Computational and Theoretical Analysis of the Association Between Gender and HSV-2 Treatment Adherence

Herpes simplex virus type 2 (HSV-2) is the most prevalent sexually transmitted infection in the world, despite the availability of effective anti-viral treatments. A mathematical model to explore the association between gender and HSV-2 treatment adherence is developed. Threshold parameters are determined and stabilities analyzed. Sensitivity analysis of the reproduction number and the numerical simulations suggest that treatment adherence for both females and males are equally important in keeping the reproduction as low as possible. The basic model is then extended to incorporate time-dependent intervention strategies. The Pontryagin's Maximum Principle is used to characterize the optimal level of the controls, and the resulting optimality system is solved numerically.

Dynamical and optimal control analysis of a seasonal Trypanosoma brucei rhodesiense model

The effects of seasonal variations on the epidemiology of Trypanosoma brucei rhodesiense disease is well documented. In particular, seasonal variations alter vector development rates and behaviour, thereby influencing the transmission dynamics of the disease. In this paper, a mathematical model for Trypanosoma brucei rhodesiense disease that incorporates seasonal effects is presented. Owing to the importance of understanding the effective ways of managing the spread of the disease, the impact of time dependent intervention strategies has been investigated. Two controls representing human awareness campaigns and insecticides use have been incorporated into the model. The main goal of introducing these controls is to minimize the number of infected host population at low implementation costs. Although insecticides usage is associated with adverse effects to the environment, in this study we have observed that by totally neglecting insecticide use, effective disease management may present a formidable challenge. However, if human awareness is combined with low insecticide usage then the disease can be effectively managed.

Optimal control applied to a temperature dependent schistosomiasis model

Schistosomiasis, the most common water-borne infection worldwide, continues to pose a serious public health challenge in developing nations and to travellers who visit these endemic regions. We apply optimal control on a temperature dependent schistosomiasis model. Our optimal control aims to minimize the pre-patent and patent human population at minimal costs. Our analysis and results throughout the paper highlight the impact of optimal control shaping the future patterns of the disease. Our results show that optimal control can significantly reduce the schistosomiasis burden in the community and in some instance by more than three-fold. In addition, our results show that with low costs the optimal strategy will be carried out at or close to its maximum strength for a sufficiently long period of time, so as minimize the exposure and infection. With high costs, however, the control have to be implemented with reduced or even minimum, strength, to achieve an optimal balance between the costs and effects of control. Our findings suggest that optimal control theory can be useful on minimizing the infected host and vector. The study and its findings can provide a useful framework for designing cost-effective control for schistosomiasis.

On the dynamics of brucellosis infection in bison population with vertical transmission and culling

We introduce a new mathematical modeling framework that seek to improve our quantitative understanding of the influence of chronic brucellosis and culling control on brucellosis dynamics in periodic and non-periodic environments. We conduct both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction numbers. In addition, we also perform an optimal control study to explore optimal culling strategy in periodic and non-periodic environment.

Modeling the intrinsic dynamics of foot-and-mouth disease

We propose a new mathematical modeling framework to investigate the transmission and spread of foot-and-mouth disease. Our models incorporate relevant biological and ecological factors, vaccination effects, and seasonal impacts during the complex interaction among susceptible, vaccinated, exposed, infected, carrier, and recovered animals. We conduct both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction numbers. In addition, numerical simulation results are presented to demonstrate the analytical findings.

Modeling the Effects of Multiple Intervention Strategies on Controlling Foot-and-Mouth Disease

Foot-and-mouth disease (FMD) is a threat to economic security and infrastructure as well as animal health, in both developed and developing countries. We propose and analyze an optimal control problem where the control system is a mathematical model for FMD that incorporates vaccination and culling of infectious animals. The control functions represent the fraction of animals that are vaccinated during an outbreak, infectious symptomatic animals that are detected and culled, and infectious nonsymptomatic animals that are detected and culled. Our aim was to study how these control measures should be implemented for a certain time period, in order to reduce or eliminate FMD in the community, while minimizing the interventions implementation costs. A cost-effectiveness analysis is carried out, to compare the application of each one of the control measures, separately or in combination.

Exploring the Impact of Prostitution on HIV/AIDS Transmission

HIV/AIDS has been somehow linked to prostitution for decades now. A mathematical model is presented to assess the link between prostitution and HIV transmission. The epidemic thresholds known as the reproduction numbers and equilibria for the model are determined and stabilities analyzed. Analysis of the reproduction numbers suggests that HIV/AIDS control using antiretroviral therapy is more effective in the absence of prostitution. Numerical simulations further show high levels of HIV/AIDS when percentage of prostitutes in the community is high. Results from this study suggest that effectively controlling HIV/AIDS requires strategies that address both prostitution and HIV/AIDS transmission. Addressing HIV/AIDS through condom use and antiretroviral therapy may not be enough to stem HIV/AIDS in the community as some drug/alcohol misusing prostitutes may not be able to negotiate for safe sex while they are in drunken stupor. Furthermore, prostitutes are likely to get infected by different HIV strains some of which may be resistant to the antiretroviral therapy regimen in use.

Modeling the impact of early therapy for latent tuberculosis patients and its optimal control analysis

Effective tuberculosis (TB) control depends on case findings to discover infectious cases, investigation of contacts of those with TB, as well as appropriate treatment. Adherence and successful completion of the treatment are equally important. Unfortunately, due to a number of personal, psychosocial, economic, medical, and health service factors, a significant number of TB patients become irregular and default from treatment. In this paper, a mathematical model is developed to assess the impact of early therapy for latent TB and non-adherence on controlling TB transmission dynamics. Equilibrium states of the model are determined and their local stability is examined. With the aid of the center manifold theory, it is established that the model undergoes a backward bifurcation. Qualitative mathematical analysis of the model suggests that a high level of latent tuberculosis case findings, coupled with a decrease of defaulting rate, may be effective in controlling TB transmission dynamics in the community. Population-level effects of organized campaigns to improve early therapy and to guarantee successful completion of each treatment are evaluated through numerical simulations and presented in support of the analytical results.

Assessing the effects of drug misuse on HIV/AIDS prevalence

Drug misuse (injecting drug users-IDU) has been recognized to have a significant effect on the spread of HIV/AIDS epidemic. A deterministic model to assess the contribution of drug misuse and sex in the spread of HIV/AIDS is investigated. The threshold parameters of the model are determined and stabilities are analysed. Analysis of the reproduction number has shown that increase in drug misuse results in an increase in HIV infections. Furthermore, numerical simulations of the model show that drug misuse enhances HIV transmission and progression to AIDS. Thus, in a population with intravenous drug users, advocating for safe sex alone will not be enough to control the HIV/AIDS epidemic.

Is HIV infection associated with an increased risk for cholera? Insights from a mathematical model

Cholera, a waterborne gastroenteric infection, remains a significant threat to public health in sub-Saharan Africa, the region most heavily affected by HIV. It is biologically plausible that immune suppression caused by HIV infection predisposes to cholera. In this paper, a simple mathematical model is developed and comprehensively analyzed to assess whether HIV infection is associated with an increased risk for cholera or not. Analytical results of the model show that the quantities R(c) and R(h), which represents the reproductive number for cholera and HIV infection, respectively, provide threshold conditions that determine cumulative new single and dual infection cases. These threshold conditions can be used to gain important insights on the epidemiological consequences of HIV and cholera coexistence in the community. Numerical results are provided to support the analytical findings. The findings suggest that in a cholera-endemic area, HIV infection is associated with an increased risk for cholera.

Modelling HIV/AIDS and monkeypox co-infection

During the last two decades, reports on emerging human monkeypox outbreaks in Africa and North America have reminded us that beside the eradicated smallpox there are other pox viruses that have great potential to harm people. A deterministic model for the co-infection of HIV/AIDS and monkeypox is formulated and analysed. The endemic equilibria are shown to be locally and globally asymptotically stable using the Centre Manifold theory and the Lyapunov function approach, respectively. Analysis of the basic reproduction numbers and numerical simulations suggest that an increase in the number of monkeypox in the animal species results in an increase of the number of people having monkeypox. Threshold conditions that determine the competitive outcomes of the two diseases are provided. Furthermore, numerical simulations using a set of reasonable parameter values support the claim that HIV infection greatly enhances monkeypox infection and vice versa.

Modeling schistosomiasis and HIV/AIDS codynamics

We formulate a mathematical model for the cointeraction of schistosomiasis and HIV/AIDS in order to assess their synergistic relationship in the presence of therapeutic measures. Comprehensive mathematical techniques are used to analyze the model steady states. The disease-free equilibrium is shown to be locally asymptotically stable when the associated disease threshold parameter known as the basic reproduction number for the model is less than unity. Centre manifold theory is used to show that the schistosomiasis-only and HIV/AIDS-only endemic equilibria are locally asymptotically stable when the associated reproduction numbers are greater than unity. The impact of schistosomiasis and its treatment on the dynamics of HIV/AIDS is also investigated. To illustrate the analytical results, numerical simulations using a set of reasonable parameter values are provided, and the results suggest that schistosomiasis treatment will always have a positive impact on the control of HIV/AIDS.

Modelling the effects of condom use and antiretroviral therapy in controlling HIV/AIDS among heterosexuals, homosexuals and bisexuals

A deterministic compartmental sex-structured HIV/AIDS model for assessing the effects of homosexuals and bisexuals in heterosexual settings in which homosexuality and bisexuality issues have remained taboo is presented. We extend the model to focus on the effects of condom use as a single strategy approach in HIV prevention in the absence of any other intervention strategies. Initially, we model the use of male condoms, followed by incorporating the use of both the female and male condoms. The model includes two primary factors in condom use to control HIV which are condom efficacy and compliance. Reproductive numbers for these models are computed and compared to assess the effectiveness of male and female condom use in a community. We also extend the basic model to consider the effects of antiretroviral therapy as a single strategy. The results from the study show that condoms can reduce the number of secondary infectives and thus can slow the development of the HIV/AIDS epidemic. Further, we note from the study that treatment of AIDS patients may enlarge the epidemic when the treatment drugs are not 100% effective and when treated AIDS patients indulge in risky sexual behaviour. Thus, the treatment with amelioration of AIDS patients should be accompanied with intense public health educational programs, which are capable of changing the attitude of treated AIDS patients towards safe sex. It is also shown from the study that the use of condoms in settings with the treatment may help in reducing the number of secondary infections thus slowing the epidemic.

Mathematical modelling of immune regulation of type 1 diabetes

Type 1 diabetes is a disease characterized by progressive loss of β cell function due to an autoimmune reaction affecting the islets of Langerhans. Two types of T cells are involved in diabetes: turncoat auto-reactive T cells, or T cells gone bad, that kill the insulin-producing cells, and regulatory T cells that are unable to control the auto-reactive T cells. We formulate a mathematical model that incorporates the role of cytotoxic T cells and regulatory T cells in type 1 diabetes. This study shows that onset of type 1 diabetes is due to a collective, dynamical instability, rather than being caused by a single etiological factor. It is also a numbers game between regulatory T cells and auto-reactive T cells. The problem in the onset of this disease is that there are not enough of the regulatory cells that suppress the immune response against the body's insulin-producing pancreatic islet cells.