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.

Vaccination and treatment are the most effective ways of controlling the transmission of most infectious diseases. While vaccination helps susceptible individuals to build either a long-term immunity or short-term immunity, treatment reduces the number of disease-induced deaths and the number of infectious individuals in a community/nation. In this paper, a nonlinear deterministic model with time-dependent controls has been proposed to describe the dynamics of bacterial meningitis in a population. The model is shown to exhibit a unique globally asymptotically stable disease-free equilibrium ℰ0, when the effective reproduction number ℛVT ≤ 1, and a globally asymptotically stable endemic equilibrium ℰ1, when ℛVT > 1; and it exhibits a transcritical bifurcation at ℛVT = 1. Carriers have been shown (by Tornado plot) to have a higher chance of spreading the infection than those with clinical symptoms who will sometimes be bound to bed during the acute phase of the infection. In order to find the best strategy for minimizing the number of carriers and ill individuals and the cost of control implementation, an optimal control problem is set up by defining a Lagrangian function L to be minimized subject to the proposed model. Numerical simulation of the optimal problem demonstrates that the best strategy to control bacterial meningitis is to combine vaccination with other interventions (such as treatment and public health education). Additionally, this research suggests that stakeholders should press hard for the production of existing/new vaccines and antibiotics and their disbursement to areas that are most affected by bacterial meningitis, especially Sub-Saharan Africa; furthermore, individuals who live in communities where the environment is relatively warm (hot/moisture) are advised to go for vaccination against bacterial meningitis.

Word count for the Abstract: 199. AbstractBackground: COVID-19 has emerged and spread at great speed globally and 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 spectrum of disease severity is not yet clear. Methods: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 coverages 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. Results: 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%). Conclusions:Findings suggest 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.

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The model of care of people living with HIV/AIDS (PLWHA) has shifted from hospital care to community home-based care (CHBC) because of shortage of space in hospitals and lack of resources. We evaluate the costs and benefits of home-based care and other HIV/AIDS intervention strategies in Zimbabwe, using an interdisciplinary approach which weaves together the techniques of an epidemic transmission model and economic evaluation concepts. The intervention strategies considered are voluntary counselling and testing (VCT), VCT combined with hospitalization (H), VCT combined with CHBC, and all the interventions implemented concurrently. The results of the study indicate that implementing all the strategies concurrently is the most cost-effective, a result which also agrees with the epidemiological model. Our results also show that the effectiveness of a strategy in the epidemiological model does not necessarily imply cost-effectiveness of the strategy and behaviour change, modelled by the parameters p and m, that accompanied the strategies, influencing both the cost-effectiveness of an intervention strategy and dynamics of the epidemic. This study shows that interdisciplinary collaborations can help in improving the accuracy of predictions of the course and cost of the epidemic and help policy makers in implementing the correct strategies.

Cross contamination that results in food-borne disease outbreaks remains a major problem in processed foods globally. In this paper, a mathematical model that takes into consideration cross contamination of Listeria monocytogenes from a food processing plant environment is formulated using a system of ordinary differential equations. The model has three equilibria: the disease-free equilibrium, Listeria-free equilibrium, and endemic equilibrium points. A contamination threshold ℛwf is determined. Analysis of the model shows that the disease-free equilibrium point is locally stable for ℛwf<1 while the Listeria-free and endemic equilibria are locally stable for ℛwf>1. The time-dependent sensitivity analysis is performed using Latin hypercube sampling to determine model input parameters that significantly affect the severity of the listeriosis. Numerical simulations are carried out, and the results are discussed. The results show that a reduction in the number of contaminated workers and removal of contaminated food products are essential in eliminating the disease in the human population and vice versa. The results have significant public health implications in the management and containment of any listeriosis disease outbreak.

There are different views on which of the two forms of viral spread is more efficient in vivo between cell-free and cell-associated virus. In this study, discrete time human immunodeficiency virus models are formulated and analysed with the goal of determining the form of viral spread that is more efficient in vivo. It is shown that on its own, cell-free viral spread cannot sustain an infection owing to the low infectivity of cell-free virus and cell-associated virus can sustain an infection because of the high infectivity of cell-associated virus. When acting concurrently, cell-associated virus is more efficient in spreading the infection upon exposure to the virus. However, in the long term, the two forms of viral spread contribute almost equally. Both forms of viral spread are shown to be able to initiate an infection.

Highlights Due to its high case fatality rate, EVD undoubtedly instills fear in the inhabitants of any affected community. We propose an Ebola model with fear, which considers the pathogens in the environment to quantify the effect of fear and environmental transmission on the EVD disease dynamics. The fear of death from Ebola is proportional to the Ebola disease transmission rate. At high levels of fear, the number of EVD cases decrease.