Open AccessThe Influence of Total Catastrophe on Simple Birth-Death-Immigration Processes
Author(s) -
Bijoy Kumar Pradhan,
Priyaranjan Dash,
. Upasana
Publication year - 2022
Publication title -
asian research journal of mathematics
Language(s) - English
Resource type - Journals
ISSN - 2456-477X
DOI - 10.9734/arjom/2022/v18i330364
Subject(s) - birth–death process , population , immigration , variance (accounting) , markov process , simple (philosophy) , econometrics , markov chain , state space , birth rate , constant (computer programming) , catastrophe theory , mathematics , statistics , computer science , demography , economics , geography , sociology , engineering , research methodology , philosophy , accounting , archaeology , epistemology , geotechnical engineering , programming language
Markov Models are very much popular in studying population dynamics subject to catastrophes. So, emphasis is given on a discrete state space models specically when the population change occurs as a result of births, deaths and immigration in presence of catastrophes. A transient solution of simple birth-death-immigration process under the influence of total catastrophes has been found where the catastrophes occur at a constant rate and the population size reduces to zero if the catastrophes occur. Since, such processes are completely explained in terms of probability generating function, the mean and variance, we have analyzed the process focusing on these aspects. A simulation study was also carried out to gather evidences towards the results.