Conservation of forest biomass and forest-dependent wildlife population: Uncertainty quantification of the model parameters.

The ecosystem is confronted with numerous challenges as a consequence of the escalating human population and its corresponding activities. Among these challenges lies the degradation of forest biomass, which directly contributes to a reduction in forested areas and poses a significant threat to the survival of wildlife species through the intensification of intraspecific competition. In this paper, a non-linear mathematical model to study the conservation of forest and wildlife species that are reliant on forest ecosystem within the framework of human population dynamics and its related activities is developed and analysed. The study assessed the impacts of economic measures in the form of incentives on reducing population pressure on forest resources as well as the potential benefits of technological efforts to accelerate the rate of reforestation. Qualitative and quantitative analyses reveals that economic and technological factors have the potential to contribute to resource conservation efforts. However, these efforts can only be used to a limited extent, and contrary to that, the system will be destabilised. Sensitivity analysis identified the parameters pertaining to human population, human activities, economic measures, and technological efforts as the most influential factors in the model.

Optimal control analysis of Taenia saginata bovine cysticercosis and human taeniasis.

Bovine cysticercosis and human taeniasis are neglected food-borne diseases that pose challenge to food safety, human health and livelihood of rural livestock farmers. In this paper, we have formulated and analyzed a deterministic model for transmission dynamics and control of taeniasis and cysticercosis in humans and cattle respectively. The analysis shows that both the disease free equilibrium (DFE) and endemic equilibrium (EE) exist. To study the dynamics of the diseases, we derived the basic reproduction number R 0 by next generation matrix method which shows whether the diseases die or persist in humans and cattle. The diseases clear if R 0 < 1 and persist when R 0 > 1. The normalized forward sensitivity index is used to derive sensitive indices of model parameters. Sensitivity analysis results indicate that human's and cattle's recruitment rates, infection rate of cattle from contaminated environment, probability of humans to acquire taeniasis due to consumption of infected meat, defecation rate of humans with taeniasis and the consumption rate of raw or undercooked infected meat are the most positive sensitive parameters whereas the natural death rates for humans, cattle, Taenia saginata eggs and the proportion of unconsumed infected meat are the most negative sensitive parameters in diseases' transmission. These results suggest that control measures such as improving meat cooking, meat inspection and treatment of infected humans will be effective for controlling taeniasis and cysticercosis in humans and cattle respectively. The optimal control theory is applied by considering three time dependent controls which are improved meat cooking, vaccination of cattle, and treatment of humans with taeniasis when they are implemented in combination. The Pontryagin's maximum principle is adopted to find the necessary conditions for existence of the optimal controls. The Runge Kutta order four forward-backward sweep method is implemented in Matlab to solve the optimal control problem. The results indicate that a strategy which focuses on improving meat cooking and treatment of humans with taeniasis is the optimal strategy for diseases' control.

Improved estimates for extinction probabilities and times to extinction for populations of tsetse (Glossina spp).

A published study used a stochastic branching process to derive equations for the mean and variance of the probability of, and time to, extinction in population of tsetse flies (Glossina spp) as a function of adult and pupal mortality, and the probabilities that a female is inseminated by a fertile male. The original derivation was partially heuristic and provided no proofs for inductive results. We provide these proofs, together with a more compact way of reaching the same results. We also show that, while the published equations hold good for the case where tsetse produce male and female offspring in equal proportion, a different solution is required for the more general case where the probability (ß) that an offspring is female lies anywhere in the interval (0, 1). We confirm previous results obtained for the special case where ß = 0.5 and show that extinction probability is at a minimum for ß > 0.5 by an amount that increases with increasing adult female mortality. Sensitivity analysis showed that the extinction probability was affected most by changes in adult female mortality, followed by the rate of production of pupae. Because females only produce a single offspring approximately every 10 days, imposing a death rate of greater than about 3.5% per day will ensure the eradication of any tsetse population. These mortality levels can be achieved for some species using insecticide-treated targets or cattle-providing thereby a simple, effective and cost-effective method of controlling and eradicating tsetse, and also human and animal trypanosomiasis. Our results are of further interest in the modern situation where increases in temperature are seeing the real possibility that tsetse will go extinct in some areas, without the need for intervention, but have an increased chance of surviving in other areas where they were previously unsustainable due to low temperatures.

Mass transfer approach and the designing of horizontal subsurface flow constructed wetland systems treating waste stabilisation pond effluent.

Pilot-scale constructed wetlands (CWs) that allowed wastewater to flow with high interstitial velocities in a controlled environment were used to evaluate the possibility of using mass transfer approach to design horizontal subsurface flow constructed wetlands (HSSF-CWs) treating waste stabilisation ponds (WSPs) effluent. Since CW design considers temperature which is irrelevant in tropics, mass transfer approach could improve the design. HSSF-CWs were operated in batch recycle mode as continuous stirred tank reactors (CSTR) at different interstitial velocities. The overall removal rate constants of chemical oxygen demand (COD) at various interstitial velocities were evaluated in mesocosms that received pretreated domestic wastewater. The mean overall removal rate constants were 0.43, 0.69, 0.74 and 0.73 d-1 corresponding to interstitial velocities of 15.43, 36, 56.57 and 72 md-1, respectively. Results showed that the interstitial velocities up to 36 md-1 represented a range where mass transfer effect was significant and, above it, insignificant to the COD removal process. Since WSPs effluent has high flow rates and low organic load, it is possible to induce high interstitial velocities in a HSSF-CW treating this effluent, without clogging and overflow. The performance of these HSSF for tertiary treatment in tropical areas could be improved by considering flow velocity when designing.

Modelling the use of insecticide-treated cattle to control tsetse and Trypanosoma brucei rhodesiense in a multi-host population.

We present a mathematical model for the transmission of Trypanosoma brucei rhodesiense by tsetse vectors to a multi-host population. To control tsetse and T. b. rhodesiense, a proportion, ψ, of cattle (one of the hosts considered in the model) is taken to be kept on treatment with insecticides. Analytical expressions are obtained for the basic reproduction number, R0n in the absence, and R(0n)(T) in the presence of insecticide-treated cattle (ITC). Stability analysis of the disease-free equilibrium was carried out for the case when there is one vertebrate host untreated with insecticide. By considering three vertebrate hosts (cattle, humans and wildlife) the sensitivity analysis was carried out on the basic reproduction number (R(0n)(T)) in the absence and presence of ITC. The results show that R(03)(T) is more sensitive to changes in the tsetse mortality. The model is then used to study the control of tsetse and T. b. rhodesiense in humans through application insecticides to cattle either over the whole-body or to restricted areas of the body known to be favoured tsetse feeding sites. Numerical results show that while both ITC strategies result in decreases in tsetse density and in the incidence of T. b. rhodesiense in humans, the restricted application technique results in improved cost-effectiveness, providing a cheap, safe, environmentally friendly and farmer based strategy for the control of vectors and T. b. rhodesiense in humans.

Modelling the Use of Insecticide-Treated Cattle to Control Tsetse and Trypanosoma brucei rhodesiense in a Multi-host Population

T. b. rhodesiense is the acute form of African human trypanosomiasis or sleeping sickness which is common in East and Southern Africa. Trypanosomiasis is caused by the parasite Trypanosoma brucei and transmitted by tsetse flies (genus Glossina spp). Treatment of livestock in sub-Saharan Africa with trypanocidal drugs has been hindered by drug resistance and proves to be too expensive for many farmers. Tsetse control methods include aerial and ground spraying; sterile insect technique; and bait technology; including the use of insecticide-treated cattle (ITC). We compared two techniques of application of insecticides on cattle using a mathematical model: whole-body (WB); where insecticides are applied on the entire animals body and restricted application (RAP); where insecticides are applied on the legs; belly and ears of the animal

Modeling the control of trypanosomiasis using trypanocides or insecticide-treated livestock.

BACKGROUND: In Uganda, Rhodesian sleeping sickness, caused by Trypanosoma brucei rhodesiense, and animal trypanosomiasis caused by T. vivax and T. congolense, are being controlled by treating cattle with trypanocides and/or insecticides. We used a mathematical model to identify treatment coverages required to break transmission when host populations consisted of various proportions of wild and domestic mammals, and reptiles. METHODOLOGY/PRINCIPAL FINDINGS: An Ro model for trypanosomiasis was generalized to allow tsetse to feed off multiple host species. Assuming populations of cattle and humans only, pre-intervention Ro values for T. vivax, T. congolense, and T. brucei were 388, 64 and 3, respectively. Treating cattle with trypanocides reduced R(0) for T. brucei to <1 if >65% of cattle were treated, vs 100% coverage necessary for T. vivax and T. congolense. The presence of wild mammalian hosts increased the coverage required and made control of T. vivax and T. congolense impossible. When tsetse fed only on cattle or humans, R(0) for T. brucei was <1 if 20% of cattle were treated with insecticide, compared to 55% for T. congolense. If wild mammalian hosts were also present, control of the two species was impossible if proportions of non-human bloodmeals from cattle were <40% or <70%, respectively. R(0) was <1 for T. vivax only when insecticide treatment led to reductions in the tsetse population. Under such circumstances R(0)<1 for T. brucei and T. congolense if cattle make up 30% and 55%, respectively of the non-human tsetse bloodmeals, as long as all cattle are treated with insecticide. CONCLUSIONS/SIGNIFICANCE: In settled areas of Uganda with few wild hosts, control of Rhodesian sleeping sickness is likely to be much more effectively controlled by treating cattle with insecticide than with trypanocides.