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Despite the lifting of COVID-19 restrictions, the COVID-19 pandemic and its effects remain a global challenge including the sub-Saharan Africa (SSA) region. Knowledge of the COVID-19 dynamics and its potential trends amidst variations in COVID-19 vaccine coverage is therefore crucial for policy makers in the SSA region where vaccine uptake is generally lower than in high-income countries. Using a compartmental epidemiological model, this study aims to forecast the potential COVID-19 trends and determine how long a wave could be, taking into consideration the current vaccination rates. The model is calibrated using South African reported data for the first four waves of COVID-19, and the data for the fifth wave are used to test the validity of the model forecast. The model is qualitatively analysed by determining equilibria and their stability, calculating the basic reproduction number R0 and investigating the local and global sensitivity analysis with respect to R0. The impact of vaccination and control interventions are investigated via a series of numerical simulations. Based on the fitted data and simulations, we observed that massive vaccination would only be beneficial (deaths averting) if a highly effective vaccine is used, particularly in combination with non-pharmaceutical interventions. Furthermore, our forecasts demonstrate that increased vaccination coverage in SSA increases population immunity leading to low daily infection numbers in potential future waves. Our findings could be helpful in guiding policy makers and governments in designing vaccination strategies and the implementation of other COVID-19 mitigation strategies.

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In drug design, there are two major causes of drug failure in the clinic. First, the drug has to work, and second, the drug should be safe. Identifying compounds that work for certain ailments require enormous experimental time and, in general, is cost intensive. In this paper, we are concerned with melanoma, a special type of cancer that affects the skin. In particular, we seek to provide a mathematical model that can predict the ability of flavonoids, a vast and natural class of compounds that are found in plants, in reversing or alleviating melanoma. The basis for our model is the conception of a new graph parameter called, for lack of better terminology, graph activity, which captures melanoma cancer healing properties of the flavonoids. With a superior coefficient of determination, [Formula: see text], the new model faithfully reproduces anti-cancer activities of some known data-sets. We demonstrate that the model can be used to rank the healing abilities of flavonoids which could be a powerful tool in the screening, and identification, of compounds for drug candidates.

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The management of HIV/AIDS has evolved ever since advent of the disease in the past three decades. Many countries have had to revise their policies as new information on the virus, and its transmission dynamics emerged. In this paper, we track the changes in Botswana's HIV/AIDS response and treatment policies using a piece-wise system of differential equations. The policy changes are easily tracked in three epochs. Models for each era are formulated from a "grand model" that can be linked to all the epochs. The grand model's steady states are determined and analysed in terms of the model reproduction number, $ R_{0}. $ The model exhibits a backward bifurcation, where a stable disease-free equilibrium coexists with a stable endemic equilibrium when $ R_{0} < 1. $ The stability of the models for the other epochs can be derived from that of the grand model by setting some parameters to zero. The models are fitted to HIV/AIDS prevalence data from Botswana for the past three decades. The changes in the populations in each compartment are tracked as the response to the disease and treatment policy changed over time. Finally, projections are made to determine the possible trajectory of HIV/AIDS in Botswana. The implications of the policy changes are easily seen, and a discussion on how these changes impacted the epidemic are articulated. The results presented have crucial impact on how policy changes affected and continue to influence the trajectory of the HIV/AIDS epidemic in Botswana.

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Migration of infected animals and humans, and mutation are considered as the source of the introduction of new pathogens and strains into a country. In this paper, we formulate a mathematical model of Ebola virus disease dynamics, that describes the introduction of a new strain of ebolavirus, through either mutation or immigration (which can be continuous or impulsive) of infectives. The mathematical analysis of the model shows that when the immigration of infectives is continuous, the new strain invades a country if its invasion reproduction number is greater than one. When the immigration is impulsive, a newly introduced strain is controllable when its reproduction number is less than the ratio of mortality to the population inflow and only locally stable equilibria exist. This ratio is one if the population size is constant. In case of mutation of the resident strain of ebolavirus, the coexistence of the resident and mutated strains is possible at least if their respective reproduction numbers are greater than one. Results indicate that the competition for the susceptible population is the immediate consequence of the coexistence of two different strains of ebolavirus in a country and this competition is favourable to the most infectious strain. Results also indicate that impulsive immigration of infectives when compared with continuous immigration of infectives gives time for the implementation of control measures. Our model results suggest controlled movements of people between countries that have had Ebola outbreaks despite the fact that closing boundaries is impossible.

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The role of human behaviour in the dynamics of infectious diseases cannot be underestimated. A clear understanding of how human behaviour influences the spread of infectious diseases is critical in establishing and designing control measures. To study the role that human behaviour plays in Ebola disease dynamics, in this paper, we design an Ebola virus disease model with disease transmission dynamics based on a new exponential nonlinear incidence function. This new incidence function that captures the reduction in disease transmission due to human behaviour innovatively considers the efficacy and the speed of behaviour change. The model's steady states are determined and suitable Lyapunov functions are built. The proofs of the global stability of equilibrium points are presented. To demonstrate the utility of the model, we fit the model to Ebola virus disease data from Liberia and Sierra Leone. The results which are comparable to existing findings from the outbreak of 2014 - 2016 show a better fit when the efficacy and the speed of behaviour change are higher. A rapid and efficacious behaviour change as a control measure to rapidly control an Ebola virus disease epidemic is advocated. Consequently, this model has implications for the management and control of future Ebola virus disease outbreaks.

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Non-pharmaceutical interventions (NPIs) play a central role in infectious disease outbreak response and control. Their usefulness cannot be overstated, especially during the early phases of a new epidemic when vaccines and effective treatments are not available yet. These interventions can be very effective in curtailing the spread of infectious diseases when adequately implemented and sufficiently adopted by the public. However, NPIs can be very disruptive, and the socioeconomic and cultural hardships that come with their implementation interfere with both the ability and willingness of affected populations to adopt such interventions. This can lead to reduced and unsteady adherence to NPIs, making disease control more challenging to achieve. Deciphering this complex interaction between disease dynamics, NPI stringency, and NPI adoption would play a critical role in informing disease control strategies. In this work, we formulate a general-purpose model that integrates government-imposed control measures and public adherence into a deterministic compartmental epidemic model and study its properties. By combining imitation dynamics and the health belief model to encode the unsteady nature of NPI adherence, we investigate how temporal variations in NPI adherence levels affect the dynamics and control of infectious diseases. Among the results, we note the occurrence of multiple epidemic waves as a result of temporal variations in NPI adherence and a trade-off between the stringency of control measures and adherence. Additionally, our results suggest that interventions that aim at increasing public adherence to NPIs are more beneficial than implementing more stringent measures. Our findings highlight the necessity of taking the socioeconomic and cultural realities of affected populations into account when devising public health interventions.

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A general perception among researchers is that boiling points, which is a key property in the optimization of lubricant performance, are difficult to predict successfully using a single-parameter model. In this contribution, we propose a new graph parameter which we call, for lack of better terminology, the conduction of a graph. We exploit the conduction of a graph to develop a single-parameter model for predicting the boiling point of any given alkane. The model was used to predict the boiling points for three sets of test data and predicted with a coefficient of determination, [Formula: see text] and 0.6488, respectively. The accuracy of our model compares favourably to the accuracy of experimental data in the literature. Our results have significant implications on the estimation of boiling points of chemical compounds in the absence of experimental data.

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BACKGROUND: The prevalence of allergies has been observed to be increasing in the past years in Zimbabwe. It is thus important to consider the long term prevalence of allergies. Our interest is in investigating the trends of allergies in the next 2 decades. METHOD: We formulate a deterministic model with 6 compartments to predict the prevalence of allergies in Zimbabwe. The human population is divided into 4 distinct epidemiological, classes based on their exposure to 2 allergen groups (food and inhalants), represented by 2 compartments. The model is used to predict the prevalence of allergen sensitization. The number of human allergen groups in each compartment are tracked through a system of differential equations. Model parameters were obtained by fitting observed data to the model. Graphical solutions of the model were developed using Matlab and Excel. RESULTS: The rate of sensitisation to food allergen sources is found to be lower than the rate of sensitisation to inhalant allergens. The rate at which individuals develop tolerance to food allergen sources is found to be almost twice the rate of developing tolerance to inhalant allergies. The equilibrium solutions (the long-term states of the populations) of the model are found to be non-zero implying that there will never be an allergy-free population. Our results also show that the prevalence of food allergy is likely to increase in the next 2 decades while inhalant allergy prevalence is expected to decrease. CONCLUSION: Our long-term solutions show endemicity in allergies in Zimbabwe. So, allergy will be endemic in the Zimbabwean population; hence there is a need for allergy care and management facilities to be increased. These results are critical in policy development and planning around allergies in the near future.

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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.

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BACKGROUND: In 2018, Zimbabwe declared another major cholera outbreak a decade after recording one of the worst cholera outbreaks in Africa. METHODS: A mathematical model for cholera was used to estimate the magnitude of the cholera outbreak and vaccination coverage using cholera cases reported data. A Markov chain Monte Carlo method based on a Bayesian framework was used to fit the model in order to estimate the basic reproductive number and required vaccination coverage for cholera control. RESULTS: The results showed that the outbreak had a basic reproductive number of 1.82 (95% credible interval [CrI] 1.53-2.11) and required vaccination coverage of at least 58% (95% Crl 45-68%) to be contained using an oral cholera vaccine of 78% efficacy. Sensitivity analysis demonstrated that a vaccine with at least 55% efficacy was sufficient to contain the outbreak but at higher coverage of 75% (95% Crl 58-88%). However, high-efficacy vaccines would greatly reduce the required coverage, with 100% efficacy vaccine reducing coverage to 45% (95% Crl 35-53%). CONCLUSIONS: These findings reinforce the crucial need for oral cholera vaccines to control cholera in Zimbabwe, considering that the decay of water reticulation and sewerage infrastructure is unlikely to be effectively addressed in the coming years.

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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.

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OBJECTIVES: We study the transmission dynamics of cholera in the presence of limited resources, a common feature of the developing world. The model is used to gain insight into the impact of available resources of the health care system on the spread and control of the disease. A deterministic model that includes a nonlinear recovery rate is formulated and rigorously analyzed. Limited treatment is described by inclusion of a special treatment function. Center manifold theory is used to show that the model exhibits the phenomenon of backward bifurcation. Matlab has been used to carry out numerical simulations to support theoretical findings. RESULTS: The model analysis shows that the disease free steady state is locally stable when the threshold [Formula: see text]. It is also shown that the model has multiple equilibria and the model exhibits the phenomenon of backward bifurcation whose implications to cholera infection are discussed. The results are useful for the public health planning in resource allocation for the control of cholera transmission.

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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.

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In this paper, we present a model for onchocerciasis that considers mass administration of ivermectin, contact prevention controls and vector elimination. The model equilibria are computed and stability analysis carried out in terms of the basic reproduction number R0. The model is found to exhibit a backward bifurcation so that for R0 less than unity is not sufficient to eradicate the disease from the population and the need is to lower R0 to below a certain threshold, R0c for effective disease control. The model is fitted to data on individuals with onchocerciasis in Ghana. A sensitivity analysis reveals that the parameters with the most control over the epidemic are the vector death rate and the effective contact rates between susceptible individuals and infected vector and susceptible vector with infected individuals. This suggests that programs aimed controlling vector will be significantly more effective in combating the disease. Optimal control theory is applied to investigate optimal control strategies for controlling onchocerciasis using insect repellent and both insecticide and larvicide as system control variables. We use Pontryagin's Maximum Principle to show the necessary conditions for the optimal control of onchocerciasis. Numerical simulations of the model show that restricted and proper use of control measures might considerably decrease the number of infections in the human population.

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The complex problem of drug abuse and drug-related crimes in communities in the Western Cape province cannot be studied in isolation but through the system they are embedded in. In this paper, a theoretical model to evaluate the syndemic of substance abuse and drug-related crimes within the Western Cape province of South Africa is constructed and explored. The dynamics of drug abuse and drug-related crimes within the Western Cape are simulated using STELLA software. The simulation results are consistent with the data from SACENDU and CrimeStats SA, highlighting the usefulness of such a model in designing and planning interventions to combat substance abuse and its related problems.

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Public involvement in Ebola Virus Disease (EVD) prevention efforts is key to reducing disease outbreaks. Targeted education through practical health information to particular groups and sub-populations is crucial to controlling the disease. In this paper, we study the dynamics of Ebola virus disease in the presence of public health education with the aim of assessing the role of behavior change induced by health education to the dynamics of an outbreak. The power of behavior change is evident in two outbreaks of EVD that took place in Sudan only 3 years apart. The first occurrence was the first documented outbreak of EVD and produced a significant number of infections. The second outbreak produced far fewer cases, presumably because the population in the region learned from the first outbreak. We derive a system of ordinary differential equations to model these two contrasting behaviors. Since the population in Sudan learned from the first outbreak of EVD and changed their behavior prior to the second outbreak, we use data from these two instances of EVD to estimate parameters relevant to two contrasting behaviors. We then simulate a future outbreak of EVD in Sudan using our model that contains two susceptible populations, one being more informed about EVD. Our finding show how a more educated population results in fewer cases of EVD and highlights the importance of ongoing public health education.

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BACKGROUND: Mycobacterium ulcerans is know to cause the Buruli ulcer. The association between the ulcer and environmental exposure has been documented. However, the epidemiology of the ulcer is not well understood. A hypothesised transmission involves humans being bitten by the water bugs that prey on mollusks, snails and young fishes. METHODS: In this paper, a model for the transmission of Mycobacterium ulcerans to humans in the presence of a preventive strategy is proposed and analysed. The model equilibria are determined and conditions for the existence of the equilibria established. The model analysis is carried out in terms of the reproduction number [Formula: see text]. The disease free equilibrium is found to be locally asymptotically stable for [Formula: see text] The model is fitted to data from Ghana. RESULTS: The model is found to exhibit a backward bifurcation and the endemic equilibrium point is globally stable when [Formula: see text] Sensitivity analysis showed that the Buruli ulcer epidemic is highly influenced by the shedding and clearance rates of Mycobacterium ulcerans in the environment. The model is found to fit reasonably well to data from Ghana and projections on the future of the Buruli ulcer epidemic are also made. CONCLUSIONS: The model reasonably fitted data from Ghana. The fitting process showed data that appeared to have reached a steady state and projections showed that the epidemic levels will remain the same for the projected time. The implications of the results to policy and future management of the disease are discussed.

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BACKGROUND: The presence of an asymptomatic phase in an HIV infection indicates that the immune system can partially control the infection. Determining the immune mechanisms that contribute significantly to the partial control of the infection enhance the HIV infection intervention strategies and is important in vaccine development. Towards this goal, a discrete time HIV model, which incorporates the life cycle aspects of the virus, the antibody (humoral) response and the cell-mediated immune response is formulated to determine immune system components that are most efficient in controlling viral levels. Ecological relationships are used to model the interplay between the immune system components and the HIV pathogen. Model simulations and transient elasticity analysis of the viral levels to immune response parameters are used to compare the different immune mechanisms. RESULTS: It is shown that cell-mediated immune response is more effective in controlling the viral levels than the antibody response. Killing of infected cells is shown to be crucial in controlling the viral levels. Our results show a negative correlation between the antibody response and the viral levels in the early stages of the infection, but we predicted this immune mechanism to be positively correlated with the viral levels in the late stage of the infection. A result that suggests lack of relevance of antibody response with infection progression. On the contrary, we predicted the cell-mediated immune response to be always negatively correlated with viral levels. CONCLUSION: Neutralizing antibodies can only control the viral levels in the early days of the HIV infection whereas cell-mediated immune response is beneficial during all the stages of the infection. This study predicts that vaccine design efforts should also focus on stimulating killer T cells that target infected cells.

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The management of the Buruli ulcer (BU) in Africa is often accompanied by limited resources, delays in treatment, and macilent capacity in medical facilities. These challenges limit the number of infected individuals that access medical facilities. While most of the mathematical models with treatment assume a treatment function proportional to the number of infected individuals, in settings with such limitations, this assumption may not be valid. To capture these challenges, a mathematical model of the Buruli ulcer with a saturated treatment function is developed and studied. The model is a coupled system of two submodels for the human population and the environment. We examine the stability of the submodels and carry out numerical simulations. The model analysis is carried out in terms of the reproduction number of the submodel of environmental dynamics. The dynamics of the human population submodel, are found to occur at the steady states of the submodel of environmental dynamics. Sensitivity analysis is carried out on the model parameters and it is observed that the BU epidemic is driven by the dynamics of the environment. The model suggests that more effort should be focused on environmental management. The paper is concluded by discussing the public implications of the results.

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