Assessing inference of the basic reproduction number in an SIR model incorporating a growth-scaling parameter

Mathematical analysis of a generalized epidemic model with nonlinear incidence function

Background

Though different forms of control measures have been deployed to curtail disease transmission, which are mostly through vaccination, treatment, isolation, etc., using mathematical models. Therefore, there is a need to consider the strict compliance or attendance of human individuals to medical awareness program through media outlets like radio, television, etc. In this work, a generalized mathematical model of two groups of infectious individuals who are compliant and non-compliant to medical awareness program is studied.

Results

A generalized Susceptible-Exposed-Infected-Recovered (SEIR) model with two groups of infectious individuals who attend or are compliant and those who do not attend or are non-compliant to medical awareness program is established. The analytical results of the model shows that the model is positive, well-posed, and epidemiologically reasonable. The two equilibria and the basic reproduction number Rr of the model is computed and analyzed and it is shown that the disease-free equilibrium is locally and globally asymptotically stable when Rr < 1 and the endemic equilibrium is globally stable when Rr > 1. Simulations are carried out by varying some parameters when Rr is less and above unity. The simulations suggest that control interventions are to be implemented and medical awareness program scaled up to mitigate the spread of diseases. Furthermore, two numerical methods of Runge-Kutta and Differential Transform Method (DTM) are employed to obtain the approximate solutions of the model system equations, and it is observed that the results of the two methods agreeably compare with each other in terms of efficiency and convergence.

Conclusion

This work should be taken into consideration by health policy makers and bio-mathematicians, because existing literature only take into consideration, how diseases spread and its management without considering the impact of strict compliance to consistent awareness program to mitigate the spread of diseases, which has been considered in this work. The limitation of this work is the unavailability of data on individuals in disease endemic regions who always and who do not comply with medical awareness programs.

Basic Reproduction Number of the 2019 Novel Coronavirus Disease in the Major Endemic Areas of China: A Latent Profile Analysis

Objective: The aim of this study is to analyze the latent class of basic reproduction number (R₀) trends of the 2019 novel coronavirus disease (COVID-19) in the major endemic areas of China.

Methods: The provinces that reported more than 500 cases of COVID-19 till February 18, 2020 were selected as the major endemic areas. The Verhulst model was used to fit the growth rate of cumulative confirmed cases. The R₀ of COVID-19 was calculated using the parameters of severe acute respiratory syndrome (SARS) and COVID-19. The latent class of R₀ was analyzed using the latent profile analysis (LPA) model.

Results: The median R₀ calculated from the SARS and COVID-19 parameters were 1.84–3.18 and 1.74–2.91, respectively. The R₀ calculated from the SARS parameters was greater than that calculated from the COVID-19 parameters (Z = −4.782 to −4.623, p < 0.01). Both R₀ can be divided into three latent classes. The initial value of R₀ in class 1 (Shandong Province, Sichuan Province, and Chongqing Municipality) was relatively low and decreased slowly. The initial value of R₀ in class 2 (Anhui Province, Hunan Province, Jiangxi Province, Henan Province, Zhejiang Province, Guangdong Province, and Jiangsu Province) was relatively high and decreased rapidly. Moreover, the initial R₀ value of class 3 (Hubei Province) was in the range between that of classes 1 and 2, but the higher R₀ level lasted longer and decreased slowly.

Conclusion: The results indicated that the overall R₀ trend is decreased with the strengthening of comprehensive prevention and control measures of China for COVID-19, however, there are regional differences.

Multi-population stochastic modeling of Ebola in Sierra Leone: Investigation of spatial heterogeneity

A major outbreak of the Ebola virus occurred in 2014 in Sierra Leone. We investigate the spatial heterogeneity of the outbreak among districts in Sierra Leone. The stochastic discrete-time susceptible-exposed-infectious-removed (SEIR) model is used, allowing for probabilistic movements from one compartment to another. Our model accounts for heterogeneity among districts by making use of a hierarchical approach. The transmission rates are considered time-varying. It is investigated whether or not incubation period, infectious period and transmission rates are different among districts. Estimation is done using the Bayesian formalism. The posterior estimates of the effective reproductive number were substantially different across the districts, with pronounced variability in districts with few cases of Ebola. The posterior estimates of the reproductive number at the district level varied between below 1.0 and 4.5, whereas at nationwide level it varied between below 1.0 and 2.5. The posterior estimate of the effective reproductive number reached a value below 1.0 around December. In some districts, the effective reproductive number pointed out for the persistence of the outbreak or for a likely resurgence of new cases of Ebola virus disease (EVD). The posterior estimates have shown to be highly sensitive to prior elicitation, mainly the incubation period and infectious period.

Inference of the generalized-growth model via maximum likelihood estimation: A reflection on the impact of overdispersion

Recently, the generalized-growth model was introduced as a flexible approach to characterize growth dynamics of disease outbreaks during the early ascending phase. In this work, by using classical maximum likelihood estimation to obtain parameter estimates, we evaluate the impact of varying levels of overdispersion on the inference of the growth scaling parameter through comparing Poisson and Negative binomial models. In particular, under exponential and sub-exponential growth scenarios, we evaluate, via simulations, the error rate of making an incorrect characterization of early outbreak growth patterns. Simulation results show that the ability to correctly identify early outbreak growth patterns can be affected by overdispersion even when accounted for using the Negative binomial model. We exemplify our findings using data on five different outbreaks. Overall, our results show that estimates should be interpreted with caution when data are overdispersed.