Application of various control strategies to Japanese encephalitic: A mathematical study with human, pig and mosquito

The effectiveness of contact tracing in mitigating COVID-19 outbreak: A model-based analysis in the context of India

The ongoing pandemic situation due to COVID-19 originated from the Wuhan city, China affects the world in an unprecedented scale. Unavailability of totally effective vaccination and proper treatment regimen forces to employ a non-pharmaceutical way of disease mitigation. The world is in desperate demand of useful control intervention to combat the deadly virus. This manuscript introduces a new mathematical model that addresses two different diagnosis efforts and isolation of confirmed cases. The basic reproductive number, R 0 , is inspected, and the model's dynamical characteristics are also studied. We found that with the condition R 0 < 1 , the disease can be eliminated from the system. Further, we fit our proposed model system with cumulative confirmed cases of six Indian states, namely, Maharashtra, Tamil Nadu, Andhra Pradesh, Karnataka, Delhi and West Bengal. Sensitivity analysis carried out to scale the impact of different parameters in determining the size of the epidemic threshold of R 0 . It reveals that unidentified symptomatic cases result in an underestimation of R 0 whereas, diagnosis based on new contact made by confirmed cases can gradually reduce the size of R 0 and hence helps to mitigate the ongoing disease. An optimal control problem is framed using a control variable u ( t ) , projecting the effectiveness of diagnosis based on traced contacts made by a confirmed COVID patient. It is noticed that optimal contact tracing effort reduces R 0 effectively over time.

The influence of vaccination on the control of JE with a standard incidence rate of mosquitoes, pigs and humans

In this article, a nonlinear mathematical model used for the impact of vaccination on the control of infectious disease, Japanese encephalitis with a standard incidence rate of mosquitoes, pigs and humans has been planned and analyzed. During the modeling process, it is expected that the disease spreads only due to get in touch with the susceptible and infected class only. It is also assumed that due to the effect of vaccination, the total human population forms a separate class and avoids contact with the infection. The dynamical behaviors of the system have been explored by using the stability theory of differential equations and numerical simulations. The local and global stability of the system for both equilibrium states under certain conditions has been studied. We have set up a threshold condition in the language of the vaccine-induced reproduction number R ( α 1 ) , which is fewer than unity, the disease dies in the absence of the infected population, otherwise, the infection remains in the population. Furthermore, it is found that vaccine coverage has a substantial effect on the basic reproduction number. Also, by continuous efforts and effectiveness of vaccine coverage, the disease can be eradicated. It is also found a more sensitive parameter for the transmission of Japanese encephalitis virus by using sensitivity analysis. In addition, numerical results are used to investigate the effect of some parameters happening the control of JE infection, for justification of analytical results.

How Socio-Environmental Factors Are Associated with Japanese Encephalitis in Shaanxi, China-A Bayesian Spatial Analysis

Evidence indicated that socio-environmental factors were associated with occurrence of Japanese encephalitis (JE). This study explored the association of climate and socioeconomic factors with JE (2006–2014) in Shaanxi, China. JE data at the county level in Shaanxi were supplied by Shaanxi Center for Disease Control and Prevention. Population and socioeconomic data were obtained from the China Population Census in 2010 and statistical yearbooks. Meteorological data were acquired from the China Meteorological Administration. A Bayesian conditional autoregressive model was used to examine the association of meteorological and socioeconomic factors with JE. A total of 1197 JE cases were included in this study. Urbanization rate was inversely associated with JE incidence during the whole study period. Meteorological variables were significantly associated with JE incidence between 2012 and 2014. The excessive precipitation at lag of 1–2 months in the north of Shaanxi in June 2013 had an impact on the increase of local JE incidence. The spatial residual variations indicated that the whole study area had more stable risk (0.80–1.19 across all the counties) between 2012 and 2014 than earlier years. Public health interventions need to be implemented to reduce JE incidence, especially in rural areas and after extreme weather.

Fish and broiler optimal harvesting models in imprecise environment

In this paper, a two-species harvesting model has been considered and developed a solution procedure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval numbers. A parametric mathematical program is formulated to find the biological equilibrium of the model for different values of parameters. This interval-valued problem is converted into an equivalent crisp model using interval mathematics. The main advantage of the proposed procedure is that different characteristics of the model can be presented in a single framework. Analytically, the existence of steady state and stabilities are looked into. Using mathematical software, the model is illustrated and the results are obtained and presented in tabular and graphical forms.