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

Optimal Control and Bifurcation Analysis of HIV Model

In this study, a very crucial stage of HIV extinction and invisibility stages are considered and a modified mathematical model is developed to describe the dynamics of infection. Moreover, the basic reproduction number R ₀ is computed using the next-generation matrix method whereas the stability of disease-free equilibrium is investigated using the eigenvalue matrix stability theory. Furthermore, if R ₀ ≤ 1, the disease-free equilibrium is stable both locally and globally whereas if R ₀ > 1, based on the forward bifurcation behavior, the endemic equilibrium is locally and globally asymptotically stable. Particularly, at the critical point R ₀ = 1, the model exhibits forward bifurcation behavior. On the other hand, the optimal control problem is constructed and Pontryagin's maximum principle is applied to form an optimality system. Further, forward fourth-order Runge-Kutta's method is applied to obtain the solution of state variables whereas Runge-Kutta's fourth-order backward sweep method is applied to obtain solution of adjoint variables. Finally, three control strategies are considered and a cost-effective analysis is performed to identify the better strategies for HIV transmission and progression. In advance, prevention control measure is identified to be the better strategy over treatment control if applied earlier and effectively. Additionally, MATLAB simulations were performed to describe the population's dynamic behavior.

The Synergistic Relationship Between Climate Change and the HIV/AIDS Epidemic: A Conceptual Framework

Climate change and HIV/AIDS represent two of the greatest threats to human health in the 21st century. However, limitations in understanding the complex relationship between these syndemics continue to constrain advancements in the prevention and management of HIV/AIDS in the context of a rapidly changing climate. Here, we present a conceptual framework that identifies four pathways linking climate change with HIV/AIDS transmission and health outcomes: increased food insecurity, increased prevalence of other infectious diseases, increased human migration, and erosion of public health infrastructure. This framework is based on an in-depth literature review in PubMed and Google Scholar from June 6 to June 27, 2019. The pathways linking climate change with HIV transmission and health outcomes are complex with multiple interacting factors. Food insecurity emerged as a particularly important mediator by driving sexual risk-taking behaviours and migration, as well as by increasing susceptibility to infections that are common among people living with HIV (PLWHIV). Future interventions should focus on decreasing carbon dioxide emissions globally and increasing education and investment in adaptation strategies, particularly in those areas of sub-Saharan Africa and southeast Asia heavily impacted by both HIV and climate change. Environmentally sustainable interventions such as urban gardening and investing in sustainable agriculture technologies also have significant health co-benefits that may help PLWHIV adapt to the environmental consequences of climate change.

A dynamic optimal control model for COVID-19 and cholera co-infection in Yemen

In this work, we propose a new dynamic mathematical model framework governed by a system of differential equations that integrates both COVID-19 and cholera outbreaks. The estimations of the model parameters are based on the outbreaks of COVID-19 and cholera in Yemen from January 1, 2020 to May 30, 2020. Moreover, we present an optimal control model for minimizing both the number of infected people and the cost associated with each control. Four preventive measures are to be taken to control the outbreaks: social distancing, lockdown, the number of tests, and the number of chlorine water tablets (CWTs). Under the current conditions and resources available in Yemen, various policies are simulated to evaluate the optimal policy. The results obtained confirm that the policy of providing resources for the distribution of CWTs, providing sufficient resources for testing with an average social distancing, and quarantining of infected individuals has significant effects on flattening the epidemic curves.

Theoretical Assessment of the Impact of Climatic Factors in a Vibrio Cholerae Model

A mathematical model for Vibrio Cholerae (V. Cholerae) in a closed environment is considered, with the aim of investigating the impact of climatic factors which exerts a direct influence on the bacterial metabolism and on the bacterial reservoir capacity. We first propose a V. Cholerae mathematical model in a closed environment. A sensitivity analysis using the eFast method was performed to show the most important parameters of the model. After, we extend this V. cholerae model by taking account climatic factors that influence the bacterial reservoir capacity. We present the theoretical analysis of the model. More precisely, we compute equilibria and study their stabilities. The stability of equilibria was investigated using the theory of periodic cooperative systems with a concave nonlinearity. Theoretical results are supported by numerical simulations which further suggest the necessity to implement sanitation campaigns of aquatic environments by using suitable products against the bacteria during the periods of growth of aquatic reservoirs.

A Game-Theoretic Model of Cholera with Optimal Personal Protection Strategies

Cholera is an acute gastro-intestinal infection that affects millions of people throughout the world each year, primarily but not exclusively in developing countries. Because of its public health ramifications, considerable mathematical attention has been paid to the disease. Here we consider one neglected aspect of combating cholera: personal participation in anti-cholera interventions. We construct a game-theoretic model of cholera in which individuals choose whether to participate in either vaccination or clean water consumption programs under assumed costs. We find that relying upon individual compliance significantly lowers the incidence of the disease as long as the cost of intervention is sufficiently low, but does not eliminate it. The relative costs of the measures determined whether a population preferentially adopts a single preventative measure or employs the measure with the strongest early adoption.

Risk Factors for Self-Reported Cholera Within HIV-Affected Households in Rural Haiti

BACKGROUND

Cholera continues to be a major cause of morbidity and mortality worldwide and is now endemic in Haiti since first being introduced in 2010. Cholera and HIV have significant geographic overlap globally, but little is known about the clinical features and risk of cholera among HIV-infected people and their households.

METHODS

We assessed HIV-affected households originally recruited for a randomized controlled trial of food supplements. We assessed for correlation between household and individual factors and reported history of cholera since 2010 using univariable and multivariable analyses.

RESULTS

There were 352 HIV-infected household members, 32 with reported history of medically attended cholera, and 1968 other household members, 55 with reported history of medically attended cholera. Among HIV-infected individuals in this study, no variables correlated with reported history of cholera in univariable analyses. Among all household members, known HIV infection (adjusted odds ratio [AOR], 3.75; 95% CI, 2.43-5.79; P < .0001), source of income in the household (AOR, 1.82; 95% CI, 1.05-3.15; P = .034), time required to fetch water (AOR, 1.07 per 5-minute increase; 95% CI, 1.01-1.12; P = .015), and severe household food insecurity (AOR, 3.23; 95% CI, 1.25-8.34; P = .016) were correlated with reported history of cholera in a multivariable analysis.

CONCLUSIONS

Known HIV infection, source of household income, time required to fetch water, and severe household food insecurity were independently associated with reported history of medically attended cholera in HIV-affected households in rural Haiti. Further research is required to better understand the interactions between HIV and cholera.

Optimal control analysis of malaria-schistosomiasis co-infection dynamics

This paper presents a mathematical model for malaria--schistosomiasis co-infection in order to investigate their synergistic relationship in the presence of treatment. We first analyse the single infection steady states, then investigate the existence and stability of equilibria and then calculate the basic reproduction numbers. Both the single-infection models and the co-infection model exhibit backward bifurcations. We carrying out a sensitivity analysis of the co-infection model and show that schistosomiasis infection may not be associated with an increased risk of malaria. Conversely, malaria infection may be associated with an increased risk of schistosomiasis. Furthermore, we found that effective treatment and prevention of schistosomiasis infection would also assist in the effective control and eradication of malaria. Finally, we apply Pontryagin's Maximum Principle to the model in order to determine optimal strategies for control of both diseases.

Clinical Features of Human Immunodeficiency Virus-Infected Patients Presenting with Cholera in Port-au-Prince, Haiti

Human immunodeficiency virus (HIV) infection has been postulated to alter the natural history of cholera, including increased susceptibility to infection, severity of illness, and chronic carriage of Vibrio cholerae Haiti has a generalized HIV epidemic with an adult HIV prevalence of 1.9% and recently suffered a cholera epidemic. We conducted a prospective study at the cholera treatment center (CTC) of GHESKIO in Haiti to characterize the coinfection. Adults admitted at the CTC for acute diarrhea were invited to participate in the study. Vital signs, frequency, and volume of stools and/or vomiting were monitored, and single-dose doxycycline was administered. After counseling, participants were screened for HIV by enzyme-linked immunosorbent assay and for cholera by culture. Of 729 adults admitted to the CTC, 99 (13.6%) had HIV infection, and 457 (63%) had culture-confirmed cholera. HIV prevalence was three times higher in patients without cholera (23%, 63/272) than in those with culture-confirmed cholera (7.9%, 36/457). HIV prevalence in patients with culture-confirmed cholera (7.9%) was four times higher than the adult prevalence in Port-au-Prince (1.9%). Of the 36 HIV-infected patients with cholera, 25 (69%) had moderate/severe dehydration versus 302/421 (72%) in the HIV negative. Of 30 HIV-infected patients with weekly stool cultures performed after discharge, 29 (97%) were negative at week 1. Of 50 HIV-negative patients with weekly stool cultures, 49 (98%) were negative at week 1. In countries with endemic HIV infection, clinicians should consider screening patients presenting with suspected cholera for HIV coinfection.

Evidence for CVD 103-HgR as an effective single-dose oral cholera vaccine

We propose the ideal oral cholera vaccine (OCV) should be an inexpensive, single, oral dose that rapidly confers immunity for a long duration, and is well tolerated by individuals vulnerable to cholera. Vaccine trials in industrialized countries of a single oral dose of 5 × 108 colony forming units (CFU) of the live, attenuated cholera strain CVD 103-HgR have shown 88–97% serum vibriocidal antibody seroconversion rates, a correlate of protection and documented vaccine efficacy of ≥80% using volunteer challenge studies with wild-type cholera. For individuals of developing countries, a 5 × 109 CFU dose of CVD 103-HgR is necessary to elicit similar antibody responses. Presently, a reformulation of CVD 103-HgR is in late-stage clinical development for prospective US FDA licensure; making a cholera vaccine for US travelers potentially accessible in 2016. The availability of CVD 103-HgR should be a welcome addition to the currently available OCVs.

A co-infection model of malaria and cholera diseases with optimal control

In this paper we formulate a mathematical model for malaria-cholera co-infection in order to investigate their synergistic relationship in the presence of treatments. We first analyze the single infection steady states, calculate the basic reproduction number and then investigate the existence and stability of equilibria. We then analyze the co-infection model, which is found to exhibit backward bifurcation. The impact of malaria and its treatment on the dynamics of cholera is further investigated. Secondly, we incorporate time dependent controls, using Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. We found that malaria infection may be associated with an increased risk of cholera but however, cholera infection is not associated with an increased risk for malaria. Therefore, to effectively control malaria, the malaria intervention strategies by policy makers must at the same time also include cholera control.

Analysis of a sex-structured HIV/AIDS model with the effect of screening of infectives

This paper presents a nonlinear sex-structured mathematical model to study the spread of HIV/AIDS by considering transmission of disease by heterosexual contact. The epidemic threshold and equilibria for the model are determined, local stability and global stability of both the "Disease-Free Equilibrium" (DFE) and "Endemic Equilibrium" (EE) are discussed in detail. The DFE is shown to be locally and globally stable when the basic reproductive number ℛ0 is less than unity. We also prove that the EE is locally and globally asymptotically stable under some conditions. Finally, numerical simulations are reported to support the analytical findings.