Dynamic modelling and analysis of human brucellosis on age heterogeneity in Jinzhou, China.

This article discusses the mathematical model of the spread of COVID-19 by considering vaccination and population migration. The former model is analyzed by determining the equilibrium point, basic reproduction number, analyzing the stability of the equilibrium point, sensitivity analysis, and accompanied by numerical simulation. Analysis of the stability of disease-free and endemic equilibrium points using the Routh-Hurwitz Criteria and the Castillo-Chaves and Song theorems. The results of the analysis show that there are two equilibrium points, namely a disease-free equilibrium point (T1), which is locally asymptotically stable when R0 1, and an endemic equilibrium point (T2), which is locally asymptotically stable when R0 1. Furthermore, the sensitivity analysis showed that the most sensitive parameters to changes in the basic reproduction number were the emigration rate parameter (m2) and the infection probability parameter after contact between infected and susceptible individuals without vaccination (h). In addition, the numerical simulation results show that the sensitive parameter values, namely m2, h, zse, g, and # have a significant effect on the basic reproduction numbers. Suppressing the chance of infection in susceptible individuals and the rate of contact between susceptible and exposed individuals, as well as increasing the number of individuals who emigrate and who are vaccinated, can reduce the transmission of COVID-19.

This study developed a model for the spread of measles based on the SEIR model by adding the factors of using the first dose of vaccination, the second dose of vaccination, and treatment. Making this model begins with making a compartment diagram of the spread of the disease, which consists of seven subpopulations, namely susceptible subpopulations, subpopulations that have received the first dose of vaccination, subpopulations that have received the second dose vaccination, exposed subpopulations, infected subpopulations, subpopulations that have received treatment, and subpopulations healed. After the model is formed, the disease-free equilibrium point, endemic equilibrium point, and basic reproduction number (R_0) are obtained. Analysis of the stability of the disease-for equilibrium point was locally asymptotically stable when (R_0)<1. The backward bifurcation analysis occurs when (R_C) is present and R_C<R_0. Numerical simulations of disease-free and endemic equilibrium points are carried out to provide an overview of the results analyzed with parameter values from several sources. The results of the numerical simulation are in line with the analysis carried out. From the model analysis, the disease will disappear more quickly when the level of vaccine used and individuals who carry out treatment are enlarged.

Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis. The disease is considered dangerous because it infects the lungs and other organs of the body and can lead to death. This study discusses a mathematical model for the spread of tuberculosis with two treatment sites as an effort to reduce the transmission rate of TB cases. Treatment for TB patients can be done at home and in hospitals. The purpose of this study was to construct a mathematical model and analyze the qualitative behavior of the TB spread model. The construction of the model uses the SEIR epidemic model which is divided into five subpopulations, namely susceptible subpopulations, latent subpopulations, infected subpopulations receiving treatment at home, and infected subpopulations receiving treatment at the hospital, and cured subpopulations. The analysis of qualitative behavior in the model includes determining the local and global equilibrium and stability points. The results of the analysis shows that the model has two equilibrium points, namely a disease-free equilibrium point and the endemic equilibrium point. The existence of endemic equilibrium point and the local and global stability of the two equilibrium points depend on the basic reproduction number denoted by . If , there is only disease-free equilibrium point. If , there are two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. Stability analysis shows that the disease-free equilibrium point is locally and globally asymptotically stable if . While, if , the endemic equilibrium point will be asymptotically stable locally and globally.

We present in this research work, mathematical modeling of the transmission dynamics of measles using treatment as a control measure. We determined the Disease Free Equilibrium (DFE) point of the model after which we obtained the Basic Reproduction Number ( R0 ) of the model using the next generation approach. The model Endemic Equilibrium (EE) point was also determined after which we performed Local Stability Analysis(LAS) of the Disease Free Equilibrium point and result shows that the Disease Free Equilibrium point of the model would be stable if ( R0 <1). Global Stability Analysis (GAS) result shows that, ( R0 ≤ 1) remains the necessary and sufficient condition for the infection to go into extinction from a population. We carried out Sensitivity Analysis of the model using the Basic Reproduction Number and we discovered that ( δ , μ, ν , θ ) are sensitive parameters that should be targeted towards control intervention strategy as an increase in these values can reduce the value of ( R0 ) to a value less than unity and such can reduce the spread of measles in a population. Model simulation was carried out using mat lab software to support our analytical results.

Pertussis is a highly contagious respiratory disease that is easily prevented by immunisation. The risk of whooping cough is particularly high for neonates. However, due to a lack of vaccinations against pertussis, the disease is still widespread in several nations, particularly in the wake of the COVID-19 pandemic. In this paper, a deterministic mathematical model that describes the transmission dynamics of pertussis for assessing the impact of booster vaccines and isolation was proposed. The model comprises two equilibrium points, the DFE (disease free equilibrium point) and the EEP (endemic equilibrium point), as demonstrated by the determination of the solution's positivity and boundedness as well as the presence of disease equilibria in the mathematical analysis section. It was discovered that if {R}_c < 1, the DFE is both locally and globally asymptotically stable. The endemic equilibrium point, has been shown to be globally asymptotically stable if the basic reproduction number is greater than unity and $\omega=\psi=\phi_1=v=\delta=0$. This has been determined using a nonlinear Lyapunov function of the Go-Volterra type. Sensitivity analysis demonstrates that isolation and vaccine rates are highly sensitive in lowering the control reproduction number. Numerical simulation of model eq. (1) shows that the isolation rate of affected people and booster are crucial parameters for managing pertussis in a community

In this paper, a fractional-order model of hepatitis C virus (HCV) with inhibition due to infection is studied. Based on the basic reproduction number, backward bifurcation of such model is investigated under some conditions. When the efficacy of interferon-α therapy is low, it is shown that the phenomenon of backward bifurcation will appear in the model. It means that there coexist disease-free and endemic equilibrium points. Then a critical basic reproduction number is given, which could be used as a threshold to control the virus. Using the generalized Lasalle invariant set principle, it is found that the disease-free equilibrium point of the model is globally asymptotically stable. The optimal efficacy of interferon-α therapy is also studied. Numerical simulations have been used to verify the theoretical analysis.

The human papillomavirus (HPV) is one of the viruses that can cause cervical cancer. However, vaccination can prevent such a virus. The spread of the virus in cervical cancer can be modelled in the SI model, however, such a model has not produced accurate results. The development and extension of the model into S1S2IRC, with S1 denoting the population aged 0–10 years and S2 representing the population over 10 years, which is susceptible to HPV infection. The results produce disease-free and endemic equilibrium points. The analysis of the equilibrium points yields that the disease-free equilibrium point will be asymptotically stable for R0 1 and R0 1 for the endemic equilibrium point. The results indicate that the higher the probability of humans being prone to the HPV virus, the greater the chance of these individuals being infected by the virus. Therefore, vaccination is required to protect against the virus infection.

This research focus on dynamical analysis of a SIQRVB (Susceptible-Infectious-Quarantined-Recovered-Vaccinated-Bacterial) model. It describe the spread of cholerae with quarantine, vaccination and two transmission paths. As is well-known, there mainly exist two transmission paths for cholerae: environment-to-human transmission and human-to-human transmission. This model has two equilibrium points, that is disease-free equilibrium point which always exists and an endemic equilibrium point that exists with some conditions. The local stability of the equilibrium points is investigated by using Routh-Hurwitz criteria. The method of Next Generation Matrix is applied to get the basic reproduction number R0 . It can be shown numerically that disease-free equilibrium point is locally asymptotic stable when R0 < 1, while the endemic equilibrium point exist and locally asymptotic stable when satisfy Routh-Hurwitz criteria. Numerical simulations are given to illustrate the theoretical results.

Psittacosis is a disease in human beings that is commonly associated with pet birds such as cockatiels and parrots, and among poultry such as ducks and turkeys. This paper proposed and developed a deterministic epidemiological model that explains the transmission dynamics of Psittacosis infection in humans and poultry. The Psittacosis deterministic model was analyzed to determine positivity of the solution set, the invariant feasible region, the basic reproduction number, the disease free equilibrium points, the endemic equilibrium points and the corresponding stability of each of the equilibrium points. The basic reproduction number is calculated using the next generation matrix and it was found to be entirely dependent on the poultry population parameters. The study established that whenever R0 < 1, Psittacosis dies out from the population and when R0 > 1, Psittacosis keeps persisting in the population. Sensitivity analysis was conducted to determine the contribution of each parameter to the basic reproduction number. The more sensitive parameters were found to be responsible for the further propagation of Psittacosis while the less sensitive parameters rarely contributed to the spread. Stability analysis of both the disease free equilibrium and the Endemic equilibrium were conducted. Lastly, numerical simulation was conducted to justify quantitative analysis of the dynamics of the transmission of Psittacosis.

A deterministic model is proposed to describe the transmission dynamics of coronavirus infection with early interventions. Epidemiological studies have employed modeling to unravel knowledge that transformed the lives of families, communities, nations and the entire globe. The study established the stability of both disease free and endemic equilibria. Stability occurs when the reproduction number, R0, is less than unity for both disease free and endemic equilibrium points. The global stability of the disease-free equilibrium point of the model is established whenever the basic reproduction number R0 is less than or equal to unity. The reproduction number is also shown to be directly related to the transmission probability (β), rate at which latently infected individuals join the infected class (δ) and rate of recruitment (Λ). It is inversely related to natural death rate (μ), rate of early treatment (τ 1), rate of hospitalization of infected individuals (θ) and Covid-induced death rate (σ). The analytical results established are confirmed by numerical simulation of the model.

Mathematical models are often used to describe phenomena in the field of biology, such as the spread of infectious diseases, one of which is HIV/AIDS. The prevention of HIV/AIDS is through education on the dangers of HIV/AIDS, and ART treatment for HIV positive individuals to increase immunity. The purpose of this study is to analyze the dynamic mathematical model of the transmission of HIV/AIDS with ART treatment and education. This research is a literature study. This study develops the SITA model, by including compartments of susceptible individuals who are aware of the spread of HIV/AIDS and add several parameters to the model. Based on the mathematical model used, two equilibrium points are obtained, namely the disease-free equilibrium point and the endemic equilibrium point, the basic reproduction number and stability analysis around the stability point. Based on the data used, a simulation of the transmission of HIV/AIDS was obtained at both equilibrium points. The stability analysis shows that the disease-free equilibrium point is locally asymptotically stable if R0&lt;1.

Modelling of infectious diseases was investigated by several authors using mathematical methods. Here, we consider the model in which inhibition effect is taken into consideration in presence of delay of the infected to become infectious. In this model two equilibrium points are found, one is disease free equilibrium point and the other is the endemic equilibrium point. The endemic equilibrium point will exists under certain condition. The character of solutions in the neighbourhood of endemic equilibrium point is directly affected by inhibitory effect. The solutions in the neighbourhood of disease free equilibrium point will be asymptotically stable when the basic reproduction number less than one and the solution in the neighbourhood of endemic equilibrium point will be asymptotically stable when the basic reproduction number greater than one.

COVID-19 pandemic has posed an unprecedented threat to global public health. Health profes sionals caring for COVID-19 patients face insomnia, mental stress, physical exhaustion, stigma, the pain of losing patients and colleagues. Many of them acquired SARS-CoV-2 and some died. Protection of this workforce is of paramount importance to ensure optimal care to patients. Thus, this study contributes to the subject by formulating a deterministic mathematical model SW E IsIaHR (Susceptible - Healthcare workers - Exposed - Symptomatic - Asymptomatic - Hospi talized - Recovered) that combines both healthcare workers (as an independent compartment) and community and focuses on the protection of the healthcare workforce against SARS-COV-2. Benefiting the next generation matrix method, the basic reproduction number (R0) was computed. Routh-Hurwitz criterion and stable Metzler matrix theory revealed that disease-free equilibrium point is locally and globally asymptotically stable whenever R0 &lt; 1, respectively. Lyapunov func tion depicted that the endemic equilibrium point is globally asymptotically stable when R0 &gt; 1. Further, the dynamics behavior of R0 was explored when varying the use personal protective equipment (ξ) and physical distancing (θ). In the absence of protective measures (ξ and θ), the value of R0 was 6.7125 which implies the expansion of the disease. When θ and ξ were introduced in the model, R0 was 0.6713, indicating the decrease of the disease in the community. Numer ical solutions were simulated by using Runge-Kutta fourth-order method. The numerical results illustrated mathematically that protection of health care workers can be achieved through effec tive use of personal protective equipment and minimization of transmission of COVID-19 in the community.

Analysis of epidemic vaccination strategies on heterogeneous networks: Based on SEIRV model and evolutionary game

Coronavirus (Covid-19) is an infectious disease that attacks the respiratory tract caused by the newly discovered corona virus. In dealing with the spread of covid-19, WHO has declared quarantine and isolation and carried out vaccinations. The implementation of quarantine and isolation during the vaccination’s period is expected to suppress the spread of covid-19. The purpose of the study was to determine the effectiveness of quarantine and isolation during the vaccination period in suppressing the spread of covid-19. In this study, an analysis of the effectiveness of quarantine and isolation against the spread of covid-19 disease was carried out during the vaccination’s period using the SEQIJR model. The SEQIJR model is in accordance with the problems that occur, which involve 6 classes are susceptible (S), exposed (E), quarantined (R), infectious (I), isolated (J), and recovered (R). Through this model, there are two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. The disease-free equilibrium point (ε0) is locally asymptotically stable with R0 < 1 and the endemic equilibrium point (ε0*) is unstable. This has the interpretation that the spread of covid-19 will disappear from the population over time. The simulation shows that tightening interventions in the form of quarantine and isolation can accelerate the decline in the rate of spread of covid-19. Meanwhile, isolation interventions are better than quarantine in suppressing the spread of covid-19.