Mathematical modeling of the infectious spread and outbreak dynamics of avian influenza with seasonality transmission for chicken farms.

A compartmental model with a time-varying contact rate, the seasonality effect, and its corresponding nonautonomous model are investigated. The model is developed based on the six compartments: susceptible, latent, infected, asymptomatic, treated, and recovered individuals. We determine the effective reproduction number for this nonautonomous system, and analytic discussion shows that at least one positive periodic solution exists for R0>1. The model is simulated using the RK-45 numerical method, and the parameter values for the model are taken from the available literature. From the numerical results, we observe that the degree of seasonality and vaccine efficacy significantly impact the amplitude of the epidemic curve. The latent-infected phase plane shows that periodic solutions exhibit a period-doubling bifurcation as the amplitude of seasonality increases. Finally, the model outcome was compared with the actual field data and found to be consistent.

Impact of vaccination on the entire population and dose-response relation of COVID-19.

Objective: The objective of this study is to develop a mathematical model for the COVID-19 pandemic including vaccination, the transmissibility of the virus-pathogen dose-response relationship, vaccine efficiency, and vaccination rate. Methods: The Runge-Kutta (RK-45) method was applied to solve the proposed model with MATLAB code and the calculated results show the dynamics of the individuals in each compartment. The data of total death due to the COVID-19 pandemic in the case of the USA were collected from GitHub and the re-use of this data needs no ethical clearance. The control reproduction number was used to assess the dose-response relationship and critical vaccination coverage. Results: We have calculated the probability of infection and the infection risk against the different exposure doses and the virus copies, respectively. The results show that the probability of infection increases with the increasing exposure dose for certain virus copies and the risk of infection decreases with the increasing of virus copies for a certain exposure dose. The results also show that the critical vaccination coverage demands increase with an increase in transmission rate and decrease with increasing vaccine efficacy. Conclusions: It was seen that the critical vaccination coverage corresponding to an increased transmission rate rise sharply in the beginning and then reached a threshold. Moreover, the real data of the total death cases in the USA were compared with the fitted curved of the model which validated the proposed model. Vaccination against COVID-19 is essential to control the pandemic, and achieving high vaccine uptake in the population can reduce the pandemic as fast as possible.

Objetivo: El objetivo de este estudio es desarrollar un modelo matemático para la pandemia de COVID-19 que incluya la vacunación, la transmisibilidad de la relación dosis-respuesta virus-patógeno, la eficacia de la vacuna y la tasa de vacunación. Métodos: Se aplicó el método de Runge-Kutta (RK-45) para resolver el modelo propuesto con código MATLAB y los resultados calculados muestran la dinámica de los individuos en cada compartimento. Los datos de muerte total por la pandemia de COVID-19 en el caso de EE. UU. se recopilaron de GitHub y la reutilización de estos datos no necesita autorización ética. El número de reproducción de control se utilizó para evaluar la relación dosis-respuesta y la cobertura de vacunación crítica. Resultados: Hemos calculado la probabilidad de infección y el riesgo de infección frente a las diferentes dosis de exposición y las copias del virus, respectivamente. Los resultados muestran que la probabilidad de infección aumenta con el aumento de la dosis de exposición para ciertas copias del virus y el riesgo de infección disminuye con el aumento de las copias del virus para una determinada dosis de exposición. Los resultados también muestran que las demandas críticas de cobertura de vacunación aumentan con el aumento de la tasa de transmisión y disminuyen con el aumento de la eficacia de la vacuna. Conclusiones: Se observó que las coberturas críticas de vacunación correspondientes a una mayor tasa de transmisión aumentaron bruscamente al principio y luego alcanzaron un umbral. Además, se compararon los datos reales del total de casos de muerte en EE. UU. con la curva ajustada del modelo que validó el modelo propuesto. La vacunación contra el COVID-19 es fundamental para controlar la pandemia, y lograr una alta captación de vacunas en la población puede reducir la pandemia lo más rápido posible.

Data analysis and prediction of the COVID-19 outbreak in the first and second waves for top 5 affected countries in the world.

In this paper, we introduce a SEIATR compartmental model to analyze and predict the COVID-19 outbreak in the Top 5 affected countries in the world, namely the USA, India, Brazil, France, and Russia. The officially confirmed cases and death due to COVID-19 from the day of the official confirmation to June 30, 2021 are considered for each country. Primarily, we use the data to make a comparison between the cumulative cases and deaths due to COVID-19 among these five different countries. This analysis allows us to infer the key parameters associated with the dynamics of the disease for these five different countries. For example, the analysis reveals that the infection rate is much higher in the USA, Brazil, and France compared to that of India and Russia, while the recovery rate is found almost the same for these countries. Further, the death rate is measured higher in Brazil as opposed to India, where it is found much lower among the remaining countries. We then use the SEIART compartmental model to characterize the first and second waves of these countries, as well as to investigate and identify the influential model parameters and nature of the virus transmissibility in respective countries. Besides estimating the time-dependent reproduction number (Rt) for these countries, we also use the model to predict the peak size and the time occurring peak in respective countries. The analysis demonstrates that COVID-19 was observed to be much more infectious in the second wave than the first wave in all countries except France. The results also demonstrate that the epidemic took off very quickly in the USA, India, and Brazil compared to two other countries considered in this study. Furthermore, the prediction of the epidemic peak size and time produced by our model provides a very good agreement with the officially confirmed cases data for all countries expect Brazil.

Mathematical modeling of bird flu with vaccination and treatment for the poultry farms.

A deterministic six-compartmental model was developed based on the progression of the disease in poultry, the epidemiological status of the individuals, and intervention measures. The Runge-Kutta method is applied to calculate the variables of the system of equations of the proposed model. The evolution of the epidemic provides some results, such as reproduction number, vaccine efficiency, and antiviral treatment. Numerical results show that the outbreak sizes known as the infected curves increase and decrease with the vaccine limitation rate and treatment rate, respectively, for a specific transmission rate. The calculated results of the reproduction number indicate that avian influenza would spread when vaccine efficiency is less than 70%, and the primary reproduction number is greater than 1. Finally, the disease-free equilibrium of the model is found locally and globally asymptotically stable for R0 < 1.

Trends of 2019-nCoV in South Asian countries and prediction of the epidemic peaks.

A deterministic compartmental model of the corona virus diseases has been introduced to investigate the current outbreak and epidemic peaks of the 2019-nCoV in South Asian countries. We have done details analysis of the above mentioning model and demonstrated its application using publicly reported data. Based on the reported data, we have determined the new infective rate, ß = 0.0017, ß = 0.00069, ß = 0.0011 and ß = 0.00047 for India, Pakistan, Bangladesh and Afghanistan, respectively and these values are not found for other countries due to insufficient data. According to present model, the epidemic under the most restrictive measures was observed of peak on around June 29 in Bangladesh with a peak size of 4100 infectious individuals which was closed to real size of 4014. In the same way, the model results also showed that the epidemic peaks were found on around September 16 in India, June 13 in Pakistan and on June 5 in Afghanistan with the peak sizes of 97,500, 6950 and 935, respectively those were closed to the real values. In addition, we have derived a model-implied basic reproduction number for each day of currently infected cases so that the mitigation and defeat strategies can be imposed to control the size of the epidemic.