scholarly journals Nonlinear Analysis of the Dynamics of Criminality and Victimisation: A Mathematical Model with Case Generation and Forwarding

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Chikodili Helen Ugwuishiwu ◽  
D. S. Sarki ◽  
G. C. E. Mbah

In this paper, a system of deterministic model is presented for the dynamical analysis of the interactional consequence of criminals and criminality on victimisation under two distinguishable forms of rehabilitation—the behavioural reformation of criminals and the emotional psychotherapy of victims. A threshold value, R0=maxRK,RV, responsible for the persistence of crime/criminality and victimisation, is obtained and, using it, stability analyses on the model performed. The impact of an effective implementation of the two forms of rehabilitation was found to be substantial on crime and criminality, while an ineffective implementation of same was observed to have a detrimental consequence. The prevention of repeat victimisation was seen to present a more viable option for containing crime than the noncriminalisation of victims. Further, the removal of criminals, either through quitting or death, among others, was also found to have a huge positive impact. Numerical simulations were performed for a variety of mixing criminal scenarios to verify the analytical results obtained.

2012 ◽  
Vol 05 (04) ◽  
pp. 1250029 ◽  
Author(s):  
S. MUSHAYABASA ◽  
C. P. BHUNU

A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemiological threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuberculosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.


2019 ◽  
Vol 10 (1) ◽  
pp. 112 ◽  
Author(s):  
KamiliaKamilia LoukilLoukil

We investigate in this paper the effect of financial development on innovation in emerging and developing countries. The estimation of panel threshold model for a sample 54 countries during the period 1980-2009 shows the presence of non linear effects in the relationship between financial development and innovation. We find a threshold value of economic development below which the financial development level has no significant impact on innovation and above which financial development has a significant positive impact on innovation. In sum, our findings suggest that the presence of a healthy economic environment is crucial for financial institutions to offer high-quality financial services, promoting more innovation.


2016 ◽  
Vol 09 (03) ◽  
pp. 1650038 ◽  
Author(s):  
Aida Mojaver ◽  
Hossein Kheiri

In this paper, we deal with the problem of optimal control of a deterministic model of hepatitis C virus (HCV). In the first part of our analysis, a mathematical modeling of HCV dynamics which can be controlled by antiretroviral therapy as fixed controls has been presented and analyzed which incorporates two mechanisms: infection by free virions and the direct cell-to-cell transmission. Basic reproduction number is calculated and the existence and stability of equilibria are investigated. In the second part, the optimal control problem representing drug treatment strategies of the model is explored considering control parameters as time-dependent in order to minimize not only the population of infected cells but also the associated costs. At the end of the paper, the impact of combination of the strategies in the control of HCV and their effectiveness are compared by numerical simulation.


Author(s):  
Liming Cai ◽  
Peixia Yue ◽  
Mini Ghosh ◽  
Xuezhi Li

Schistosomiasis is a snail-borne parasitic disease, which is affecting almost 240 million people worldwide. The number of humans affected by schistosomiasis is continuously increasing with the rise in the use of agrochemicals. In this paper, a mathematical model is formulated and analyzed to assess the effect of agrochemicals on the transmission of schistosomiasis. The proposed model incorporates the effects of fertilizers, herbicides and insecticides on susceptible snails and snail predators along with schistosomiasis disease transmission. The existence and stability of the equilibria in the model are discussed. Sensitivity analysis is performed to identify the key parameters of the proposed model, which contributes most in the transmission of this disease. Numerical simulations are also performed to assess the impact of fertilizers, herbicides and insecticides on schistosomiasis outbreaks. Our study reveals that the agricultural pollution can enhance the transmission intensity of schistosomiasis, and in order to prevent the outbreak of schistosomiasis, the use of pesticides should be controlled.


2013 ◽  
Vol 724 ◽  
pp. 553-580 ◽  
Author(s):  
Ivo R. Peters ◽  
Devaraj van der Meer ◽  
J. M. Gordillo

AbstractIn this paper we analyse the impact of a circular disc on a free surface using experiments, potential flow numerical simulations and theory. We focus our attention both on the study of the generation and possible breakup of the splash wave created after the impact and on the calculation of the force on the disc. We have experimentally found that drops are only ejected from the rim located at the top part of the splash – giving rise to what is known as the crown splash – if the impact Weber number exceeds a threshold value ${\mathit{We}}_{crit} \simeq 140$. We explain this threshold by defining a local Bond number $B{o}_{\mathit{tip}} $ based on the rim deceleration and its radius of curvature, with which we show using both numerical simulations and experiments that a crown splash only occurs when $B{o}_{\mathit{tip}} \gtrsim 1$, revealing that the rim disrupts due to a Rayleigh–Taylor instability. Neglecting the effect of air, we show that the flow in the region close to the disc edge possesses a Weber-number-dependent self-similar structure for every Weber number. From this we demonstrate that ${\mathit{Bo}}_{\mathit{tip}} \propto \mathit{We}$, explaining both why the transition to crown splash can be characterized in terms of the impact Weber number and why this transition occurs for $W{e}_{crit} \simeq 140$. Next, including the effect of air, we have developed a theory which predicts the time-varying thickness of the very thin air cushion that is entrapped between the impacting solid and the liquid. Our analysis reveals that gas critically affects the velocity of propagation of the splash wave as well as the time-varying force on the disc, ${F}_{D} $. The existence of the air layer also limits the range of times in which the self-similar solution is valid and, accordingly, the maximum deceleration experienced by the liquid rim, that sets the length scale of the splash drops ejected when $We\gt {\mathit{We}}_{crit} $.


2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Cai Shukai ◽  
Wang Haochen ◽  
Zhou Xiaohong

This paper proposed a substantial gap to a large-scale population density and city size on regional innovation output. To measure the impact of population density and city size on regional innovation output, this study employs the threshold effect model with panel data of 230 prefectures and cities from 2007 to 2016. Based on the econometric analysis, the results exhibit a positive and significant relationship between population density, city size, and innovation output. This correlation suggests that when one factor increases, the other increases in the parallel direction and vice versa. Moreover, when the city size expands the threshold value of 2.934 percent, the innovation promotes and increases the effects of urban-scale expansion. On the other hand, for medium- and low-density cities, the increase of urban population density has a significant and positive impact on urban innovation output. However, for high-density cities, the increase of population density has no significant impact on innovation output.


2020 ◽  
Vol 28 (02) ◽  
pp. 475-513
Author(s):  
KATIA VOGT-GEISSE ◽  
CALISTUS N. NGONGHALA ◽  
ZHILAN FENG

A deterministic model for the effects on disease prevalence of the most advanced pre-erythrocytic vaccine against malaria is proposed and studied. The model includes two vaccinated classes that correspond to initially vaccinated and booster dose vaccinated individuals. These two classes are structured by time-since-initial-vaccination (vaccine-age). This structure is a novelty for vector–host models; it allows us to explore the effects of parameters that describe timed and delayed delivery of a booster dose, and immunity waning on disease prevalence. Incorporating two vaccinated classes can predict more accurately threshold vaccination coverages for disease eradication under multi-dose vaccination programs. We derive a vaccine-age-structured control reproduction number [Formula: see text] and establish conditions for the existence and stability of equilibria to the system. The model is bistable when [Formula: see text]. In particular, it exhibits a backward (sub-critical) bifurcation, indicating that [Formula: see text] is no longer the threshold value for disease eradication. Thus, to achieve eradication we must identify and implement control measures that will reduce [Formula: see text] to a value smaller than unity. Therefore, it is crucial to be cautious when using [Formula: see text] to guide public health policy, although it remains a key quantity for decision making. Our results show that if the booster vaccine dose is administered with delay, individuals may not acquire its full protective effect, and that incorporating waning efficacy into the system improves the accuracy of the model outcomes. This study suggests that it is critical to follow vaccination schedules closely, and anticipate the consequences of delays in those schedules.


2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Augustine S. Mbitila ◽  
Jean M. Tchuenche

A classical epidemiological framework is used to qualitatively assess the impact of early detection and treatment on the dynamics of HIV/AIDS. Within this theoretical framework, two classes of infected populations: those infected but unaware of their serological status and those who are aware of their disease status, are considered. In this context, we formulate and analyze a deterministic model for the transmission dynamics of HIV/AIDS and assess the potential population-level impact of early detection in curtailing the epidemic. A critical threshold parameter for which case detection will have a positive impact is derived. Model parameters sensitivity analysis indicates that the number of partners is the most sensitive (in increasing the average number of secondary transmission) parameter. However, the case detection coverage is the main drivers in reducing the initial disease transmission. Numerical simulations of the model are provided to support the analytical results. Early detection and treatment alone are insufficient to eliminate the disease, and other control strategies are to be explored.


2019 ◽  
Vol 45 (2) ◽  
pp. 190-221 ◽  
Author(s):  
Domenico Piatti ◽  
Peter Cincinelli

PurposeThe purpose of this paper is to investigate whether the quality of the credit process is sensitive to reaching a particular threshold level of non-performing loans (NPLs) and, more importantly, whether higher NPLs ratios could make the monitoring activity ineffective.Design/methodology/approachThe empirical design is composed of two steps: in the first step, the authors introduce a monitoring performance indicator (MPI) of the credit process by combining the non-parametric technique Data Envelopment Analysis with some financial ratios adopted as input and output variables. As second step, the authors apply a threshold panel regression model to a sample of 298 Italian banks, over the time period 2006–2014, and the authors investigate whether the quality of the credit process is sensitive to reaching a particular threshold level of NPLs.FindingsThis paper finds that, first, when the NPLs ratio remains below the threshold value estimated endogenously, an increase in the quality of monitoring has a positive impact on the NPLs ratio. Second, if the NPLs ratio exceeds the estimated threshold, the relationship between the NPLs ratio and quality of monitoring assumes a positive value and is statistically significant.Research limitations/implicationsDue to the lack of data, the investigation of NPLs in the Italian industry across loan types combined with the monitoring effort by banks management was not possible. The authors plan to investigate this topic in future studies.Practical implicationsThe identification of the threshold has a double operational valence. The first regards the Supervisory Authority, the threshold approach could be used as an early warning in order to introduce active control strategies based on the additional information requested or by on-site inspections. The second implication is highlighted in relation to the individual banks, the monitoring of credit control quality, if objective and comparable, could facilitate the emergence of best practices among banks.Social implicationsA high NPLs ratio requires greater loan provisions, which reduces capital resources available for lending, and dents bank profitability. Moreover, structural weaknesses on banks’ balance sheets still persist particularly in relation to the inadequate internal governance structures. This means that bank management must able to recognise in advance early warning signals by providing prudent measurement together with an in-depth valuation of loans portfolio.Originality/valueThe originality of the paper is twofold: the authors introduce a new proxy of credit monitoring, called MPI; the authors provide an empirical proof of the Diamond’s (1991) economic intuition: for riskier borrowers, the monitoring activity is an inappropriate instrument depending on the bad reputational quality of borrowers.


2019 ◽  
Vol 12 (03) ◽  
pp. 1950030 ◽  
Author(s):  
Wei Liu ◽  
Yaolin Jiang

In this paper, an eco-economic model with harvesting on biological population is established, which takes the form of a differential-algebra system. The impact of the economic profit from harvesting upon the dynamics of the model is studied. By using a suitable parameterization for the differential-algebra system, we derive an equivalent parameterized system which gives the stability results for the positive equilibrium point of our model. Moreover, based on the parameterized system as well as the approaches of normal form and formal series, the conditions on the Hopf bifurcation and the stability of center are obtained. Several numerical simulations for demonstrating the theoretical results are also presented. Lastly, according to the dynamical analysis, we provide a threshold value for the economic profit, which can maintain the sustainable development of our eco-economic system.


Sign in / Sign up

Export Citation Format

Share Document