Substance addiction such as tobacco, alcohol, opioids, drug addiction and so on are increasing day by day. Awareness about the harmful effects of substance addiction on health and strong will power of people to get rid of the addiction have positive impact on controlling substance addiction. The aim of this research is to examine the impact of awareness and strong determination, the two cognitive factors that have greater impact in preventing substance addiction. Addiction adversely affects self‐efficacy of younger generation, thought processing, metabolisms in human body, psychosocial effects and cardiovascular diseases. In this paper, we have developed a mathematical model regarding substance addiction. It consist of six compartments namely, susceptible class, light substance addict class, risk substance addict class, potential substance addict class, rehabilitation class and quitter class. The substance addiction generation number false(scriptRAfalse) has been determined, and the model is locally asymptotically stable at substance addictions free equilibrium point (SAFEP) scriptD∘ when scriptRA<1. It is found that, when scriptRA=1, a backward bifurcation can occur and when scriptRA>1, the substance addictions persistent equilibrium point (SAPEP) scriptD⋆ becomes stable. Further analysis gives the global asymptotic stability of SAFEP. An application of this model, smoking model, is explored. Smoking model gives a different comparative study which proves the relevance and the importance of our model. We get a clear idea about smokers' behaviour at different stages of high determination and knowledge and also establish the relationship between scriptRA and these parameters. Finally, we give some recommendations for preventing addiction which can be implemented in society.

The asymptotic behavior of four integrated pest management models with stage structure is analyzed in this article. Stage structuring is suggested because almost all pests pass through two stages in their lives, namely immature larvae and mature adults. It is believed that immature susceptible pests and exposed pests are targeted by a natural enemy and infected pests that make them exposed are contacted by susceptible pests (immature and mature). After fixed times, infected pests, and natural enemies are infused impulsively. And we have also

Considering the prevailing situations, the mathematical modeling and dynamics of novel coronavirus (2019-nCoV) particularly in India are studied in this paper. The goal of this work is to create an effective SEIRS model to study about the epidemic. Four different SEIRS models are considered and solved in this paper using an efficient homotopy perturbation method. A clear picture of disease spreading can be obtained from the solutions derived using this method. We parametrized the model by considering the number of infection cases from 1 April 2020 to 30 June 2020. Finally, numerical analysis and graphical representations are provided to interpret the spread of virus.

The primary objective of the current study was to create a mathematical model utilizing fractional-order calculus for the purpose of analyzing the symmetrical characteristics of Wolbachia dissemination among Aedesaegypti mosquitoes. We investigated various strains of Wolbachia to determine the most sustainable one through predicting their dynamics. Wolbachia is an effective tool for controlling mosquito-borne diseases, and several strains have been tested in laboratories and released into outbreak locations. This study aimed to determine the symmetrical features of the most efficient strain from a mathematical perspective. This was accomplished by integrating a density-dependent death rate and the rate of cytoplasmic incompatibility (CI) into the model to examine the spread of Wolbachia and non-Wolbachia mosquitoes. The fractional-order mathematical model developed here is physically meaningful and was assessed for equilibrium points in the presence and absence of disease. Eight equilibrium points were determined, and their local and global stability were determined using the Routh–Hurwitz criterion and linear matrix inequality theory. The basic reproduction number was calculated using the next-generation matrix method. The research also involved conducting numerical simulations to evaluate the behavior of the basic reproduction number for different equilibrium points and identify the optimal CI value for reducing disease spread.