Mathematical Modeling and Stability Analysis of Japanese Encephalitis

Abstract

Mathematical modeling of Japanese encephalitis (JE) disease in human population with pig and mosquito has been presented in this paper. The proposed model, which involves three compartments of human (Susceptible, Vaccinated, Infected), two compartments of mosquito (Susceptible, Infected) and three compartments of the pig (Susceptible, Vaccinated, Infected). In this work, it is assumed that JE spreads between susceptible class and infected mosquitoes only. Basic results like boundedness of the model, the existence of equilibrium and local stability issues are investigated. Here, to measure the disease transmission potential in the population the basic reproduction number (R0) from the system has been analyzed w.r.t. control parameters both numerically and theoretically. The dynamical behaviors of the system have been analyzed by using the stability theory of differential equations and numerical simulations at equilibrium points. A numerical verification of results is carried out of the model under consideration.

Scoping review of Japanese encephalitis virus transmission models

“…Eleven models included parameters on the vaccination rate of susceptible humans or treatment rate of JEV infected humans (Baniya and Keval 2021c, 2020b, 2021bDe et al 2016;Dwivedi, Keval, and Baniya 2022;Goswami 2022;Kalita and Devi 2020b;Kharismawati and Fatmawati 2019;Mukhopadhyay and Tapaswi 1994;Panja, Mondal, and Chattopadhyay 2016), nine models included parameters on the vaccination rate of susceptible reservoir-animal populations or treatment of JEV infected reservoir-animal populations Keval 2020b, 2020a;De et al 2016;Goswami 2022;Khan et al 2014;Kharismawati and Fatmawati 2019;Panja, Mondal, and Chattopadhyay 2016;Wada 1975;Zhao et al 2018), and four models included an insecticide control parameter which influenced the total mosquito population (De et al 2016;Goswami 2022;Kharismawati and Fatmawati 2019;Panja, Mondal, and Chattopadhyay 2016). Six models evaluated the effectiveness and cost-effectiveness of various prevention and control strategies to recommend best approaches (Baniya and Keval 2020a;De et al 2016;Goswami 2022;Kharismawati and Fatmawati 2019;Ladreyt, Chevalier, and Durand 2022;Panja, Mondal, and Chattopadhyay 2016). Lastly, two models assessed the impact of changing the proportions of competent and non-competent hosts within a community (Ladreyt, Chevalier, and Durand 2022;Zahid and Kribs 2021) and one explored the use of dogs as sentinel surveillance for JEV circulation (Ladreyt, Chevalier, and Durand 2022).…”

The impact of time delay in the transmission of Japanese encephalitis without vaccination

“…In this way, an investigation of the dynamics of JEV transmission and the methodology for its control is funda-P r o y e c c i o n e s ( A n t o f a g a s t a ) -P r e -p r o o f Proyecciones (Antofagasta) -Pre-proof -doi: 10.22199/issn.0717-6279-4629 mental. The modified model of Japanese encephalitis has been constructed by the work of Tapaswi et al, [9], De et al, [16] and Baniya et al, [13,17].…”

A comparative series solutions of Japanese encephalitis model using differential transform method and variational iteration method

“…Lately, there has been an increasing interest in an infectious transmission disease model. The researchers 2‐10 have developed a mathematical epidemic model and studied it mathematically. Furthermore, several researchers have been working in different real‐world situations and engineering sectors to find analytical and numerical solutions by using a variety of numerical techniques, for instance, Shah et al 11 have implemented two well‐known analytical techniques to solve fractional‐order multidimensional Navier–Stokes equation.…”