Fig 1.
The relationship between the force of spillover (λ) and the average age at infection .
The blue line shows the case of permanent immunity, the read line immunity that lasts, on average, for the expected lifespan of the human population, and the green line immunity that lasts for, on average, only 1/4 of the expected human lifespan. The remaining parameters were: μ = 2.89, δ = 1/60, v = 0, γ = 365/14.
Fig 2.
The health burden of zoonotic disease, , as a function of the force of spillover (λ) for disease severity that increases at different rates with advancing age.
As the severity of disease increases more rapidly with advancing age, the scope for spillover reduction to negatively impact human health grows. In this example, the rate at which infected individuals become diseased increases following Eq (8) with the intercept set to μ0 = 1.0 and the slope set such that the rate of transition to disease is independent of age (blue line; α = 0), increases 5-fold (red line; α = 1/15), or increases 10-fold (yellow line; α = 3/20) from the time of birth to age at which an individual reaches their expected natural lifespan (1/δ). The dotted lines are numerical solutions to the exact model that do not assume the rate of transition to clinical disease is rare. The analytical approximations slightly overestimate the clinical burden because individuals leaving the I class as they become diseased are ignored. This gap between approximation and exact solution grows as the rate of progression to clinical disease (μ) increases, although the general shape of the curves remains consistent. The remaining parameters were: b = 100, δ = 1/60, v = 1, γ = 365/14.
Fig 3.
The health burden of zoonotic disease, , as a function of the force of spillover (λ) for immunity that wanes at three different rates.
As immunity becomes more transient, the scope for spillover reduction to negatively impact human health shrinks. The blue line is a point of reference and shows the case where immunity is lifelong and spillover reduction can negatively impact human health. The red line shows a case where immunity wanes extremely slowly, lasting on average, three times the expected human lifespan. In this case, negative impacts can still occur, but they are extremely weak. Finally, the green line shows a case where immunity wanes sufficiently rapidly for negative impacts on human health to no longer be possible. Remarkably, this occurs even though this green line illustrates a scenario where immunity still lasts, on average, for the average lifespan of the human population. The dotted lines are numerical solutions to the exact model that do not assume the rate of transition to clinical disease is rare, but instead explicitly track the movement of individuals from the I class into the M class. The analytical approximation overestimates the clinical burden as in Fig 2, but here the discrepancy between the analytical prediction and the numerical solution to the exact model becomes more appreciable as immunity wanes more rapidly. This occurs because waning immunity increases the proportion of the population in the diseased state, and this state is ignored by our analytical approximation. In this example, the rate at which infected individuals become diseased increases following Eq (8) with the intercept set to μ0 = 1.0 and the slope set to α = 3/20 such that the rate of transition to disease increases 10-fold from the time of birth to the age at which an individual reaches their expected natural lifespan (1/δ). The remaining parameters were: b = 100, δ = 1/60, v = 1, γ = 365/14.
Fig 4.
The temporal dynamics of infection before (years 200–400) and after (years 401–600) an 87.5% drop in the force of spillover for a case with lifelong immunity and where negative impacts of spillover reduction are predicted to occur.
Each panel shows the output from ten replicate simulation runs, with each line showing a ten year rolling average of the value for each individual simulation run. Panel A shows the percentage of the human population with active infection, Panel B depicts the average age at which individuals are infected, Panel C reports the burden of disease, , and Panel D shows the average human lifespan. Parameters were: α = 0.15, μ0 = 1.0, b = 500, δ = 1/60, v = 365/7, γ = 365/14.
Fig 5.
The temporal dynamics of infection before (years 200–400) and after (years 401–600) an 87.5% drop in the force of spillover for a case with lifelong immunity and where negative impacts of spillover reduction are not predicted to occur.
Each panel shows the output from ten replicate simulation runs, with each line showing a ten year rolling average of the value for each individual simulation run. Panel A shows the percentage of the human population with active infection, Panel B depicts the average age at which individuals are infected, Panel C reports the burden of disease, , and Panel D shows the average human lifespan. Parameters were: α = 0.0167, μ0 = 1.0, b = 500, δ = 1/60, v = 365/7, γ = 365/14.
Fig 6.
The temporal dynamics of infection before (years 200–400) and after (years 401–600) an 87.5% drop in the force of spillover for a case with slowly waning immunity.
Parameters were identical to those used in Fig 4 except that immunity lasts, on average, only as long as the expected human lifespan (ω = 1/60). As in Fig 4, each panel shows the output from ten replicate simulation runs, with each line showing a ten year rolling average of the value for each individual simulation run. Panel A shows the percentage of the human population with active infection, Panel B depicts the average age at which individuals are infected, Panel C reports the burden of disease, , and Panel D shows the average human lifespan. Parameters were: α = 0.0167, μ0 = 1.0, b = 500, δ = 1/60, v = 365/7, γ = 365/14.
Fig 7.
The predicted disease burden of Lassa virus infection for the case of lifelong immunity (left panel) and waning immunity (right panel).
The black line is the theoretical prediction for each case as a function of the force of spillover. The red dots show the force of spillover estimated for actual sites in West Africa where systematic serosurveys have been conducted. The blue dots show hypothetical populations with a force of spillover estimated for seroprevalences of ,
, and
. For the case of waning immunity, the expected duration of immunity is set to 15.63 years (ω = 0.064) as estimated by [34]. Note that the burden of zoonotic disease is significantly greater with waning immunity because reinfection is possible. Parameter values were as described in the S1 Text. Birth rate of the human population was set to b = 24.75 which yields a local population size of 1500.