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Cholera is a disease of poverty affecting people with inadequate access to safe water and basic sanitation. Conflict, unplanned urbanization and climate change all increase the risk of cholera. In this article, an optimal control deterministic mathematical model of cholera disease with cost-effectiveness analysis is developed and analyzed considering both direct and indirect contact transmission pathways. The model qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction number of the model is obtained. We also performed sensitivity analysis of the basic parameters of the model. Then an optimal control problem is designed with a control functional having five controls: vaccination, treatment, environment sanitation and personal hygiene, and water quality improvement program. We examined the existence and uniqueness of the optimal controls of the system. Through the implementation of Pontryagin's maximum principle, the characterization of the optimal controls optimality system is established. The numerical simulation results the integrated control strategies demonstrated that strategy 2, 7, and 12 are effective programs to combat cholera disease from the community. Based on the local circumstances, available funds, and resources, it is recommended to the government stakeholders and policymakers to execute any one of the three integrated intervention programs. [ABSTRACT FROM AUTHOR]

A mathematical model of the dual addiction dissemination dynamics of alcoholism and smoking was created and examined in this work, along with cost-effectiveness and optimal control techniques. The primary goal of the research is to determine which cost-efficient management techniques are most helpful in lowering the problem of dual addiction dispersion in the community. The smoking addiction sub-model, the alcohol addiction sub-model, and the dual addiction model between alcohol and smoking were all calculated, and their stability was examined in this study. The effective reproduction numbers of the models are computed using the next-generation operator technique. When the model's effective reproduction number is smaller than one, the backward bifurcation phenomenon is seen. Six time-dependent control measures are taken into consideration when formulating and analyzing the optimum control issue. Utilizing and applying the parameter values and using MATLAB ode45 solver we performed numerical simulations for both the dual addiction model and its optimal control problem. Furthermore, using the incremental cost-effectiveness ratio (ICER), we carried out the cost-effectiveness analyses. The cost-effectiveness analysis shows that implementing all the protection (education) control measures simultaneously (i.e., implementing Strategy A) is the most cost-effective strategy. Finally, we recommend that the public health stakeholders must put great effort into the implementation of Strategy A to reduce the smoking and alcoholism dual addiction dissemination problem in the community. [ABSTRACT FROM AUTHOR]

This study presents a reliable mathematical model to explain the spread of typhoid fever, covering stages of susceptibility, infection, carrying, and recovery, specifically in the Sheno town community. A detailed analysis is done to ensure the solutions are positive, stay within certain limits, and are stable for both situations where the disease is absent and where it is consistently present. The Routh-Hurwitz stability criterion has been used and applied for the purpose of stability analysis. Using the next-generation matrix, we determined the intrinsic potential for disease transmission. It showing that typhoid fever is spreading actively in Sheno town, with cases above a critical level. Our findings reveal the instability of the disease-free equilibrium point alongside the stability of the endemic equilibrium point. We identified two pivotal factors for transmission of the disease: the infectious rate, representing the speed of disease transmission, and the recruitment rate, indicating the rate at which new individuals enter the susceptible population. These parameters are indispensable for devising effective control measures. It is imperative to keep these parameters below specific thresholds to maintain a basic reproduction number favorable for disease control. Additionally, the study carefully examines how different factors affect the spread of typhoid fever, giving a detailed understanding of its dynamics. At the end, this study provides valuable insights and specific strategies for managing the disease in the Sheno town community. [ABSTRACT FROM AUTHOR]

The prevalence of the varicella-zoster virus (VZV) and its correlation underscore its impact on a significant segment of the population. Notably contagious, VZV serves as a risk factor for the manifestation of HIV/AIDS, with its reactivation often signaling the onset of immunodeficiency. Recognizing the concurrent existence of these two diseases, this study focuses on the co-infection dynamics through a deterministic mathematical model. The population is categorized into seven exclusive groups, considering the complexities arising from the interplay of HIV and Zoster. We establish the non-negativity and boundedness of solutions, examine equilibrium points, calculate basic reproduction numbers via the next-generation matrix approach, and analyze the existence and local stabilities of equilibriums using the Routh-Hurwitz stability criteria. The numerical simulations reveal that the model converges to an endemic equilibrium point when the reproduction number exceeds unity. The primary objectives of this study are to comprehensively understand the transmission dynamics of HIV and Zoster in a co-infected population and to provide valuable insights for developing effective intervention strategies. The findings emphasize the importance of addressing these co-infections to mitigate their impact on public health. [ABSTRACT FROM AUTHOR]

HIV/AIDS-COVID-19 co-infection is a major public health concern especially in developing countries of the world. This paper presents HIV/AIDS-COVID-19 co-infection to investigate the impact of interventions on its transmission using ordinary differential equation. In the analysis of the model, the solutions are shown to be non-negative and bounded, using next-generation matrix approach the basic reproduction numbers are computed, sufficient conditions for stabilities of equilibrium points are established. The sensitivity analysis showed that transmission rates are the most sensitive parameters that have direct impact on the basic reproduction numbers and protection and treatment rates are more sensitive and have indirect impact to the basic reproduction numbers. Numerical simulations shown that some parameter effects on the transmission of single infections as well as co-infection, and applying the protection rates and treatment rates have effective roles to minimize and also to eradicate the HIV/AIDS-COVID-19 co-infection spreading in the community. [ABSTRACT FROM AUTHOR]

HIV/AIDS and COVID-19 co-infection is a common global health and socio-economic problem. In this paper, a mathematical model for the transmission dynamics of HIV/AIDS and COVID-19 co-infection that incorporates protection and treatment for the infected (and infectious) groups is formulated and analyzed. Firstly, we proved the non-negativity and boundedness of the co-infection model solutions, analyzed the single infection models steady states, calculated the basic reproduction numbers using next generation matrix approach and then investigated the existence and local stabilities of equilibriums using Routh-Hurwiz stability criteria. Then using the Center Manifold criteria to investigate the proposed model exhibited the phenomenon of backward bifurcation whenever its effective reproduction number is less than unity. Secondly, we incorporate time dependent optimal control strategies, using Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. Finally, we carried out numerical simulations for both the deterministic model and the model incorporating optimal controls and we found the results that the model solutions are converging to the model endemic equilibrium point whenever the model effective reproduction number is greater than unity, and also from numerical simulations of the optimal control problem applying the combinations of all the possible protection and treatment strategies together is the most effective strategy to drastically minimizing the transmission of the HIV/AIDS and COVID-19 co-infection in the community under consideration of the study. [ABSTRACT FROM AUTHOR]

The membranes that encompass the brain and spinal cord become inflamed by the potentially fatal infectious disease called pneumococcal meningitis. Pneumonia and meningitis "coinfection" refers to the presence of both conditions in a single host. In this work, we accounted for the dynamics of pneumonia and meningitis coinfection in communities by erroneously using a compartment model to analyze and suggest management techniques to stakeholders. We have used the next generation matrix approach and derived the effective reproduction numbers. When the reproduction number is less than one, the constructed model yields a locally asymptotically stable disease-free equilibrium point. Additionally, we conducted a sensitivity analysis to determine how different factors affected the incidence and transmission rate, which revealed that both the pneumonia and meningitis transmission rates are extremely sensitive. The performance of our numerical simulation demonstrates that the endemic equilibrium point of the pneumonia and meningitis coinfection model is locally asymptotically stable when max R 1 , R 2 > 1. Finally, as preventative and control measures for the coinfection of pneumonia and meningitis illness, the stakeholders must concentrate on reducing the transmission rates, reducing vaccination wane rates, and boosting the portion of vaccination rates for both pneumonia and meningitis. [ABSTRACT FROM AUTHOR]

Racism and corruption are mind infections which affect almost all public and governmental sectors. However, we cannot find enough published literatures on mathematical model analyses of racism and corruption coexistence. In this study, we have contemplated the dynamics of racism and corruption coexistence in communities, using deterministic compartmental model to analyze and suggest proper control strategies to stakeholders. We used qualitative and comprehensive mathematical methods and analyzed both the racism model in the absence of corruption and the corruption model in the absence of racism. We have computed basic reproduction numbers by applying the next generation matrix method. The developed model has a disease-free equilibrium point that is locally asymptotically stable whenever the reproduction number is less than one. Additionally, we have done sensitivity analysis to observe the effect of the parameters on the incidence and transmission of the mind infections that deduce the transmission rates of both the racism and corruption are highly sensitive. The numerical simulation we have simulated showed that the endemic equilibrium point of racism and corruption coexistence model is locally asymptotically stable when max R r , R c > 1 , the effects of parameters on the basic reproduction numbers, and the effect of parameter on the infectious groups. Finally, the stakeholders must focus on minimizing the transmission rates and increasing the recovery (removed) rate for both racism and corruption action which can be considered prevention and controlling strategies. [ABSTRACT FROM AUTHOR]