Management strategies in a malaria model combining human and transmission-blocking vaccines

Abstract

We propose a new mathematical model studying control strategies of malaria transmission. The control is a combination of human and transmission-blocking vaccines and vector control (larvacide). When the disease induced death rate is large enough, we show the existence of a backward bifurcation analytically if vaccination control is not used, and numerically if vaccination is used. The basic reproduction number is a decreasing function of the vaccination controls as well as the vector control parameters, which means that any effort on these controls will reduce the burden of the disease. Numerical simulation suggests that the combination of the vaccinations and vector control may help to eradicate the disease. We investigate optimal strategies using the vaccinations and vector controls to gain qualitative understanding on how the combinations of these controls should be used to reduce disease prevalence in malaria endemic setting. Our results show that the combination of the two vaccination controls integrated with vector control has the highest impact on reducing the number of infected humans and mosquitoes.

Mathematical assessment of the role of vector insecticide resistance and feeding/resting behavior on malaria transmission dynamics: Optimal control analysis

“…It is assumed that mosquitoes are not produced indoors (i.e., it is assumed there is no suitable breeding habitats indoors for mosquitoes to breed). For the wild-type and resistant-type adult female mosquitoes outdoors, the following Verhulst-Pearl logistic growth functions, Bvw (for outdoor wild-type adult female mosquitoes) and Bvr (for outdoor resistant-type adult female mosquitoes), are chosen (Mohammed-Awel et al., 2017):Bvwtrue(Nvtrue)=rvwtrue(1−NvKvtrue)andBvrtrue(Nvtrue)=rvrtrue(1−NvKvtrue),where rvw>0 and rvr>0 are the production (birth) rates of new adult wild-type and resistant-type mosquitoes, respectively. Furthermore, Kv>0 is the environmental carrying capacity of adult female mosquitoes, and it is assum...…”

“…The Proof of Theorem 4.2, based on using the techniques in (Mohammed-Awel et al., 2017; Mohammed-Awel & Numfor, 2017), is given in Appendix A.…”

“…Numerous control strategies, such as the use of insecticide-treated mosquito bednets (ITNs) or long-lasting insecticidal nets (LLINs) and indoor residual spraying (IRS) with chemical insecticides, antimalarial drugs (such as Artemisinin -based combination therapies (ACTs) (WHO, 2016)), and intermittent preventive treatment of pregnant women and infants, are being used to reduce (or prevent) malaria transmission in endemic areas. Furthermore, several candidate anti-malaria vaccines are being developed (Asale et al., 2014; Churcher, Lissenden, Griffin, Worrall, & Ranson, 2016; Mohammed-Awel, Zhao, Numfor, & Lenhart, 2017; Mohammed-Awel & Numfor, 2017; Ngonghala, Del Valle, Zhao, & Mohammed-Awel, 2014; Ngonghala, Mohammed, Zhao, & Prosper, 2016; Okumu & Moore, 2011; WHO, 2016). Owing to these efforts (i.e., implementation of ITNs and/or IRS strategies), malaria incidence and malaria mortality have been significantly reduced during the period 2010–2015 (WHO, 2016).…”

“…Mathematical models have been widely used to assess the population-level impact and effectiveness of various control strategies against malaria (see, for instance, (Agusto et al., 2013; Anderson & May, 1991; Chitnis et al., 2008; Mohammed-Awel et al., 2017; Mohammed-Awel & Numfor, 2017; Ngonghala et al., 2014; Ngonghala et al., 2016; Prosper, Ruktanonchai, & Martcheva, 2014; White, Griffin, et al., 2011)). However, only few of these models, which incorporate ITNs and/or IRS, considered the effect of insecticide resistance (Barbosa & Hastings, 2012; Birget & Koella, 2015; Brown et al., 2013; Gourley et al., 2011; Wairimu & Ronoh, 2016).…”

A mathematical model of spatial transmission of vector-borne disease

“…Для математического моделирования используется аппарат отображений и дифференциальных уравнений, а при описании происходящих процессов -различные уровни детализации. Результативность многих из перечисленных математических исследований была подтверждена натурными наблюдениями и экспериментами, что позволило предложить эффективные способы профилактики болезней и борьбы с переносчиками заболеваний [15]. Перечисленные математические подходы могут применяться и при моделировании других трансмиссивных заболеваний, в частности, дирофиляриоза.…”