To estimate the reduction in severe malaria incidence required for an intervention to be cost effective, or very cost effective, we developed a mathematical model of malaria transmission calibrated to the malaria transmission intensities and population demographics of 41 sub-Saharan Africa countries. As the complete prevention of severe malaria incidence is unlikely, at least until the time that malaria eradication is feasible, we base the modulation of malaria severity on recent data of the effects of gut microbiota on parasite burden in mice [10]. In addition, we only consider the effect of the intervention scenarios on malaria incidence reported to healthcare settings and classified as a severe malaria incidence in accordance to WHO standards [1]. Based on these data, we consider interventions that cause 2-, 7-, and 14-fold reductions in severe malaria incidence over the course of a 5-year time horizon. We consider the absence of any reduction in severe malaria incidence as the baseline scenario for our analysis. From these intervention scenarios, the outcomes measured include annual severe malaria incidence averted, disease burden, as measured through DALYs averted [11], and the cost-effectiveness of the intervention, as measure by ICER [12]. To classify an intervention as cost-effective or very cost-effective, we apply the World Health Organization recommendations in relation to the GDP per capita for each country [13].
The mathematical model. The developed mathematical model of malaria transmission considers an approach [14] that divides the population into six parts: susceptible individuals (S), infected individuals with clinical disease (D), asymptomatically infected individuals (A), individuals with present, but not detectable, subpatent infection (U), treated individuals (T), and individuals using prophylaxis (P) [14–16]. The rate susceptible individuals acquire malaria, λ, is given by the force of infection [17, 18]:
[Due to technical limitations, this equation is only available as a download in the supplemental files section.] (1)
Here c is the mosquito biting rate, α is the mosquito-to-human transmission probability, β is the human-to-mosquito transmission probability, m is the mosquito to human ratio, 1∕d0 is the mean mosquito lifespan, Iis the total number of humans infected with malaria, and N is the human population size. The mathematical model also considers the probabilities of symptomatic infection, ϕ, and effective treatment of clinical malaria, fT, in addition to the rates of recovery from clinical malaria, rT, asymptomatic malaria, rA, severe malaria, rD, the period of protection provided by prophylaxis, 1∕rP, and the clearance rate of sub-patent infection, rU [14–16].
We parameterize our mathematical model according to one of the main measures of malaria transmission intensities, the EIR. The EIR is the number of infectious bites of malaria per person per year (ibpppy). We consider EIR values for 41 countries in sub-Saharan African (Table S1), which range from 0.05 to 220 ibpppy [19]. These EIR estimates, with the assumption that the mosquito population is at equilibrium, and the transmission probabilities between humans and mosquitoes (Table 1) allows us to estimate the mosquito to human ratio for each considered country. In addition, to estimate the proportion of malaria incidence that is severe, we use published data on malaria incidence and severe malaria incidence reported to health care providers [20] (Table S1). We use these country specific estimates of the proportion of malaria incidence that is severe (Table S1), together with the predicted trajectory of malaria incidence under each countries’ EIR to evaluate the considered intervention scenarios. Further details of the model parameters and model equations are available in Table 1 and the supplementary materials.
The intervention. We considered an intervention that targets reducing severe malaria incidence over a 5-year period. The intervention is based upon modulating the severity of malaria, as recent studies illustrate the potential to accomplish such a feat through the promotion of a microbiome that includes the microbiota, Lactobacillus and Bifidobacterium [10]. Specifically, the microbiota, Lactobacillus and Bifidobacterium, are associated with a 14-fold reduction in parasite burden [39]. So, we evaluate up to a 14-fold reduction in severe malaria incidence to determine the per person costs so that such an intervention is cost-effective or very cost-effective.
To conduct such an evaluation, we parameterized our model with freely available demographic data of the considered 41 countries in sub-Saharan Africa [40], and published data on the malaria transmission intensity, as described by the EIR [19], for each respective country.
Intervention costs. The treatment of uncomplicated malaria is assumed to correspond to the WHO recommended guidelines for first-line treatment of uncomplicated Plasmodium falciparum malaria [41]. The treatment of uncomplicated malaria typically corresponds to the use of an artemisinin-based combination therapy, such as artemether-lumefantrine, over the course of a 3 day treatment period [41], with a median cost of $5.84 USD [35]. Similarly, we also assume that the treatment of severe malaria corresponds to WHO recommended guidelines [41] with estimated median costs to treat an incidence of severe malaria of $30.26 USD [35].
For an intervention based on the ability of gut microbiota to modulate malaria severity [10], we also consider the costs associated to the distribution of gut microbiota through a freeze-dried yogurt [42]. Specifically, we consider intervention costs based on yogurt prices of $0.20–0.29 USD for a 4–6 ounce serving [36], along with estimates that 2.27 servings of yogurt are consumed per week [38]. In addition, we assume that the distribution costs associated to the distribution of the freeze-dried yogurt are in line with the $0.06–0.09 per unit cost for the distribution of antimalarial drugs [37].
Intervention effectiveness. We quantified the effectiveness of the intervention that targets reducing severe malaria incidence in terms of Disability Adjusted Life Years (DALYs), which is a common measure of the health burden resulting from years of life lost and years lived with disability [43–45]. We calculated time-discounted DALYs lost to malaria, severe malaria, cerebral malaria, neurological sequelae, and severe malaria anemia (Table 1). Annual DALYs averted were calculated by subtracting each intervention scenario from the base scenario for each respective country.
Intervention cost-effectiveness. We calculated the per person costs so that the proposed intervention would qualify as cost-effective or very cost-effective under the malaria transmission settings occurring in the 41 considered countries in sub-Saharan Africa. For each of these countries, we obtained GDP per capital estimates [46] to determine the willingness-to-pay for a i) cost-effective intervention, and ii) a very cost-effective intervention. To do so, we made use of the incremental cost-effectiveness ratio (ICER),
[Due to technical limitations, this equation is only available as a download in the supplemental files section.] (2)
where ΔD is the annual DALYs averted per person, relative to the baseline intervention, and ΔC = C1-C0 is the change in the average cost of a malaria incidence per person. Here, C1 is the average cost of a malaria incidence per person under the intervention, and C0 is the average cost of a malaria incidence per person under the base line scenarios, respectively. Furthermore, the average costs of a malaria incidence per person are determine by the reduction factor ψ, the average cost of an uncomplicated malaria incidence υ, and the average cost of a severe malaria incidence σ:
[Due to technical limitations, this equation is only available as a download in the supplemental files section.] (3)
where x is the proportion of incidence that are uncomplicated and g is the per person cost of the gut microbiota intervention.
In accordance with the WHO standards [47], a cost-effective intervention for a country occurs when ICER≤3GDP, and a very cost-effective intervention occurs when ICER≤GDP. Thus, from (3) it follows that the per person cost of a cost-effective intervention involving gut microbiota must satisfy
[Due to technical limitations, this equation is only available as a download in the supplemental files section.] (4)
and the per person cost of a very cost-effective intervention must satisfy
[Due to technical limitations, this equation is only available as a download in the supplemental files section.] (5)
Sensitivity analysis. To quantify the contribution of parameters to the variability of predicted outcomes, we calculated first-order sensitivity indices [48]. First-order sensitivity indices indicate how uncertainty in each parameter contributes to the variability of model outcomes. Details of the parameters and probability distributions used in this calculation are available in Table 1.