Bulletin of Biomathematics

Mathematical modeling for the transmission dynamics of cholera with an optimal control strategy

Umar Tasiu Mustapha — 2024-04-30

Cholera is an acute diarrheal disease caused by Vibrio cholera, its prevalence occurs in almost all the continents of the world, annually there are about 1.3 to 4.0 million cases of cholera and 21,000 to 143,000 deaths worldwide. In this paper, we propose a deterministic model for the transmission dynamics of cholera to assess the impact of vaccines in decreasing the spread of cholera infection in Nigeria. Moreover, we develop an optimal control strategy, in which we consider personal hygiene a control strategy on infection class, with u(t) as the control function. The best values of the fitting parameters have been obtained using least square minimization to validate the model with the help of experimental data obtained from Nigeria. We perform sensitivity analysis to determine the key parameters that have impacts on the control of the spread of cholera infections in the population. In addition, the numerical simulation of the model reveals that the use of vaccines and personal hygiene will effectively control the spread of cholera infection.

Dynamical analysis of HIV-TB co-infection transmission model in the presence of treatment for TB

Bolarinwa Bolaji — 2024-04-30

The immense disease burden of tuberculosis (TB) infection is well-documented, particularly among those co-infected with HIV and TB. To better understand the transmission dynamics of HIV-TB co-infection in the absence of readily available HIV treatment, we develop a deterministic compartmental co-infection model. Our model helps to identify the effects of TB infection on the co-infection dynamics of the two diseases, especially when treatment for TB is readily available. We find that susceptibility to TB reinfection after a previous infection leads to backward bifurcation in the TB-only model when the associated reproduction number (R_0) is less than unity. However, when we make the susceptibility to TB re-infection insignificant in the model, the disease-free equilibrium of the TB-only model is locally asymptotically stable when the associated R_0 is less than unity. We conduct sensitivity and uncertainty analyses to identify the key parameters driving TB infection dynamics, using the R_0 as the response function. We discover that the transmission rate for TB, the modification parameters accounting for the infectiousness of infected individuals with TB-only, and the treatment rates for singly infected individuals with latently infected TB are the top drivers of TB infection in the given population. Our numerical simulations suggest that concentrating treatment on TB-infected individuals in the diagnosed latently infected stage (singly or dually infected with HIV) could effectively reduce the co-infection disease burden and HIV incidence in the population under study.

The impact of the COVID-19 pandemic on education in Bangladesh and its mitigation

Md. Kamrujjaman — 2024-04-30

The global COVID-19 pandemic disrupted various facets of societal functioning, with the education sector facing unprecedented challenges. The sudden closure of schools and universities, coupled with the shift towards remote learning, created a dynamic educational environment. It significantly affected academic performance, psychological health, dropout rates, school closures, and even increased early marriage rates in Bangladesh. In 2021, the dropout rate stood at 14.15 percent. This study delves into the specific repercussions of the pandemic on the education landscape in Bangladesh. The research reveals the disparities in access to online education, shedding light on the socio-economic factors influencing digital learning engagement. Through a comprehensive analysis of quantitative and qualitative data, we explore the multifaceted effects on educational institutions, students, and educators. We present the impact of COVID-19 on education graphically using interpolation polynomials. Mitigating the impact of COVID-19 on the education sector in Bangladesh necessitates a multifaceted approach that addresses various interconnected challenges. Moreover, prioritizing mental health support for students, teachers, and parents is paramount in navigating the emotional toll of the pandemic. Collaboration and partnerships with international organizations, non-government organizations (NGOs), and private sector entities are indispensable for mobilizing resources and expertise. Bangladesh can effectively manage the pandemic's complications and ensure the continued viability of its educational system by implementing such an all-encompassing approach.

Study of fractional order SIR model with M-H type treatment rate and its stability analysis

Subrata Paul — 2024-04-30

In this manuscript, we analyze a fractional-order susceptible-infected-recovered (SIR) mathematical model with a nonlinear incidence rate and nonlinear treatment rate for the control of infectious illness. The incidence rate of infection is considered as Holling type II and the treatment rate is considered as Monod-Haldane (MH) type. The existence and uniqueness criteria for the new model, as well as the non-negativity and boundedness, have been established. We also provide an ideal control strategy for the SIR model using the treatment rate as a control parameter. The solution of the suggested model is approximated using the fractional-order Taylor's method. With the help of MATLAB (2018a), we perform numerical simulations and illustrate the results through graphical representations.

Fractional-order brucellosis transmission model between interspecies with a saturated incidence rate

Dilara Yapışkan — 2024-04-30

In this study, brucellosis dynamics between interspecies are discussed with the Atangana-Baleanu fractional derivative to examine the transmission of brucellosis by its behavior. The recovered compartment, recruitment, and natural death rate for humans are considered for the fractional order model to analyze the transmission dynamics in more detail from an epidemiological point of view. Additionally, the saturated incidence rate is suggested for brucellosis as indirectly transmitted to individuals from the environment. By fixed point theory, it is verified that developed fractional transmission dynamics have a unique solution. The model under consideration employs the Adams-type predictor-corrector method for numerical solution. All comparative results are plotted by MATLAB.