Cholera remains an important global cause of morbidity and mortality, capable of causing periodic epidemic disease. Beginning in August 2008, a major cholera epidemic occurred in Zimbabwe, with 98,585 reported cases and 4,287 deaths. The dynamics of such outbreaks, particularly in nonestuarine regions, are not well understood. We explored the utility of mathematical models in understanding transmission dynamics of cholera and in assessing the magnitude of interventions necessary to control epidemic disease. Weekly data on reported cholera cases were obtained from the Zimbabwe Ministry of Health and Child Welfare (MoHCW) for the period from November 13, 2008 to July 31, 2009. A mathematical model was formulated and fitted to cumulative cholera cases to estimate the basic reproductive numbers R 0 and the partial reproductive numbers from all 10 provinces for the 2008–2009 Zimbabwe cholera epidemic. Estimated basic reproductive numbers were highly heterogeneous, ranging from a low value of just above unity to 2.72. Partial reproductive numbers were also highly heterogeneous, suggesting that the transmission routes varied by province; human-to-human transmission accounted for 41–95% of all transmission. Our models suggest that the underlying patterns of cholera transmission varied widely from province to province, with a corresponding variation in the amenability of outbreaks in different provinces to control measures such as immunization. These data underscore the heterogeneity of cholera transmission dynamics, potentially linked to differences in environment, socio-economic conditions, and cultural practices. The lack of traditional estuarine reservoirs combined with these estimates of R 0 suggest that mass vaccination against cholera deployed strategically in Zimbabwe and surrounding regions could prevent future cholera epidemics and eventually eliminate cholera from the region.

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The emergence and fast global spread of COVID-19 has presented one of the greatest public health challenges in modern times with no proven cure or vaccine. Africa is still early in this epidemic, therefore the extent of disease severity is not yet clear. We used a mathematical model to fit to the observed cases of COVID-19 in South Africa to estimate the basic reproductive number and critical vaccination coverage to control the disease for different hypothetical vaccine efficacy scenarios. We also estimated the percentage reduction in effective contacts due to the social distancing measures implemented. Early model estimates show that COVID-19 outbreak in South Africa had a basic reproductive number of 2.95 (95% credible interval [CrI] 2.83–3.33). A vaccine with 70% efficacy had the capacity to contain COVID-19 outbreak but at very higher vaccination coverage 94.44% (95% Crl 92.44–99.92%) with a vaccine of 100% efficacy requiring 66.10% (95% Crl 64.72–69.95%) coverage. Social distancing measures put in place have so far reduced the number of social contacts by 80.31% (95% Crl 79.76–80.85%). These findings suggest that a highly efficacious vaccine would have been required to contain COVID-19 in South Africa. Therefore, the current social distancing measures to reduce contacts will remain key in controlling the infection in the absence of vaccines and other therapeutics.

Cholera reappeared in Haiti in October, 2010 after decades of absence. Cases were first detected in Artibonite region and in the ensuing months the disease spread to every department in the country. The rate of increase in the number of cases at the start of epidemics provides valuable information about the basic reproductive number (). Quantitative analysis of such data gives useful information for planning and evaluating disease control interventions, including vaccination. Using a mathematical model, we fitted data on the cumulative number of reported hospitalized cholera cases in Haiti. varied by department, ranging from 1.06 to 2.63. At a national level, 46% vaccination coverage would result in an () <1, which would suppress transmission. In the current debate on the use of cholera vaccines in endemic and non-endemic regions, our results suggest that moderate cholera vaccine coverage would be an important element of disease control in Haiti.

An HIV/AIDS and TB coinfection model which considers antiretroviral therapy for the AIDS cases and treatment of all forms of TB, i.e., latent and active forms of TB, is presented. We begin by presenting an HIV/AIDS-TB coinfection model and analyze the TB and HIV/AIDS submodels separately without any intervention strategy. The TB-only model is shown to exhibit backward bifurcation when its corresponding reproduction number is less than unity. On the other hand, the HIV/AIDS-only model has a globally asymptotically stable disease-free equilibrium when its corresponding reproduction number is less than unity. We proceed to analyze the full HIV-TB coinfection model and extend the model to incorporate antiretroviral therapy for the AIDS cases and treatment of active and latent forms of TB. The thresholds and equilibria quantities for the models are determined and stabilities analyzed. From the study we conclude that treatment of AIDS cases results in a significant reductions of numbers of individuals progressing to active TB. Further, treatment of latent and active forms of TB results in delayed onset of the AIDS stage of HIV infection.

A tuberculosis model which incorporates treatment of infectives and chemoprophylaxis is presented. The model assumes that latently infected individuals develop active disease as a result of endogenous re-activation, exogenous re-infection and disease relapse, though a small fraction is assumed to develop active disease soon after infection. We start by formulating and analyzing a TB model without any intervention strategy that we extend to incorporate chemoprophylaxis and treatment of infectives. The epidemic thresholds known as reproduction numbers and equilibria for the models are determined, and stabilities analyzed. The reproduction numbers for the models are compared to assess the possible community benefits achieved by treatment of infectives, chemoprophylaxis and a holistic approach of these intervention strategies. The study shows that treatment of infectives is more effective in the first years of implementation (approximately 10 years) as treatment results in clearing active TB immediately and there after chemoprophylaxis will do better in controlling the number of infectives due to reduced progression to active TB.

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The role of geospatial disparities in the dynamics of the COVID-19 pandemic is poorly understood. We developed a spatially-explicit mathematical model to simulate transmission dynamics of COVID-19 disease infection in relation with the uneven distribution of the healthcare capacity in Ohio, U.S. The results showed substantial spatial variation in the spread of the disease, with localized areas showing marked differences in disease attack rates. Higher COVID-19 attack rates experienced in some highly connected and urbanized areas (274 cases per 100,000 people) could substantially impact the critical health care response of these areas regardless of their potentially high healthcare capacity compared to more rural and less connected counterparts (85 cases per 100,000). Accounting for the spatially uneven disease diffusion linked to the geographical distribution of the critical care resources is essential in designing effective prevention and control programmes aimed at reducing the impact of COVID-19 pandemic.