Narrow Results

In this work, we present a deterministic model to examine how socioeconomic levels affect the co-dynamics of COVID-19 and cholera in the Haitian community. The threshold quantities called the basic and control reproduction numbers of both diseases were obtained by using the next-generation matrix method. To validate the model’s ability to predict a realistic result, each respective sub-model was fitted using the reported number of COVID-19 cases from March 20, 2020 to June 25, 2023 and the reported number of cholera cases from October 8, 2022 to August 26, 2023 from Haiti. A numerical simulation was performed to investigate the impact of socioeconomic levels on the threshold quantities and the projected infected cases of each disease. The overall result shows that, in comparison to medium or low socioeconomic levels, a high socioeconomic level lowers the threshold reproduction number more efficiently. This suggests that the burden of COVID-19 and cholera would decrease if Haiti’s socioeconomic status was raised to a better standard and the diseases’ related reproduction numbers were kept below the disease-free thresholds. Additionally, our results show that improving socioeconomic status is essential to reducing the number of predicted COVID-19 and cholera cases among Haitians. Our results also established that cholera disease would dominate in the Haiti population and drive COVID-19 into extinction when they are both at their endemic equilibria (i.e., cholera will dominate when ${{ℛ}}_1>1$ and ${{ℛ}}_2>1$). However, for COVID-19 to dominate and drive cholera into extinction in the Haiti population, only COVID-19 must be in an endemic state (i.e., COVID-19 will dominate when ${{ℛ}}_1>1$ and ${{ℛ}}_2<1$). Based on the study’s findings, the government and policymakers of Haiti were advised to ensure that the country’s socioeconomic status is improved in order to lower the population’s burden of disease.

In this paper, we propose a stochastic cholera model that incorporates media coverage and two time delays driven by Lévy noise in order to deeply understand the propagation process of cholera in the real world, generalized nonlinear incidence rates ${\beta }_1(M)$ and ${\beta }_2(M)$ are also introduced. First, we discuss the existence and uniqueness of the global positive solution of the stochastic model by using the Lyapunov method. Moreover, the dynamic properties of stochastic solution around the disease-free and endemic equilibria are demonstrated. At last, we present numerical simulation results to reveal how Lévy jumps, time delays and media coverage affect the asymptotic properties of the stochastic model.

In this paper, a nonlinear deterministic model is proposed with a saturated treatment function. The expression of the basic reproduction number for the proposed model was obtained. The global dynamics of the proposed model was studied using the basic reproduction number and theory of dynamical systems. It is observed that proposed model exhibits backward bifurcation as multiple endemic equilibrium points exist when $R_0<1$. The existence of backward bifurcation implies that making $R_0<1$ is not enough for disease eradication. This, in turn, makes it difficult to control the spread of cholera in the community. We also obtain a unique endemic equilibria when $R_0>1$. The global stability of unique endemic equilibria is performed using the geometric approach. An extensive numerical study is performed to support our analytical results. Finally, we investigate two major cholera outbreaks, Zimbabwe (2008–09) and Haiti (2010), with the help of the present study.

This paper describes a cholera disease transmission model in the human population through the consumption of zooplankton as food by humans. Here the plankton population is classified into two subpopulations such as phytoplankton and zooplankton. Also, human population is classified into two subpopulations such as susceptible human and infected human. The proposed system reflects the impacts of using time delay in the cholera disease transmission. Different possible equilibrium points of our proposed system have been determined. Here local and global stabilities of our proposed system have been analyzed. The existence of Hopf bifurcation has been studied at the interior equilibrium point. The normal form method and center manifold theorem have been used to test the nature of Hopf bifurcation. It is observed that the interior equilibrium is locally asymptotically stable when the time delay in disease transmission term is large, while the change of stability of positive equilibrium will cause a bifurcating periodic solution at the time delay $\tau$ to be at less than its critical value. Finally, some numerical simulation results have been presented for the better understanding of our proposed system.

Cholera, characterized by severe diarrhea and rapid dehydration, is a water-borne infectious disease caused by the bacterium Vibrio cholerae. Haiti offers the most recent example of the tragedy that can befall a country and its people when cholera strikes. While cholera has been a recognized disease for two centuries, there is no strategy for its effective control. We formulate and analyze a mathematical model that includes two essential and affordable control measures: water chlorination and education. We calculate the basic reproduction number and determine the global stability of the disease-free equilibrium for the model without chlorination. We use Latin Hypercube Sampling to demonstrate that the model is most sensitive to education. We also derive the minimal effective chlorination period required to control the disease for both fixed and variable chlorination. Numerical simulations suggest that education is more effective than chlorination in decreasing bacteria and the number of cholera cases.

Cholera has been a public health threat for centuries. Unlike the biological characteristics, relatively less effort has been paid to comprehend the spatial dynamics of this disease. Therefore, in this paper, we have proposed a cholera epidemic model for variable population size and studied the spatial patterns in two-dimensional space. First, we have performed the equilibrium and local stability analysis of steady states obtained for temporal system. Afterwards, the local and global stability behavior of the endemic steady state in a spatially extended setting has been investigated. The numerical simulations have been done to investigate the spatial patterns. They show that dynamics of the cholera epidemic varies with time and space.

Cholera is a water-borne disease and a major threat to human society affecting about 3–5 million people annually. A considerable number of research works have already been done to understand the disease transmission route and preventive measures in spatial or non-spatial scale. However, how the control strategies are to be linked up with the human migration in different locations in a country are not well studied. The present investigation is carried out in this direction by proposing and analyzing cholera meta-population models. The basic dynamical properties including the domain basic reproduction number are studied. Several important model parameters are estimated using cholera incidence data (2008–2009) and inter-provincial migration data from Census 2012 for the five provinces in Zimbabwe. By defining some migration index, and interlinking these indices with different cholera control strategies, namely, promotion of hand-hygiene and clean water supply and treatment, we carried out an optimal cost effectiveness analysis using optimal control theory. Our analysis suggests that there is no need to provide control measures for all the five provinces, and the control measures should be provided only to those provinces where in-migration flow is moderate. We also observe that such selective control measures which are also cost effective may reduce the overall cases and deaths.

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.

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• ASIA-PACIFIC — Overcoming Chemotherapy Resistance in Ovarian Cancer
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Based on our deterministic models for cholera epidemics, we propose a stochastic model for cholera epidemics to incorporate environmental fluctuations which is a nonlinear system of Itô stochastic differential equations. We conduct an asymptotical analysis of dynamical behaviors for the model. The basic stochastic reproduction value ${\mathcal{ℛ}}_s$ is defined in terms of the basic reproduction number $R_0$ for the corresponding deterministic model and noise intensities. The basic stochastic reproduction value determines the dynamical patterns of the stochastic model. When ${\mathcal{ℛ}}_s<1$, the cholera infection will extinct within finite periods of time almost surely. When ${\mathcal{ℛ}}_s>1$, the cholera infection will persist most of time, and there exists a unique stationary ergodic distribution to which all solutions of the stochastic model will approach almost surely as noise intensities are bounded. When the basic reproduction number $R_0$ for the corresponding deterministic model is greater than 1, and the noise intensities are large enough such that ${\mathcal{ℛ}}_s<1$, the cholera infection is suppressed by environmental noises. We carry out numerical simulations to illustrate our analysis, and to compare with the corresponding deterministic model. Biological implications are pointed out.

In this paper, we investigated the dynamical behavior of a fractional-order model of the cholera epidemic in Mayo-Tsanaga Department. We extended the model of Lemos-Paião et al. [A. P. Lemos-Paião, C. J. Silva and D. F. M. Torres, J. Comput. Appl. Math.16, 427 (2016)] by incorporating the contact rate $\sigma$ by handling cholera death and optimal control strategies such as vaccination $v$, water sanitation $w$. We provide a theoretical study of the model. We derive the basic reproduction number ${{ℛ}}_0$ which determines the extinction and the persistence of the infection. We show that the disease-free equilibrium is globally asymptotically stable whenever ${{ℛ}}_0\le 1$, while when ${{ℛ}}_0>1$, the disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is locally asymptotically stable on a positively invariant region of the positive orthant. Using the sensitivity analysis, we find that the parameter related to vaccination and therapeutic treatment is more influencing the model. Theoretical results are supported by numerical simulations, which further suggest use of vaccination in endemic area. In case of a lack of necessary funding to fight again cholera, Figure 6 revealed that efforts should focus to keep contamination rate $\sigma <0.24$ (susceptible-to-cholera death) in other to die out the disease.

We propose a multi-scale modeling framework to investigate the transmission dynamics of cholera. At the population level, we employ a SIR model for the between-host transmission of the disease. At the individual host level, we describe the evolution of the pathogen within the human body. The between-host and within-host dynamics are connected through an environmental equation that characterizes the growth of the pathogen and its interaction with the hosts outside the human body. We put a special emphasis on the within-host dynamics by making a distinction for each individual host. We conduct both mathematical analysis and numerical simulation for our model in order to explore various scenarios associated with cholera transmission and to better understand the complex, multi-scale disease dynamics.