Modelling scholastic underachievement as a contagious disease

Abstract

Communicated by: R. Anguelov MSC Classification: 92D25; 92D30 Some factors related to students behaviour are perceived to be important for academic failure. Such of these factors and some other factors contribute immensely to the problem of scholastic underachievement that is spreading among students of Kano University of Science and Technology, Wudil-Nigeria.Considering such a problem as a contagious disease, we propose a mathematical model to study how this problem is spread in Kano University of Science and Technology, Wudil campus. The model analysis reveals that the reproduction numbers are sufficient to predict whether the problem can persist in the campus environment. Indeed, endemic persistence occurs if the pattern of recruiting new members is through both transition and progression. The sensitivity analysis of the parameters of the model threshold quantities shows that reducing the rates of recruiting new students to weak class through both transition and progression is an effective measure of containing the problem.

Dynamics of Toxoplasmosis Disease in Cats population with vaccination

“…One can observe from Section 3, that the disease persistence or otherwise in a community is determined by the threshold parameter R v . Moreover, the uniqueness properties of both disease-free (P 0 ) and endemic (P e ) equilibria indicate that there is an exchange of stability between P 0 and P e when R v = 1 (i.e., P 0 undergoes a transcritical bifurcation at R v = 1, see for instance [23,Theorem 4]). However, it is instructive to investigate the model parameter that has greatest effect on this threshold parameter, thereby having same effect on the toxoplasmosis disease persistence.…”

E‐cigarette smoking with peer pressure

“…In particular, SIR models and ramifications thereof, such as those involving conformity bias (Walters, Walters and Kendal, and Bissell), incorporating external information (Buonomo et al and Giacobbe et al), and allowing for multi‐patch models (Wang and Mulone), have been employed in modelling alcohol studies (Mulone and Straughan,) Huo and Song, Huo and Wang, Giacobbe et al, and Walters, in drug models (Mushanyu, Nyabadza, Mulone and Straughan), in smoking (Sharomi and Gumel, Bissell, Caiado, and Bissell et al), in bulimia studies (Gonzalez et al and Ciarcia et al), in modelling possible eradication of polio (Pomeroy), in analysing rabies in dogs (Ruan), in childhood disease (Srivastava and Günerhan), in academic underachievement (Usaini et al), and many others.…”

“…Our objective here is to present and analyse an SIR or SI like ODE model for non-smokers, tobacco smokers, and those who smoke e-cigarettes, incorporating peer pressure in the switch from tobacco to e-cigarette smoking. We note that differential equation models have been used extensively in modelling social problems and related issues, including the spread of infections; see, eg, Bissell,7,8 Bissell et al, 9 Buonomo et al, 10 Caiado, 11 Ciarcia et al, 12 Giacobbe and Mulone, 13 Giacobbe et al, 14 Gonzalez et al, 15 Guo et al, 16 Hethcote et al, 17 Huo and Song, 18 Huo and Wang, 19 Jung et al, 20 Mulone and Straughan, 21,22 Mulone et al, 23 Mushanyu et al, 24 Nyabadza et al, 25 Pomeroy, 26 Sharomi and Gumel, 27 Srivastava and Günerhan, 28 Straughan, 29 Takeuchi et al, 30 Usaini et al, 31 Walters, 32 Walters and Kendal, 33 Wang, 34 Wang et al, 35 Wang and Mulone, 36 Wang and Zhao, 37,38 Wang and Zou, 39 and Zhou et al 40 In particular, SIR models and ramifications thereof, such as those involving conformity bias (Walters, 32 Walters and Kendal, 33 and Bissell 8 ), incorporating external information (Buonomo et al 10 and Giacobbe et al 14 ), and allowing for multi-patch models (Wang and Mulone 36 ), have been employed in...…”

“…Our objective here is to present and analyse an SIR or SI like ODE model for non‐smokers, tobacco smokers, and those who smoke e‐cigarettes, incorporating peer pressure in the switch from tobacco to e‐cigarette smoking. We note that differential equation models have been used extensively in modelling social problems and related issues, including the spread of infections; see, eg, Bissell, Bissell et al, Buonomo et al, Caiado, Ciarcia et al, Giacobbe and Mulone, Giacobbe et al, Gonzalez et al, Guo et al, Hethcote et al, Huo and Song, Huo and Wang, Jung et al, Mulone and Straughan, Mulone et al, Mushanyu et al, Nyabadza et al, Pomeroy, Sharomi and Gumel, Srivastava and Günerhan, Straughan, Takeuchi et al, Usaini et al, Walters, Walters and Kendal, Wang, Wang et al, Wang and Mulone, Wang and Zhao, Wang and Zou, and Zhou et al …”

Dynamical analysis of chikungunya and dengue co-infection model

“…Thus, the region Ω is positive-invariant, and it is sufficient to consider solutions restricted in Ω. In this region, the usual existence, uniqueness and continuation results hold for the model Eqns (1)-(2) [21,43]. Table 2. 3.…”