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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.

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.