Abstract
In this paper we modify a standard SIR model used to study the spread of some diseases by incorporating a disease that destroys the immunity that is conferred by having one of the other diseases or being vaccinated against the disease. A specific biological example of this occurs with measles. Studies of recent measles’ patients has shown that many patients have lost some (or all) of their immunity to other diseases from which they were previously protected. In the future, models like those developed here might be helpful in understanding how viruses that affect multiple organ systems can impact the effect the disease has on at risk populations.
Highlights
In situations such as this, the percentage that needs to be vaccinated to prevent the disease from being spread among the population is referred to as herd immunity and used interchangeably with basic reproductive ratio
We summarize the case when the disease under consideration spreads and confers immunity, as is the case with many viral infections, such as chickenpox mentioned above, that was discussed by Kermack and McKendrick [8], for completeness purposes
We assume that the first disease is well understood and that the population is vaccinated at a high enough rate to achieve herd immunity
Summary
Many viral infections (such as measles and chickenpox) are frequently included in this category because if an individual recovers from the disease, they are immune to subsequent occurrences of the disease. R0 is interpreted to mean the percentage of the population of individuals that need to be vaccinated so that an infected individual is not statistically likely to interact with a susceptible individual and, increase the spread of the disease In situations such as this, the percentage that needs to be vaccinated to prevent the disease from being spread among the population is referred to as herd immunity and used interchangeably with basic reproductive ratio. Many of the terms and concepts presented here were first introduced in the article that forms the foundations for the mathematical models of epidemics by Kermack and McKendrick [8], in 1927, which we summarize
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