Modelling the burden of disease for cattle-A case of ticks and tick-borne diseases in cattle in a rural set-up in South Africa.

BACKGROUND: The study aimed to estimate the burden of ticks and tick-borne diseases (TBDs) among rural cattle-keeping households of the Eastern Cape province of South Africa using Productivity Adjusted Life Years (PALYs). We modified Disability Adjusted Life Year (DALY) equations for humans to PALYs to estimate the societal burden of tick-borne animal diseases. Whilst the World Health Organization has indicated the adaptability of DALYs to assess burden of animal diseases, nothing has been done in this regard. This could be due to several reasons including that the assessment of animal disease burden is often less of a priority compared to human diseases, particularly in low- and middle-income countries where resources may be limited. As a result, less funding and attention may be given to developing and implementing PALYs for animal diseases. Furthermore, technical and conceptual challenges may be associated with applying DALYs equations to animal diseases, such as determining appropriate measures of productivity loss for different types and categories of animals and diseases. This motivated our study, which is focused on modelling the burden of ticks and TBDs in cattle (cows, oxen and bulls) reared in resource-poor settings. METHOD: We formulated a PALYs approach for cattle populations by adapting the DALYs approach to assess the burden of ticks and TBDs for cattle populations in 20 villages in the Eastern Cape province of South Africa. PALYs is a measurement used to assess the burden of disease in cattle populations, quantifying the years of life lost due to premature mortality and disability. It encompasses years of life lost due to premature mortality (YLL) and years lost due to disability (YLD) caused by health conditions. PALYs provide a comprehensive perspective on the effective number of years lost due to disability and premature death in cattle populations. The PALYs model involves several parameters that are examined to understand their impact on the model's behavior. To illustrate this, we used a structured questionnaire to collect data on parameters that feed into PALY equations. We coded and entered data from questionnaires directly into Statistical Package of Social Sciences (IBM SPSS Version 20) and entered the estimated values of PALY parameters to calculate PALYs equations, which were to estimate the societal disease burden of ticks and TBDs in cattle. PALYs calculations were done in three categories; PALYs without discounting and age weighting, PALYs with only discounting, and PALYs with discounting and age weighting in a practical example to study how these parameters influence the outcomes of the PALYs model. RESULTS: Our results revealed that the years of productivity lost by a cow, bull, and ox that suffered from ticks and TBDs could be estimated at various disability weights. Approximately 26%, 23% and 35% of the productivity years of a cow, ox and bull, respectively, reared by resource-poor livestock owners are lost due to the burden of ticks and TBDs in the Eastern Cape province of South Africa. However, introducing tick control measures reduces the loss to approximately 3%, 2% and 3% of their lifespan productivity, an indication that tick control will save approximately 23%, 21% and 32% of years of the productive life of cows, oxen and bulls, respectively. Therefore, it is evident that using ticks and TBD prevention measures at an early age of cattle will improve cattle productivity and hence the socioeconomic welfare of resource-poor rural farming communities in the Eastern Cape province of South Africa. CONCLUSION: The findings generated from the PALYs approach are helpful in projections for the future burden of any livestock disease. They may be used as a basis in policy formulation and decision-making by various stakeholders, and hence a priority in animal health economics. We recommend that a classification of livestock diseases of national economic importance should consider both the societal burden (non-monetary) and economic impact instead of the common practice of only considering the economic (monetary) impact. Adding a societal burden measure to existing economic measures provides a holistic understanding of the impact of a disease on society especially in resource-limited settings where the livestock value goes beyond monetary value.

Charged Shear-Free Fluids and Complexity in First Integrals.

The equation yxx=f(x)y2+g(x)y3 is the charged generalization of the Emden-Fowler equation that is crucial in the study of spherically symmetric shear-free spacetimes. This version arises from the Einstein-Maxwell system for a charged shear-free matter distribution. We integrate this equation and find a new first integral. For this solution to exist, two integral equations arise as integrability conditions. The integrability conditions can be transformed to nonlinear differential equations, which give explicit forms for f(x) and g(x) in terms of elementary and special functions. The explicit forms f(x)∼1x51-1x-11/5 and g(x)∼1x61-1x-12/5 arise as repeated roots of a fourth order polynomial. This is a new solution to the Einstein-Maxwell equations. Our result complements earlier work in neutral and charged matter showing that the complexity of a charged self-gravitating fluid is connected to the existence of a first integral.

First Integrals of Shear-Free Fluids and Complexity.

A single master equation governs the behaviour of shear-free neutral perfect fluid distributions arising in gravity theories. In this paper, we study the integrability of yxx=f(x)y2, find new solutions, and generate a new first integral. The first integral is subject to an integrability condition which is an integral equation which restricts the function f(x). We find that the integrability condition can be written as a third order differential equation whose solution can be expressed in terms of elementary functions and elliptic integrals. The solution of the integrability condition is generally given parametrically. A particular form of f(x)∼1x51-1x-15/7 which corresponds to repeated roots of a cubic equation is given explicitly, which is a new result. Our investigation demonstrates that complexity of a self-gravitating shear-free fluid is related to the existence of a first integral, and this may be extendable to general matter distributions.

A stochastic epidemic model for the dynamics of two pathogens in a single tick population.

Understanding tick-transmitted pathogens in tick infested areas is crucial for the development of preventive and control measures in response to the increasing cases of tick-borne diseases. A stochastic model for the dynamics of two pathogens, Rickettsia parkeri and Rickettsia amblyommii, in a single tick, Amblyomma americanum, is developed and analysed. The model, a continuous-time Markov chain, is based on a deterministic tick-borne disease model. The extinction threshold for the stochastic model is computed using the multitype branching process and conditions for pathogen extinction or persistence are presented. The probability of pathogen extinction is computed using numerical simulations and is shown to be a good estimate of the probability of extinction calculated from the branching process. A sensitivity analysis is undertaken to illustrate the relationship between co-feeding and transovarial transmission rates and the probability of pathogen extinction. Expected epidemic duration is estimated using sample paths and we show that R. amblyommii is likely to persist slightly longer than R. parkeri. Further, we estimate the duration of possible coexistence of the two pathogens.

A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence.

We formulate and analyse a stochastic epidemic model for the transmission dynamics of a tick-borne disease in a single population using a continuous-time Markov chain approach. The stochastic model is based on an existing deterministic metapopulation tick-borne disease model. We compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in tick-borne disease dynamics. The probability of disease extinction and that of a major outbreak are computed and approximated using the multitype Galton-Watson branching process and numerical simulations, respectively. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that a disease outbreak is more likely if the disease is introduced by infected deer as opposed to infected ticks. These insights demonstrate the importance of host movement in the expansion of tick-borne diseases into new geographic areas.

Pre-exposure prophylaxis and antiretroviral treatment interventions with drug resistance.

We introduce a model for HIV/AIDS which can be utilized to assess the impact of combining pre-exposure prophylaxis (PrEP) and antiretroviral drugs (ARVs) use interventions (incorporating drug resistance). Mathematical and numerical analyses are carried out to investigate the effects of the combined controls in the presence of PrEP drug resistance. Our results predict a significant decrease in the number of new HIV infections when PrEP and ARVs are concurrently implemented at high levels. The results also reveal that PrEP drug resistance has the potential to slow down or reverse the effects of PrEP, especially at low efficacy levels.

Modelling the role of multi-transmission routes in the epidemiology of bovine tuberculosis in cattle and buffalo populations.

A mathematical model that describes the transmission dynamics of bovine tuberculosis (BTB) in both buffalo and cattle populations is proposed. The model incorporates cross-infection and contaminated environment transmission routes. A full analysis of the model is undertaken. The reproduction number of the entire model is comprised of cross-infection and contaminated parameters. This underscores the importance of including both cross-infection and contaminated environment transmission routes. Crucially our simulations suggest that the disease has a more devastating effect on cattle populations than on buffalo populations when all transmission routes are involved. This has important implications for agriculture and tourism.