Mathematical modelling of vector-borne diseases and insecticide resistance evolution

Mathematics of a single-locus model for assessing the impacts of pyrethroid resistance and temperature on population abundance of malaria mosquitoes

This study presents a genetic-ecology modeling framework for assessing the combined impacts of insecticide resistance, temperature variability, and insecticide-based interventions on the population abundance and control of malaria mosquitoes by genotype. Rigorous analyses of the model we developed reveal that the boundary equilibrium with only mosquitoes of homozygous sensitive (resistant) genotype is locally-asymptotically stable whenever a certain ecological threshold, denoted by R0SS(R0RR), is less than one. Furthermore, genotype i drives genotype j to extinction whenever R0j>1 and R0i<1 (where i, j = SS or RR, with i ≠ j). The model exhibits the phenomenon of bistability when both thresholds are less than one. In such a bistable situation, convergence to any of the two boundary equilibria depends on the initial allele distribution in the state variables of the model. Furthermore, in this bistable case, where max{R0SS,R0RR}<1, the basin of attraction of the boundary equilibrium of the mosquito genotype with lower value of the ecological threshold is larger. Specifically, the basin of attraction of the boundary equilibrium for genotype i is larger than that of genotype j if R0i<R0j<1. When both ecological thresholds exceed one (min{R0SS,R0RR}>1), the two boundary equilibria lose their stability, and a coexistence equilibrium (where all three mosquito genotypes coexist) becomes locally-asymptotically stable. Global sensitivity analysis shows that the key parameters that greatly influence the dynamics and population abundance of resistant mosquitoes include the proportion of new adult mosquitoes that are females, the insecticide-induced mortality rate of adult female mosquitoes, the coverage level and efficacy of adulticides used in the community, the oviposition rates for eggs of heterozygous and homozygous resistant genotypes, and the modification parameter accounting for the reduction in insecticide-induced mortality due to resistance. Numerical simulations show that the adult mosquito population increases with increasing temperature until a peak is reached at 31 °C, and declines thereafter. Simulating the model for moderate and high adulticide coverage, together with varying fitness costs of resistance, shows a switch in the dominant genotype at equilibrium as temperature is varied. In other words, this study shows that, for certain combinations of adulticide coverage and fitness costs of insecticide resistance, increases in temperature could result in effective management of resistance (by causing the switch from a stable resistant-only boundary equilibrium (at 18 °C) to a stable sensitive-only boundary equilibrium (at 25 °C)). Finally, this study shows that, for moderate fitness costs of resistance, density-dependent larval mortality suppresses the total population of adult mosquitoes with the resistant allele for all temperature values in the range [18 °C–36 °C].

Insecticide resistance and malaria control: A genetics-epidemiology modeling approach

Malaria, a deadly infectious disease caused by the protozoan Plasmodium, remains a major public health menace affecting at least half the human race. Although the large-scale usage of insecticides-based control measures, notably long-lasting insecticidal nets (LLINs) and indoor residual spraying (IRS), have led to a dramatic reduction of the burden of this global scourge between the period 2000 to 2015, the fact that the malaria vector (adult female Anopheles mosquito) has become resistant to all currently-available insecticides potentially makes the current laudable global effort to eradicate malaria by 2040 more challenging. This study presents a novel mathematical model, which couples malaria epidemiology with mosquito population genetics, for assessing the impact of insecticides resistance on malaria epidemiology. Numerical simulations of the model, using data relevant to malaria transmission dynamics in the Jimma Zone of Southwestern Ethiopia, show that the implementation of a control strategy based on using LLINs alone can lead to the effective control of malaria, while also effectively managing insecticide resistance, if the LLINs coverage in the community is high enough (over 90%). It is further shown that combining LLINs with IRS (both at reduced and realistically-attainable coverage levels) can lead to the aforementioned effective control of malaria and effective management of insecticide resistance if their coverage levels lie within a certain effective control window in the LLINs-IRS coverage parameter space (this result generally holds regardless of whether or not larviciding is implemented in the community). The study identifies three key parameters of the model that negatively affect the size of the effective control window, namely parameters related with the coverage level of larviciding, the number of new adult mosquitoes that are females and the initial size of the frequency of resistant allele in the community. For the coverage of LLINs and IRS within the effective control window, an additional increase in the values of the aforementioned three parameters may lead to a shrinkage in the size of the effective control window (thereby causing the failure of the insecticides-based control).

Dynamical analysis of a mean-field vector-borne diseases model on complex networks: An edge based compartmental approach

In this paper, we propose a concise method to investigate the global dynamics of a mean-field vector-borne diseases model on complex networks. We obtain an explicit formula of the basic reproduction number by a renewal equation. We show that the model exhibits a threshold dynamics in terms of the basic reproduction number by constructing subtle Lyapunov functions. Roughly speaking, if the basic reproduction number R₀<1, the vector-borne diseases die out; otherwise, it persists. Moreover, numerical simulations show that vector-control is an effective measure for slowing down the spread of vector-borne diseases.

Mathematics of an epidemiology-genetics model for assessing the role of insecticides resistance on malaria transmission dynamics

Although the widespread use of indoors residual spraying (IRS) and insecticides treated bednets (ITNs; later replaced by long-lasting insecticidal nets (LLINs)) has led to a dramatic reduction of malaria burden in endemic areas, such usage has also resulted in the major challenge of the evolution of insecticide resistance in the mosquito population in those areas. Thus, efforts to combat malaria also include the urgent problem of effectively managing insecticide resistance. This study is based on the design and analysis of a new mathematical model for assessing the impact of insecticides resistance in the mosquito population (due to widespread use of IRS and ITNs) on the transmission dynamics and control of malaria in a community. The model, which couples disease epidemiology with vector population genetics, incorporates several fitness costs associated with insecticide resistance. Detailed rigorous analysis of the model is presented. Using data and parameter values relevant to malaria dynamics in moderate and high malaria transmission settings in some parts of Ethiopia, simulations of the model show that, while the ITNs-IRS strategy can lead to the effective control of the disease in both the moderate and high malaria transmission setting if the ITNs coverage level in the community is high enough (regardless of the level of IRS coverage), it fails to manage insecticide resistance (as measured in terms of the frequency of resistant allele at equilibrium in the community). It is further shown that the effective size of the coverage level of the ITNs and IRS required to effectively control the disease, while effectively managing insecticide resistance in the mosquito population, depends on the magnitude of the level of resistant allele dominance (in mosquitoes with heterozygous genotype) and several fitness costs associated with the insecticide resistance in the vector population. For instance, in a moderate transmission setting, malaria burden can be reduced to low levels of endemicity (even with low coverage of ITNs and IRS), and insecticide resistance effectively managed, if the fitness costs of resistance are at their assumed baseline values. Such reduction is not achievable if the fitness costs of resistance are lower than the baseline values.