Rate, Systematic Review, Meta-analysis

A Computational Model for Estimating the Evolution of COVID-19 in Rondônia-Brazil

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 Rondônia-Brazil, between March 20 and April 22. The basic reproduction rate did not remain constant during the period, showing variations eventually due to social behavior. The results show that the increase in the proportion of testing to about 56% provided a significant decrease in the confirmed cases since the expansion of the tested cases beyond the current testing criterion (20%) would help to identify and isolate also mild and moderate cases, generally referred to as asymptomatic.

COVID-19 Epidemic Dynamics and Population Projections from Early Days of Case Reporting in a 40 million population from Southern India

India reported its first COVID19 case on 30 January 2020. Since then the epidemic has taken different trajectories across different geographical locations in the country. This study explores the population aggregated trajectories of COVID19 susceptible, infected and recovered or dead cases in the south Indian state of Telangana with a population of approximately 40 million. Information on cases reported from March 2 to April 4 was collated from government records. The susceptible-infected-removed (SIR) model for the spread of an infectious disease was used. Transmission parameters were extracted from existing literature that has emerged over past weeks from other regions with similar population densities as Telangana. Optimisation algorithms were used to get basic reproduction rate for different phases of nonpharmaceutical interventions rolled by the government. Peak accumulation is projected towards end of July with 36% of the population being infected by August 2020 if the population lockdown or social distancing mechanism is not continued. The number of deaths assuming no intervention is projected to be 488000 (95% CI: (329400, 646600)). A draconian enforcement of population lockdown combined with hand and face hygiene adherence would reduce the transmission by at least 99.7% whereas partial social distancing and hygiene would reduce it by 51.2%. Transmission parameters reported should be interpreted with caution as they are population aggregated and do not consider unique characteristics of susceptibility among micro-clusters and vulnerable individuals. More data will need to be collected to optimize transmission parameters and evaluate the full complexity, to simulate real world scenarios in the models.