Mathematical Model and Analysis of Corruption Dynamics with Optimal Control

In this study, a deterministic mathematical model that explains the transmission dynamics of corruption is proposed and analyzed by considering social influence on honest individuals. Positivity and boundedness of solution of the model are proved and basic reproduction number R 0 is computed using the next-generation matrix method. The analysis shows that corruption-free equilibrium is locally and globally asymptotically stable whenever R 0 < 1 . Also, the endemic equilibrium point is locally and globally asymptotically stable whenever R 0 > 1 . Then, the model was extended to optimal control, and some numerical simulations with and without optimal control are also performed to verify the theoretical analysis using MATLAB. Numerical simulation of optimal control model shows that the prevention and punishment strategy is the most effective strategy to reduce the dynamic transmission of corruption.

Drug-sensitivity and passive immunity mathematical epidemiological model for tuberculosis

Regardless of many decades of research, the widespread availability of a vaccine and more recently highly visible WHO efforts to promote a unified global control strategy, Tuberculosis remains a leading cause of infectious mortality. In this paper, a Mathematical Model for Tuberculosis Epidemic with Passive Immunity and Drug-Sensitivity is presented. We carried out analytical studies of the model where the population comprises of eight compartments: passively immune infants, susceptible, latently infected with DS-TB. The Disease Free Equilibrium (DFE) and the Endemic Equilibrium (EE) points were established. The next generation matrix method was used to obtain the reproduction number for drug sensitive (𝑅𝑜𝑠) Tuberculosis. We obtained the disease-free equilibrium for drug sensitive TB which is locally asymptotically stable when 𝑅𝑜𝑠 < 1 indicating that tuberculosis eradication is possible within the population. We also obtained the global stability of the disease-free equilibrium and results showed that the disease-free equilibrium point is globally asymptotically stable when 𝑅𝑜𝑠 ≤ 1 which indicates that tuberculosis naturally dies out.

Mathematical Model of the Transmission Dynamics of Novel Corona Virus (COVID-19) Pandamic Disease with Optimal Control

In this paper, we have developed a deterministic mathematical model that discribe the transmission dynamics of novel corona virus with prevention control. The disease free and endemic equilibrium point of the model were calculated and its stability analysis were prformed. The reproduction number R0 of the model which determine the persistence of the disease or not was calculated by using next generation matrix and also used to determine the stability of the disease free and endemic equilibrium points which exists conditionally. Furthermore, sensitivity analysis of the model was performed on the parameters in the equation of reproduction to determine their relative significance on the transmission dynamics of COVID- 19 pandemic disease. Finally the simulations were carried out using MATLAB R2015b with ode45 solver. The simulation results illustrated that applying prevention control can successfully reduces the transmission dynamic of COVID-19 infectious disease.

Susceptible-Infectious-Critical-Recovered rumor spreading model in social networks

As an important area of social networks, rumor spread has attracted the attention of many scholars. It aims to explore the rumor propagation, and to propose effective measures to curb the further spread of rumors. Different from some existing works, this paper believes that susceptible persons affected by rumor-refuting information will first enter the critical state, while ones who related to rumors will directly turn into the spread state. Therefore, this paper proposes a Susceptible-Infectious-Critical-Recovered (SICR) rumor model. In addition, considering that infectious persons with high levels of refuting rumors may cause emotional resonance among individuals, this model adds a connecting edge from the recovered to the infectious who are triggered by the information of refuting the rumors. First, the basic regeneration number [Formula: see text] is obtained by using the next generation matrix method. Then, the global stability of the rumor-free equilibrium [Formula: see text] and the persistence of rumor propagation are proved in detail in theoretical analysis. The simulation results show that the existence of a critical state can reduce the influence of rumors. Rumor refutation mechanism, as soon as possible to curb the spread of rumors, is an effective measure.

THE IMPACT OF TESTING AND TREATMENT ON THE DYNAMICS OF HEPATITIS B VIRUS

Despite the intervention of WHO on vaccination for reducing the spread of Hepatitis B Virus (HBV), there are records of the high prevalence of HBV in some regions. In this paper, a mathematical model was formulated to analyze the acquisition and transmission process of the virus with the view of identifying the possible way of reducing the menace and mitigating the risk of the virus. The models' positivity and boundedness were demonstrated using well-known theorems. Equating the differential equations to zero demonstrates the equilibria of the solutions i.e., the disease-free and endemic equilibrium. The next Generation Matrix method was used to compute the basic reproduction number for the models. Local and global stabilities of the models were shown via linearization and Lyapunov function methods respectively. The importance of testing and treatment on the dynamics of HBV were fully discussed in this paper. It was discovered that testing at the acute stage of the virus and chronic unaware state helps in better management of the virus.

SCIR rumor propagation model with the chord mechanism in social networks

Rumors, as a typical social phenomenon in real life, have a negative impact on the harmony of the society. When people hear rumors, they may not resonate with rumors because they do not trust them during the process of rumors transmission. Thus, they will not spread rumors. The essential difference between chord mechanism and spreader mechanism is that spreaders will spread regardless of whether they think it is true or false. The chord needs to believe that the rumor is true in order to keep spreading it, otherwise they become immune to spreading it. Therefore, this paper proposes a new Spreader-Chord-Ignorant-Restorer (SCIR) model, which considers that the trust may affect the level of empathy. Since the level of trust affects the spread of rumors and the extent to which the immune person trusts the rumor is different, the connecting edges from the restorer to the chord and the restorer to the ignorant were added to the model. First, the basic reproductive number [Formula: see text] is derived by the next generation matrix method and thus equilibriums are obtained. Then, the global stability of the rumor-free equilibrium [Formula: see text] and the persistence of rumor propagation are proved in detail during the theoretical analysis.

A Mathematical Model of COVID-19 Pandemic: A Case Study of Bangkok, Thailand

In this study, we propose a new mathematical model and analyze it to understand the transmission dynamics of the COVID-19 pandemic in Bangkok, Thailand. It is divided into seven compartmental classes, namely, susceptible S , exposed E , symptomatically infected I s , asymptomatically infected I a , quarantined Q , recovered R , and death D , respectively. The next-generation matrix approach was used to compute the basic reproduction number denoted as R cvd 19 of the proposed model. The results show that the disease-free equilibrium is globally asymptotically stable if R cvd 19 < 1 . On the other hand, the global asymptotic stability of the endemic equilibrium occurs if R cvd 19 > 1 . The mathematical analysis of the model is supported using numerical simulations. Moreover, the model’s analysis and numerical results prove that the consistent use of face masks would go on a long way in reducing the COVID-19 pandemic.

Mathematical modelling of the COVID-19 pandemic with demographic effects

In this paper, a latent infection susceptible–exposed–infectious–recovered model with demographic effects is used to understand the dynamics of the COVID-19 pandemics. We calculate the basic reproduction number ($${R}_{0}$$ R 0 ) by solving the differential equations of the model and also using next-generation matrix method. We also prove the global stability of the model using the Lyapunov method. We showed that when the $${R}_{0}<1$$ R 0 < 1 or $${R}_{0}\le 1$$ R 0 ≤ 1 and $${R}_{0}>1$$ R 0 > 1 or $${R}_{0}\ge 1$$ R 0 ≥ 1 the disease-free and endemic equilibria asymptotic stability exist theoretically. We provide numerical simulations to demonstrate the detrimental impact of the direct and latent infections for the COVID-19 pandemic.

Projecting a second wave of COVID-19 in Japan with variable interventions in high-risk settings

An initial set of interventions, including the closure of host and hostess clubs and voluntary limitation of non-household contact, probably greatly contributed to reducing the disease incidence of coronavirus disease (COVID-19) in Japan, but this approach must eventually be replaced by a more sustainable strategy. To characterize such a possible exit strategy from the restrictive guidelines, we quantified the next-generation matrix, accounting for high- and low-risk transmission settings. This matrix was used to project the future incidence in Tokyo and Osaka after the state of emergency is lifted, presenting multiple ‘post-emergency’ scenarios with different levels of restriction. The effective reproduction numbers ( R ) for the increasing phase, the transition phase and the state-of-emergency phase in the first wave of the disease were estimated as 1.78 (95% credible interval (CrI): 1.73–1.82), 0.74 (95% CrI: 0.71–0.78) and 0.63 (95% CrI: 0.61–0.65), respectively, in Tokyo and as 1.58 (95% CrI: 1.51–1.64), 1.20 (95% CrI: 1.15–1.25) and 0.48 (95% CrI: 0.44–0.51), respectively, in Osaka. Projections showed that a 50% decrease in the high-risk transmission is required to keep R less than 1 in both locations—a level necessary to maintain control of the epidemic and minimize the risk of resurgence.

Dynamical Analysis of a Mathematical Model of COVID-19 Spreading on Networks

In this article, an SEAIRS model of COVID-19 epidemic on networks is established and analyzed. Following the method of the next-generation matrix, we derive the basic reproduction number R0, and it shows that the asymptomatic infector plays an important role in disease spreading. We analytically show that the disease-free equilibrium E0 is asymptotically stable if R0≤1; moreover, the effects of various quarantine strategies are investigated and compared by numerical simulations. The results obtained are informative for us to further understand the asymptomatic infector in COVID-19 propagation and get some effective strategies to control the disease.