On the intrinsic dynamics of bacteria in waterborne infections

Impact of a multi-pronged cholera intervention in an endemic setting

Cholera is a bacterial water-borne diarrheal disease transmitted via the fecal-oral route that causes high morbidity in sub-Saharan Africa and Asia. It is preventable with vaccination, and Water, Sanitation, and Hygiene (WASH) improvements. However, the impact of vaccination in endemic settings remains unclear. Cholera is endemic in the city of Kalemie, on the shore of Lake Tanganyika, in the Democratic Republic of Congo, where both seasonal mobility and the lake, a potential environmental reservoir, may promote transmission. Kalemie received a vaccination campaign and WASH improvements in 2013-2016. We assessed the impact of this intervention to inform future control strategies in endemic settings. We fit compartmental models considering seasonal mobility and environmentally-based transmission. We estimated the number of cases the intervention avoided, and the relative contributions of the elements promoting local cholera transmission. We estimated the intervention avoided 5,259 cases (95% credible interval: 1,576.6-11,337.8) over 118 weeks. Transmission did not rely on seasonal mobility and was primarily environmentally-driven. Removing environmental exposure or contamination could control local transmission. Repeated environmental exposure could maintain high population immunity and decrease the impact of vaccination in similar endemic areas. Addressing environmental exposure and contamination should be the primary target of interventions in such settings.

Global analysis of a diffusive Cholera model with multiple transmission pathways, general incidence and incomplete immunity in a heterogeneous environment

With the consideration of the complexity of the transmission of Cholera, a partially degenerated reaction-diffusion model with multiple transmission pathways, incorporating the spatial heterogeneity, general incidence, incomplete immunity, and Holling type Ⅱ treatment was proposed. First, the existence, boundedness, uniqueness, and global attractiveness of solutions for this model were investigated. Second, one obtained the threshold condition $ \mathcal{R}_{0} $ and gave its expression, which described global asymptotic stability of disease-free steady state when $ \mathcal{R}_{0} < 1 $, as well as the maximum treatment rate as zero. Further, we obtained the disease was uniformly persistent when $ \mathcal{R}_{0} > 1 $. Moreover, one used the mortality due to disease as a branching parameter for the steady state, and the results showed that the model undergoes a forward bifurcation at $ \mathcal{R}_{0} $ and completely excludes the presence of endemic steady state when $ \mathcal{R}_{0} < 1 $. Finally, the theoretical results were explained through examples of numerical simulations.

Mathematical modeling of cholera dynamics with intrinsic growth considering constant interventions

A mathematical model that describes the dynamics of bacterium vibrio cholera within a fixed population considering intrinsic bacteria growth, therapeutic treatment, sanitation and vaccination rates is developed. The developed mathematical model is validated against real cholera data. A sensitivity analysis of some of the model parameters is also conducted. The intervention rates are found to be very important parameters in reducing the values of the basic reproduction number. The existence and stability of equilibrium solutions to the mathematical model are also carried out using analytical methods. The effect of some model parameters on the stability of equilibrium solutions, number of infected individuals, number of susceptible individuals and bacteria density is rigorously analyzed. One very important finding of this research work is that keeping the vaccination rate fixed and varying the treatment and sanitation rates provide a rapid decline of infection. The fourth order Runge-Kutta numerical scheme is implemented in MATLAB to generate the numerical solutions.

A mathematical model for frogeye leaf spot epidemics in soybean

We propose a new mathematical model based on differential equations to investigate the transmission and spread of frogeye leaf spot, a major soybean disease caused by the fungus Cercospora sojina. The model incorporates the primary and secondary transmission routes of the disease as well as the intrinsic dynamics of the pathogen in the contaminated soil. We conduct detailed equilibrium and stability analyses for this model using theories of dynamical systems. We additionally conduct numerical simulations to verify the analytical predictions and to implement the model for a practical application.

Mathematical Models for Cholera Dynamics-A Review

Cholera remains a significant public health burden in many countries and regions of the world, highlighting the need for a deeper understanding of the mechanisms associated with its transmission, spread, and control. Mathematical modeling offers a valuable research tool to investigate cholera dynamics and explore effective intervention strategies. In this article, we provide a review of the current state in the modeling studies of cholera. Starting from an introduction of basic cholera transmission models and their applications, we survey model extensions in several directions that include spatial and temporal heterogeneities, effects of disease control, impacts of human behavior, and multi-scale infection dynamics. We discuss some challenges and opportunities for future modeling efforts on cholera dynamics, and emphasize the importance of collaborations between different modeling groups and different disciplines in advancing this research area.

Chemical and bacterial quality monitoring of the Nile River water and associated health risks in Qena-Sohag sector, Egypt

The River Nile is the primary source of freshwater for drinking, irrigation, and industrial purposes in Egypt. Thus, the water quality in this river concerns the health of local inhabitants. The present study reveals seasonal variations of various physicochemical and heavy metals parameters and microbial load of water at 15 sites from Qena to Sohag cities, Egypt. The water is fresh with TDS ≤ 270 and 410 mg L^-1 in summer and winter, respectively. Fe, Mn, Cd, Cr, Cu, Ni, and Zn concentrations were within drinking water specification in both seasons except Cr and Cd in summer. Viable numbers of total coliform, fecal coliform, and fecal streptococci were recorded in both seasons with fecal streptococci's disappearing in winter. The concentrations of salts and ions in winter were higher than summer due to decreased water quantity and flow rate in this season. On the other hand, heavy metals and bacteria were higher in summer owing to the rain and weathering of upstream rocks and increasing of human activities during the summer. The calculated water quality index (WQI) depicted that the chemical quality of water was poor for drinking and treatment, especially biological treatment, which is required before the water is supplied for drinking. Human health risk assessment factors such as probable daily intake, hazard quotient, and carcinogenic risk indicated high risks of Cr, Cd, and Ni for adults and children in both seasons. The non-carcinogenic and carcinogenic risks are mainly posed by Cr. The WQI values for the other water uses indicated the marginal quality for aquatic life, fair for irrigation, and fair in summer to good in winter for livestock consumption. The irrigation water quality parameters indicated that the water could be used to irrigate all soils and crops except the hazard of biological contamination. The water-rock interaction controls water chemistry besides the contribution of human activities. The agricultural, industrial, and municipal wastewaters were the main contributors to water pollution and should be treated before discharge into the Nile River. Source and drinking water should be monitored continuously to prevent related human waterborne diseases.

Modeling the Effectiveness of TV and Social Media Advertisements on the Dynamics of Water-Borne Diseases

Cholera is a serious threat to the health of human-kind all over the world and its control is a problem of great concern. In this context, a nonlinear mathematical model to control the prevalence of cholera disease is proposed and analyzed by incorporating TV and social media advertisements as a dynamic variable. It is considered that TV and social media ads propagate the knowledge among the people regarding the severe effects of cholera disease on human health along with its precautionary measures. It is also assumed that the mode of transmission of cholera disease among susceptible individuals is due to consumption of contaminated drinking water containing Vibrio cholerae. Moreover, the propagation of knowledge through TV and social media ads makes the people aware to adopt precautionary measures and also the aware people make some effectual efforts to washout the bacteria from the aquatic environment. Model analysis reveals that increase in the washout rate of bacteria due to aware individuals causes the stability switch. It is found that TV and social media ads have the potential to reduce the number of infectives in the region and thus control the cholera epidemic. Numerical simulation is performed for a particular set of parameter values to support the analytical findings.

Prevalence of Hypopigmentary Disorders in Primary School Children in Zagazig City, Sharkia Governorate, Egypt

BACKGROUND

Epidemiologic data derived from population-based studies are very important to understand human diseases and their implications. Highlighting skin problems by identifying their incidence and prevalence is vital to direct suitable medical attention toward them.

AIM

The aim of the study was to detect the prevalence and most common causes of hypopigmentation in primary school children in Zagazig City.

METHODS

Cross-sectional study on 185 students selected from two schools. Data were collected by filling a questionnaire, clinical examination, and Wood's light examination to detect hypopigmented skin disorders.

RESULTS

The prevalence of hypopigmentation among studied population was 45.4%; the commonest cause was pityriasis alba 58.3%, followed by pityriasis versicolor 17.9%, postinflammatory hypopigmentation 10.7%, hypopigmented nevus 9.5%, and finally 3.6% vitiligo.

CONCLUSION

Hypopigmented skin disorders are important and easy to diagnosis skin diseases that need medical attention.

A mathematical model for Vibrio-phage interactions

A cholera model has been formulated to incorporate the interaction of bacteria and phage. It is shown that there may exist three equilibria: one disease free and two endemic equilibria. Threshold parameters have been derived to characterize stability of these equilibria. Sensitivity analysis and disease control strategies have been employed to characterize the impact of bacteria-phage interaction on cholera dynamics.

Coupling the modeling of phage-bacteria interaction and cholera epidemiological model with and without optimal control

In this work, we assess the impact of the phage-bacteria infection and optimal control on the indirectly transmitted cholera disease. The phage-bacteria interactions are described by predator-prey system using the Smith functional response, which takes into account the number of bacteria binding sites. The study is done in two steps, namely the model without control and the model with control. For the first scenario, we explicitly compute the basic reproduction number R₀ which serves as stability threshold and bifurcation parameter. The proposed model exhibits a bi-stability phenomenon via the existence of backward bifurcation, which implies that the classical requirement of bringing the reproduction number under unity, while necessary, is no longer sufficient for cholera elimination from the population. We intuitively introduce a new threshold number N₀ needed for the global stability of the disease free equilibrium point which is achieved when R₀⩽1 and N₀⩽1. It is further shown that the phage absorption is a possible cause of bi-stability, since in its absence, the condition R₀⩽1 is sufficient for cholera to die out. The existence of endemic equilibrium points depends on the range of both R₀ and N₀. Regarding the model extended to an optimal control problem, which involves the use of virulent vibriophages to reduce or eliminate the bacteria population, we use optimal control theory techniques. We establish the conditions under which the spread of cholera can be stopped, and examine the impact of control measures on the transmission dynamic of cholera. The Pontryagin's maximum principle is used to characterize the optimal control. Numerical simulations suggest that, the release of lytic vibriophages can significantly reduce the spread of the disease. We discuss opportunities for phage therapy as treatment of some bacterial-borne diseases without side effects.

MODELING CHOLERA TRANSMISSION UNDER DISEASE CONTROL MEASURES

We present a new mathematical model to investigate the transmission dynamics of cholera under disease control measures that include education programs and water sanitation. The model incorporates the impact of education programs into the disease transmission rates and that of water sanitation into the environmental pathogen dynamics. We conduct a detailed analysis to the autonomous system of the model and establish the local and global stabilities of its equilibria that characterize the threshold dynamics of cholera. We then perform an optimal control study on the general model with time-dependent controls and explore effective approaches to implement the education programs and water sanitation while balancing their costs. Our analysis and simulation highlight the complex interaction among the direct and indirect transmission pathways of the disease, the intrinsic growth of the environmental pathogen and the impact of multiple control measures, and their roles in collectively shaping the transmission dynamics of cholera.

Bifurcation analysis of a phage-bacteria interaction model with prophage induction

A predator-prey model is used to investigate the interactions between phages and bacteria by considering the lytic and lysogenic life cycles of phages and the prophage induction. We provide answers to the following conflictual research questions: (1) what are conditions under which the presence of phages can purify a bacterial infected environment? (2) Can the presence of phages triggers virulent bacterial outbreaks? We derive the basic offspring number $\mathcal N_0$ that serves as a threshold and the bifurcation parameter to study the dynamics and bifurcation of the system. The model exhibits three equilibria: an unstable environment-free equilibrium, a globally asymptotically stable (GAS) phage-free equilibrium (PFE) whenever $\mathcal N_0<1$, and a locally asymptotically stable environment-persistent equilibrium (EPE) when $\mathcal N_0>1$. The Lyapunov-LaSalle techniques are used to prove the GAS of the PFE and estimate the EPE basin of attraction. Through the center manifold approximation, topological types of the PFE are precised. Existence of transcritical and Hopf bifurcations are established. Precisely, when $\mathcal N_0>1$, the EPE loses its stability and periodic solutions arise. Furthermore, increasing $\mathcal N_0$ can purify an environment where bacteriophages are introduced. Purposely, we prove that for large values of $\mathcal N_0$, the overall bacterial population asymptotically approaches zero, while the phage population sustains. Ecologically, our results show that for small values of $\mathcal N_0$, the existence of periodic solutions could explain the occurrence of repetitive bacteria-borne disease outbreaks, while large value of $\mathcal N_0$ clears bacteria from the environment. Numerical simulations support our theoretical results.