Impact of mating behaviour on the success of malaria control through a single inundative release of transgenic mosquitoes.

Transgenic mosquitoes are a potential tool for the control or eradication of insect-vectored diseases. For malaria, one possible strategy relies on the introduction of malaria-refractory transgenes into wild Anopheles mosquito populations that would limit their capacity to transmit the disease. The success of such an approach obviously depends on a variety of factors. By developing a model that integrates both population genetics and epidemiology, we explore how mosquito mating preferences and the cost and efficacy of refractoriness affects the long-term prevalence of malaria in humans subsequent to a single generation inundative release of male transgenic mosquitoes. As may be intuitively expected, mating discrimination by wild-type individuals against transgenic ones generally reduces the probability that transgenes become stably established at a high frequency in mosquito populations. We also show that in circumstances where transgenic individuals exhibit some degree of discrimination against wild-type individuals, this can favour the spread of refractory alleles and lead to a significant reduction in malaria prevalence in the human population (if the efficacy of a dominant refractory mechanism exceeds at least 75%). The existence of such a non-intuitive outcome highlights the practical value of increasing the understanding of Anopheles mating preferences in the wild as a means to harness them in the implementation of population replacement approaches. Potential strategies by which previously described mating preferences of Anopheles gambiae populations could be exploited to manipulate the mate choice of transgenic release stocks are discussed.

Malaria drug resistance: the impact of human movement and spatial heterogeneity.

Human habitat connectivity, movement rates, and spatial heterogeneity have tremendous impact on malaria transmission. In this paper, a deterministic system of differential equations for malaria transmission incorporating human movements and the development of drug resistance malaria in an [Formula: see text] patch system is presented. The disease-free equilibrium of the model is globally asymptotically stable when the associated reproduction number is less than unity. For a two patch case, the boundary equilibria (drug sensitive-only and drug resistance-only boundary equilibria) when there is no movement between the patches are shown to be locally asymptotically stable when they exist; the co-existence equilibrium is locally asymptotically stable whenever the reproduction number for the drug sensitive malaria is greater than the reproduction number for the resistance malaria. Furthermore, numerical simulations of the connected two patch model (when there is movement between the patches) suggest that co-existence or competitive exclusion of the two strains can occur when the respective reproduction numbers of the two strains exceed unity. With slow movement (or low migration) between the patches, the drug sensitive strain dominates the drug resistance strain. However, with fast movement (or high migration) between the patches, the drug resistance strain dominates the drug sensitive strain.

Optimal control and sensitivity analysis of an influenza model with treatment and vaccination.

We formulate and analyze the dynamics of an influenza pandemic model with vaccination and treatment using two preventive scenarios: increase and decrease in vaccine uptake. Due to the seasonality of the influenza pandemic, the dynamics is studied in a finite time interval. We focus primarily on controlling the disease with a possible minimal cost and side effects using control theory which is therefore applied via the Pontryagin's maximum principle, and it is observed that full treatment effort should be given while increasing vaccination at the onset of the outbreak. Next, sensitivity analysis and simulations (using the fourth order Runge-Kutta scheme) are carried out in order to determine the relative importance of different factors responsible for disease transmission and prevalence. The most sensitive parameter of the various reproductive numbers apart from the death rate is the inflow rate, while the proportion of new recruits and the vaccine efficacy are the most sensitive parameters for the endemic equilibrium point.

Optimal control and cost-effective analysis of the 2017 meningitis outbreak in Nigeria.

This paper presents a deterministic model for Neisseria meningitidis, a bacterium that causes meningitis. The model was parameterized using data from the 2017 meningitis outbreak in Nigeria. Optimal control theory was applied to investigate the optimal strategy for curtailing the spread of the disease using control variables determined from sensitivity analysis. These control variables are personal-protection such as the use of facial masks, and vaccination. The results show that the two controls avert more infections at low costs. Furthermore, a reciprocal relationship exists between the use of facial masks and vaccine. That is, when the use of facial masks is high, the use of vaccine is low and vice versa. Cost-effective analysis was applied to investigate the most cost-effective strategy from various combination of control strategies. The results show that strategy combining all the control variables is the most cost-effective strategy followed by the strategy involving both personal-protection, the vaccination-only strategy was the least cost-effective. Although vaccination strategy is not cost-effective in this study, it is as effective in curtailing the infection as the other two control strategies. The study suggests that governments of communities with limited resources should consider complementing the use of vaccine with the use of facial mask particularly in hard-to-reach places in their communities.

Optimal control strategies for dengue transmission in pakistan.

This paper presents a deterministic model for dengue virus transmission. The model is parameterized using data from the 2017 dengue outbreak in Pakistan. We estimated the basic reproduction number (R0) without any interventions for the 2017 dengue outbreak in Peshawar district of Pakistan as R0≈2.64, the distribution of the reproduction number lies in the range R0∈[1.21,5.24] (with a mean R0≈2.64). Optimal control theory is then applied to investigate the optimal strategy for curtailing the spread of the disease using two time-dependent control variables determined from sensitivity analysis. These control variables are insecticide use and vaccination. The results show that the two controls avert the same number of infections in the district regardless of the weights on the costs this is due to the reciprocal relationship between the cost of insecticide use and vaccination. A strong reciprocal relationship exists between the use of insecticide and vaccination; as the cost of insecticide increases the use of vaccination increases. The use of insecticide on the other hand slightly increases when vaccination level decreases due to increase in cost.

Mathematical model of Ebola transmission dynamics with relapse and reinfection.

The Ebola virus disease is caused by the Ebola virus which belongs to the filoviridae virus family. The 2014 outbreaks were estimated to have caused over 11,000 fatalities. In this paper, we formulate and analyze a system of ordinary differential equations which incorporates disease relapse and reinfection. The Ebola model with disease relapse and reinfection is locally-asymptotically stable when the basic reproduction number is less than unity. The model exhibits in the presence of disease reinfection, the phenomenon of backward bifurcation, where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The feasibility of backward bifurcation occurring increases with increasing values of both relapse and reinfection. The total number of new cases of Ebola-infected individuals increases with increasing values of the relapse and reinfection parameters. Further simulations show that Ebola transmission models that do not incorporate relapse and reinfection may under-estimate disease burden in the community. Similar under-estimation is observed in models that include only one infected and recovered classes. Using results obtained from sensitivity analysis indicates that Ebola (given disease relapse and reinfection) can be effectively curtailed in the community by using control measures with a high-effectiveness level. This strategy is more effective than either the moderate- or low-effectiveness levels.

Mathematical model of Zika virus with vertical transmission.

Zika is a flavivirus transmitted to humans through either the bites of infected Aedes mosquitoes or sexual transmission. Zika has been linked to congenital anomalies such as microcephaly. In this paper, we analyze a new system of ordinary differential equations which incorporates human vertical transmission of Zika virus, the birth of babies with microcephaly and asymptomatically infected individuals. The Zika model is locally and globally asymptotically stable when the basic reproduction number is less than unity. Our model shows that asymptomatic individuals amplify the disease burden in the community, and the most important parameters for ZIKV spread are the death rate of mosquitoes, the mosquito biting rate, the mosquito recruitment rate, and the transmission per contact to mosquitoes and to adult humans. Scenario exploration indicates that personal-protection is a more effective control strategy than mosquito-reduction strategy. It also shows that delaying conception reduces the number of microcephaly cases, although this does little to prevent Zika transmission in the broader community. However, by coupling aggressive vector control and personal protection use, it is possible to reduce both microcephaly and Zika transmission. 2000 Mathematics Subject Classifications: 92B05, 93A30, 93C15.

Optimal control of a two-strain tuberculosis-HIV/AIDS co-infection model.

Tuberculosis is a bacterial disease caused by Mycobacterium tuberculosis (TB). The risk for TB infection greatly increases with HIV infection; TB disease occurs in 7-10% of patients with HIV infection each year, increasing the potential for transmission of drug-resistant Mycobacterium tuberculosis strains. In this paper a deterministic model is presented and studied for the transmission of TB-HIV/AIDS co-infection. Optimal control theory is then applied to investigate optimal strategies for controlling the spread of the disease using treatment of infected individuals with TB as the system control variables. Various combination strategies were examined so as to investigate the impact of the controls on the spread of the disease. And incremental cost-effectiveness ratio (ICER) was used to investigate the cost effectiveness of all the control strategies. Our results show that the implementation of the combination strategy involving the prevention of treatment failure in drug-sensitive TB infectious individuals and the treatment of individuals with drug-resistant TB is the most cost-effective control strategy. Similar results were obtained with different objective functionals involving the minimization of the number of individuals with drug-sensitive TB-only and drug-resistant TB-only with the efforts involved in applying the control.

Optimal isolation control strategies and cost-effectiveness analysis of a two-strain avian influenza model.

The most important and effective measures against disease outbreaks in the absence of valid medicines or vaccine are quarantine and isolation strategies. In this paper optimal control theory is applied to a system of ordinary differential equation describing a two-strain avian influenza transmission via the Pontryagin's Maximum Principle. To this end, a pair of control variables representing the isolation strategies for individuals with avian and mutant strains were incorporated into the transmission model. The infection averted ratio (IAR) and the incremental cost-effectiveness ratio (ICER) were calculated to investigate the cost-effectiveness of all possible combinations of the control strategies. The simulation results show that the implementation of the combination strategy during the epidemic is the most cost-effective strategy for avian influenza transmission. This is followed by the control strategy involving isolation of individuals with the mutant strain. Also observed was the fact that low mutating and more virulent virus results in an increased control effort of isolating individuals with the avian strain; and high mutating with more virulent virus results in increased efforts in isolating individuals with the mutant strain.

Qualitative dynamics of lowly- and highly-pathogenic avian influenza strains.

A new deterministic model for the transmission dynamics of the lowly- and highly-pathogenic avian influenza (LPAI and HPAI) strains is designed and rigorously analyzed. The model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium whenever the associated reproduction number is less than unity. It is shown that the re-infection of birds infected with the LPAI strain causes the backward bifurcation phenomenon. In the absence of such re-infection, the disease-free equilibrium of the model is globally-asymptotically stable when the associated reproduction number is less than unity. Using non-linear Lyapunov functions of Goh-Volterra type, the LPAI-only and HPAI-only boundary equilibria of the model are shown to be globally-asymptotically stable when they exist. A special case of the model is shown to have a continuum of co-existence equilibria whenever the associated reproduction numbers of the two strains are equal and exceed unity. Furthermore, numerical simulations of the model suggest that co-existence or competitive exclusion of the two strains can occur when the respective reproduction numbers of the two strains exceed unity.